4 ANALYSIS SUPPLEMENT 8860 8861 MEMORY HiCORDER Using analysis functions to analyze measurement data
i Contents Contents Introduction.................................................................................1 Chapter 1 Numerical Calculation Functions _______________ 3 1.1 Numerical Value Calculation Workflow ............................... 4 1.2 Settings for Numerical Value Calculation ............................ 6 1.3 Judging Calculation Results ..............................................11 1.4 Saving Numerical Calculation Results .............................. 14 1.4.1 1.4.2 1.4.
ii Contents 3.4.6 3.4.7 3.4.8 3.4.9 3.4.10 Averaging Waveforms ............................................................ 58 Emphasizing Analysis Results (phase spectra only) ............. 61 Analysis Mode Settings .......................................................... 62 Setting the Display Range of the Vertical Axis (Scaling) ....... 66 Setting and Changing Analysis Conditions on the Waveform Screen .................................................................. 67 3.5 Selecting Channels .....
1 Introduction Introduction In this manual, “the instrument” means the Model 8860 or 8861 Memory HiCorder. The following documents are provided with this instrument. Refer to them as appropriate for your application. Document Description 1 Read this first. Quick Start Manual 2 Input Module Guide 3 Instruction Manual 4 Analysis Supplement It describes preparations for use, basic operating procedures and usage methods.
2 Introduction Symbols and Indicators in This Manual The following symbols in this manual indicate the relative importance of cautions and warnings. Indicates advisory items related to performance or correct operation of the instrument. Other Indicators (⇒ p. ) Indicates the location of reference information. * Indicates that descriptive information is provided below. A→B Indicates an operation sequence.
3 Numerical Calculation Chapter 1 Functions Numerical calculations can only be used with the Memory function. Results calculated from the acquired waveform are displayed as numerical values on the Waveform screen. Judgments can also be made based on calculation results. Numerical calculation settings are made on the Numerical Calculations Setting screen (Num Calc).
4 1.1 Numerical Value Calculation Workflow 1.1 Numerical Value Calculation Workflow Before Setting When specifying a waveform range for calculation: [A-B] Before executing a calculation, specify the calculation range using the A/B cursors (Vertical or Trace cursors) on the Waveform screen. Set the calculation range on the Num Calc Settings screen to [A-B]. • Horizontal cursors cannot be used to specify the range. • When one cursor is used, the calculation range is from the cursor to the end of the data.
5 1.1 Numerical Value Calculation Workflow Calculating While Measuring _____________________________________ Make Calculation Settings Make calculation settings on the Numerical Calculation Settings screen (⇒ p. 6). When judging based on calculation results: (⇒ p. 11) To automatically print or save calculation results: make printing and saving settings before measuring. • Printing calculation results automatically ([Printer] page on the Print Settings screen: Calculation Results [On]) See "11.
6 1.2 Settings for Numerical Value Calculation 1.2 Settings for Numerical Value Calculation Numerical Calculations To open the screen: Press the SET key → Select Operating Key 1 2 3 with the SUB MENU keys →Num Calc Settings screen Procedure Enable the Numerical Calculation function. CURSOR Move the cursor to the [Numerical Calc.] item. F2 Select [On]. 2 1 Specify the numerical calculation range. CURSOR Move the cursor to the [Calculation Area] item. F1 to F8 Select either choice.
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8 1.2 Settings for Numerical Value Calculation Making settings in the [Calculation] dialog Calculation Marker Markers are displayed next to the calculation No. of enabled calculations. To copy settings between calculation Nos.: Select F2 [Copy]. (⇒ p. 10) F1 Move the cursor to the [No.] column of the calculation to set, and select F1 [All Settings] to open the [Calculation] dialog.
9 1.2 Settings for Numerical Value Calculation Numerical Calculation Results Numerical calculation results are displayed on the Waveform screen. Calculation Results If the display is hard to view because of overlapping numerical values and waveforms Press the DISP key. Numerical values and waveforms are displayed separately. To recalculate after changing calculation type settings Select your choices for the calculation setting items on the Waveform screen, and execute calculation.
10 1.2 Settings for Numerical Value Calculation Copying Settings Between Calculation Nos. To open the screen: Press the SET key → Select Operating Key 1 with the SUB MENU keys →Num Calc Settings screen Procedure Open the dialog. CURSOR Move the cursor to the [No.] column of the calculation to copy. F2 Select [Copy]. The [Copy Settings] dialog appears. Calculation Number of Copy Source Copy Contents 1 2 3 4 Calculation Number of Copy Destination 2 3 4 5 Selection Button Select the copy source.
11 1.3 Judging Calculation Results 1.3 Judging Calculation Results Set the judgment criteria (upper and lower threshold values) by which to judge numerical calculation results. Judgment criteria can be set for every numerical calculation. Waveform acquisition processing depends on the trigger mode setting (Single or Repeat) and the criteria specified to stop measuring upon judgment (GO, NG or GO & NG ).
12 1.3 Judging Calculation Results Judging Numerical Value Calculation Results To open the screen: Press the SET key → Select Operating Key 1 2 with the SUB MENU keys →Num Calc Settings screen Procedure Make settings for calculation (⇒ p. 6). Select the appropriate calculation judgment settings. Group of Calculation Calculation Setting Contents Calculation No. Settings can also be made in a dialog (⇒ p. 8).
13 1.3 Judging Calculation Results Description About judgment results Judgment results of numerical calculations are displayed on the Waveform screen. Within the judgment threshold range: GO judgment Out of the judgment threshold range: NG judgment (displayed in red) When printing, judgment results for each parameter are also printed. When performing external control When the external I/O terminals are enabled, the signal is output from the next sampling period. See "14.2.
14 1.4 Saving Numerical Calculation Results 1.4 Saving Numerical Calculation Results 1.4.1 Automatically Saving Numerical Calculation Results Calculate and automatically save during data acquisition. Before measurement begins, the calculation settings need to be set. When using auto save during measurement, do not remove the storage media specified as the save destination until the measurement operation is completely finished. Doing so may damage data on the storage media.
15 1.4 Saving Numerical Calculation Results 1.4.2 Optionally Selecting Numerical Calculation Results & Saving (SAVE Key) Perform calculations on data saved to storage media and internal memory and save the calculation results by pressing the SAVE key. Before calculation results can be saved, the calculation settings needs to be set and the calculations need to be performed.
16 1.4 Saving Numerical Calculation Results 1.4.3 Example of Saving Numerical Calculation Results If you save numerical calculation results or data in text format, characters or display items used on the instrument are converted as shown below. (Characters used on the instrument → Saved characters) 2 → ^2, 3 → ^3 , n → ^n, μ→ ~u, Ω→ ~o, ε → ~e, ° → ~c , ±→ ~+, με (display only) → uE, °C (display only)→ C Calculation No. 1: Maximum value of analog channel 1-1 Calculation No.
17 1.5 Reading Numerical Calculation Results on a PC 1.5 Reading Numerical Calculation Results on a PC The following explains how to import data into Excel on Windows. The capacity of Excel to import data from a text file is limited to 256 columns and 65,536 rows. Text files containing data that exceeds these limits cannot be imported into Excel. To avoid exceeding these limits when saving text data, select [Displayed Ch] as the channels to save, or specify the saving range as that between A/B cursors.
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19 1.6 Numerical Value Calculation Expressions 1.6 Numerical Value Calculation Expressions Numerical Calculation Type Description Average Obtains the average value of waveform data. n Avg: Average value 1 Avg = --- ∑ di n: Data count n di: Data on channel number i i=1 Obtains the RMS value of waveform data. If Scaling is enabled, calculations are applied to the waveform after scaling.
20 1.6 Numerical Value Calculation Expressions Numerical Calculation Type Description Rise Time and Fall Time The rise time of the acquired waveform from B% A% to B% (or fall time from B% to A%) is obtained by calculation using a histogram (frequency distribution) of the 0 and 100% levels A% of the acquired waveform. As waveform data is acquired, the rise time Rise Time Fall Time (or fall time) is obtained from the first rising (or falling) edge.
21 1.6 Numerical Value Calculation Expressions Numerical Calculation Type Description Time to Level Pulse Width Finds the point where the signal crosses a specified level from the start of the calculation range, and obtains the time elapsed from the last trigger event. Setting Choices: Level, Slope (↑ or ↓) and Filter Obtains pulse width as the time difference between one rising or falling intersection of the waveform through a specified level to the next intersection (with opposite slope).
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23 Waveform Calculation Chapter 2 Functions Waveform calculations can only be used with the Memory function. A pre-specified calculation equation is applied to acquired waveform data, and the calculation results are displayed as a waveform on the Waveform screen. Waveform calculation settings are made on the Waveform Calculations Setting screen (Wave Calc).
24 2.1 Waveform Calculation Workflow 2.1 Waveform Calculation Workflow Before Setting When specifying a waveform range for calculation: [A-B] Before executing a calculation, specify the calculation range using the A/B cursors (Vertical or Trace cursors) on the Waveform screen. Set the calculation range on the Wave Calc Settings screen to [A-B]. • Horizontal cursors cannot be used to specify the range. • When one cursor is used, the calculation range is from the cursor to the end of the data. See "8.
25 2.1 Waveform Calculation Workflow The following two calculation methods are available: • Calculate while measuring Requires making waveform calculation settings beforehand. • Apply calculations to existing data Calculations can be applied to data after waveforms are acquired, or after data has been saved to storage media. Calculating While Measuring _____________________________________ Make Calculation Settings Make calculation settings on the Waveform Calculation Settings screen (⇒ p. 26).
26 2.2 Settings for Waveform Calculation 2.2 Settings for Waveform Calculation Waveform Calculations To open the screen: Press the SET key → Select Operating Key 1 2 3 with the SUB MENU keys →Wave Calc Settings screen Procedure Enable the Waveform Calculation function. CURSOR Move the cursor to the [Waveform Calc.] item. F2 Select [On]. 2 1 Specify the waveform calculation range. CURSOR Move the cursor to the [Calculation Area] item. F1 to F8 Select either choice.
27 2.2 Settings for Waveform Calculation Operating Key 4 5 Procedure (As occasion demands) Make display settings for waveform calculation results on the Sheet Settings screen (⇒ p. 33) Set auto saving and auto printing as needed (Instruction Manual) Execute the calculations. Applying Calculations to Existing Data CURSOR Move the cursor to the [Execute] button. F1 Select [Execute]. To calculate while measuring START Starts measurement. Calculation waveforms are displayed after loading waveforms.
28 2.2 Settings for Waveform Calculation Description About calculation equations Operators: Operator Name Operator Name ABS Absolute Value DIF2 2nd Derivative EXP Exponent INT2 2nd Integral LOG Common Logarithm SIN Sine SQR Square Root COS Cosine MOV Moving Average TAN Tangent SLI Movement parallel to the ASIN time axis Inverse Sine DIF 1st Derivative ACOS Inverse Cosine ATAN Inverse Tangent INT 1 st Integral See "2.
29 2.2 Settings for Waveform Calculation When calculation results overflow (OVER) • The displayed A/B cursor values (and those printed when the printer recording type is set to [Numeric]) are incorrect. • When [Scale] is set to [Auto], waveforms appear at the top or bottom edge of the screen. This makes calculation result overflow obvious.
30 2.2 Settings for Waveform Calculation Calculation Waveform Display Settings To open the screen: Press the SET key → Select 1 Operating Key Procedure SHEET/PAGE Select the [Scale] page. with the SUB MENU keys →Wave Calc Settings screen Calculation No. Settings can also be made in a dialog. (⇒ p. 31) To copy settings between Calculation Nos.: Select F2 [Copy].
31 2.2 Settings for Waveform Calculation Making settings in the [Calculation] dialog Calculation No. Move the cursor to the [No.] column of the calculation to set, and F1 select F1 [All Settings] to open the [Calculation] dialog. Upper and Lower Limit Settings Set the Value per Division. Set the Zero Position (same as the Variable Function Setting).
32 2.2 Settings for Waveform Calculation Waveform Calculation Example Operating Key 1 2 3 Calculate the RMS waveform from the instantaneous waveform The RMS values of the waveform input on Unit 1 Channel 1 are calculated and displayed. This example describes the calculation of waveform data measured for one cycle over two divisions. Procedure Enable the Waveform Calculation function. CURSOR Move the cursor to the [Waveform Calc.] item. F2 Select [On]. 2 1 Specify the waveform calculation range.
33 2.3 Calculation Waveform Display 2.3 Calculation Waveform Display Assignment of calculation results and split-screen graph display arrangement can be set. These settings are effective when Waveform Calculation is enabled. Waveform Calculation Display Settings To open the screen: Press the SET key → Select with the SUB MENU keys →Sheet Settings screen Operating Key Procedure 1 SHEET/PAGE Select the [Wcal] page. 2 Select whether to display calculation waveforms.
34 2.4 Waveform Processing Calculation Operators and Results 2.4 Waveform Processing Calculation Operators and Results bi: ith member of calculation result data, di: ith member of source channel data Description Four Arithmetic Operators ( +, −, ∗, / ) Executes the corresponding arithmetic operation. Absolute Value (ABS) bi = | di | (i = 1, 2, .... n) Exponent (EXP) bi = exp(di) (i = 1, 2, ....
35 2.4 Waveform Processing Calculation Operators and Results bi: ith member of calculation result data, di: ith member of source channel data Waveform Calculation Type Description Arccosine (ACOS) When di > 1, bi = 0 When -1 ≤ di ≤ 1, bi = acos(di) When di < -1 , bi = π (i = 1, 2, .... n) Trigonometric functions employ radian (rad) units. Arctangent (ATAN) bi = atan(di) (i = 1, 2, .... n) Trigonometric functions employ radian (rad) units.
36 2.4 Waveform Processing Calculation Operators and Results bi: ith member of calculation result data, di: ith member of source channel data Waveform Calculation Type Description First and second integrals are calculated using the trapezoidal rule. d1 to dn are the integrals calculated for sample times t1 to tn.
37 3.1 Overview and Features FFT Function 3.1 Chapter 3 Overview and Features FFT analysis can only be used with the FFT function. The FFT (Fast-Fourier Transform) functions provide frequency analysis of input signal data. Use these functions for frequency analysis of rotating objects, vibrations, sounds and etc. For details, refer to "3.11 FFT Definitions" (⇒ p. 103).
38 3.2 Screen Organization (FFT Function) 3.2 Screen Organization (FFT Function) Measurement-related settings for FFT analysis are made on the Settings screens (Status, Channel, Trigger and Sheet); saving and printing settings are made on the Save Settings and Print Settings screens; and measurement data display settings are made on the Waveform screen. The Channel Settings, Trigger Settings, Save Settings and Print Settings screens are nearly the same as for the other operating functions. 3.2.
39 3.2 Screen Organization (FFT Function) Setting Items and Choices FFT Function Settings [FFT(1/2)] See "3.4.10 Setting and Changing Analysis Conditions on the Waveform Screen" (⇒ p. 67) Frequency Range Frequency Resolution Setting Item Category Number of Analysis Points FFT Window Function Type Trigger Mode Setting Switch with the SUB MENU keys FFT Function Settings [FFT(2/2)] See "3.4.10 Setting and Changing Analysis Conditions on the Waveform Screen" (⇒ p.
40 3.2 Screen Organization (FFT Function) 3.2.2 Settings Screen To open the Settings screen 1 Press the SET key. (The Settings screen appears.) 3 Press the SHEET/PAGE keys to select a page. 2 Press the SUB MENU keys to select from the Settings menu. Status Settings Screen Make settings here for FFT analysis. Input Data Selection (⇒ p. 52) Select whether FFT analysis is to be applied to newly acquired data, or to a pre-existing waveform (Memory waveform).
41 3.2 Screen Organization (FFT Function) Channel Settings Screen Set analog channels. Comment Setting Make this setting to enter channel-specific comments. This setting is also available on the [Comment] page. Comments can be displayed on the Waveform screen. All Channel Settings List (The Logic page is not accessible) Setting Unit (Module) and Channel Nos. Input Module Settings Set the input channels for the installed input modules. See "Chapter 3 Input Channel Settings" in the Input Module Guide.
42 3.2 Screen Organization (FFT Function) Settings on the [Analog] and [Wcal] pages are the same as for the Memory function. Sheet Settings Screen Set the display method for the Waveform screen. Screen Layout Setting (⇒ p. 72) Assigning Channels to Sheets Set the data type and display arrangement for each sheet to be displayed. • Sheet Name setting • Display type • Split screen Assigns the channel, calculation results and waveform display position for each display sheet.
43 3.2 Screen Organization (FFT Function) Setting procedures on the Save Settings screen are the same for all functions. See "Chapter 10 Saving/Loading Data & Managing Files" in the Instruction Manual for details. Save Settings Screen [Auto Save] Page Make these settings to specify automatic saving. The factory default setting for auto save is [Off].
44 3.2 Screen Organization (FFT Function) Setting procedures on the Print Settings screen are the same for all functions. See "Chapter 11 Printing" in the Instruction Manual for details. Print Settings Screen [Printer] Page Select the printing method and printer for automatic or manual printing. The factory default setting for auto print is [Off]. Auto Print Settings Make these setting to print automatically. Internal Printer Settings Set the printer’s print density and quality.
45 3.3 Operation Workflow 3.
46 3.3 Operation Workflow Settings Procedure for FFT Analysis Function Selection Select the FFT function (⇒ p. 51). Opening screen: Press the F3 [FFT] key. Waveform screen or Settings screen: Using the CURSOR keys, move the cursor to the Function menu, and press the F3 [FFT] key.
47 3.3 Operation Workflow Measurement Configuration Settings Press the SET key to open the Settings screen Press the SUB MENU keys to select the menu 1 2 Make settings on the Status Settings screen. 1 2 3 Select the input data Select whether to analyze newly acquired data, or existing data. See "3.4 Setting FFT Analysis Conditions" (⇒ p. 51) Select the desired window function Set the window function to be applied to the input signal.
48 3.3 Operation Workflow Input Channel Settings Make settings on the Channel Settings screen. Press the SUB MENU keys to select the menu Press the SHEET/PAGE keys to select the [One Ch] page 9 Select the Unit (module) and Channel 10 Select the measurement range (vertical axis) Make input-module-related settings 11 Perform zero adjustment (after warm-up) 12 Press the SUB MENU keys to select the menu Set the trigger mode Default setting: [Auto] 14 11 10 12 See "3.5 Selecting Channels" (⇒ p.
49 3.3 Operation Workflow Display Sheet Settings Press the SUB MENU keys to select the menu 17 Select the Sheet No. on which to display FFT analysis results (Enter a Sheet name as needed) 18 Select the Display Type 19 Select the split-screen number for the graph 20 Select the Analysis No. (F1 to F8) to be displayed Select the Analysis No. to display on each Sheet. (Configure the Waveform screen display layout) Set on the Sheet Settings screen. 17 18 20 19 See "3.
50 3.3 Operation Workflow Printing Settings Press the SUB MENU keys to select the menu Press the SHEET/PAGE keys to select the [Printer] page 23 Set on the Print Settings screen. 23 24 Select automatic or manual printing Verify that the paper is loaded correctly. When printing manually, settings can be made after measurement.
51 3.4 Setting FFT Analysis Conditions 3.4 Setting FFT Analysis Conditions Basic measurement configuration settings are performed on the Status Settings screen. Measurement configuration can be performed from the Waveform screen (⇒ p. 67). 1 Open the Settings screen 2 Menu selection 3.4.1 Selecting the FFT Function The FFT function can be selected from the Opening, Waveform or Settings screen. Function Selection: From the Opening Screen Operating Key Procedure 1 CURSOR Move to the desired function.
52 3.4 Setting FFT Analysis Conditions F 3.4.2 Selecting the Data Source for Analysis Select the data to be used for FFT analysis. Analysis can be applied either to new data as it is measured, or to existing data (previously recorded to memory). Selecting Input Data To open the screen: Press the SET key → Select with the SUB MENU keys →Status Settings screen See Screen Layout (⇒ p. 40), To set from the Waveform screen (⇒ p. 67) Operating Key 1 2 Procedure Select the input data source.
53 3.4 Setting FFT Analysis Conditions 3.4.3 Setting the Frequency Range and Number of Analysis Points About the frequency range and number of analysis points The settings for the frequency range and number of analysis points determine the input signal acquisition time and frequency resolution. The frequency range setting for the FFT function corresponds to the timebase (time/division) setting of the Memory function. Changing the frequency range also changes the data sampling period.
54 3.4 Setting FFT Analysis Conditions Frequency Range and No. of Analysis Points Settings: Using the Operating Keys To open the screen: Press the SET key → Select with the SUB MENU keys →Status Settings screen See Screen Layout (⇒ p. 40), To set from the Waveform screen (⇒ p. 67) Operating Key 1 2 Procedure Select the sampling clock. CURSOR Move the cursor to the [Sampling Clock] item. F1 Select [INT] (Internal). (default setting) Select the frequency range.
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56 3.4 Setting FFT Analysis Conditions 3.4.4 Setting the Window Function The window function defines the segment of the input signal to be analyzed. Use the window function to minimize leakage errors. There are three general types of window functions: • Rectangular window • • • • • Hann window Hamming window Blackman window Blackman-Harris window Flat top window • Exponential window The non-rectangular window functions generally produce lower-level analysis results.
57 3.4 Setting FFT Analysis Conditions 3.4.5 Setting Peak Values of Analysis Results Either local or global maxima ([maximal]/ [maximum]) of the input signal and analysis results can be displayed on the Waveform screen. However, if Nyquist display is selected on the Sheet Settings screen, no peak values are displayed. Selecting Displayed Values To open the screen: Press the SET key → Select with the SUB MENU keys →Status Settings screen See Screen Layout (⇒ p.
58 3.4 Setting FFT Analysis Conditions 3.4.6 Averaging Waveforms The averaging function calculates the average of the values obtained from multiple measurements of a periodic waveform. This can reduce noise and other nonperiodic signal components. Averaging can be applied to a time-domain waveform or to a spectrum. Averaging Settings To open the screen: Press the SET key → Select with the SUB MENU keys →Status Settings screen See Screen Layout (⇒ p.
59 3.4 Setting FFT Analysis Conditions Description See "Trigger Modes and Averaging" (⇒ p. 60) When averaging time-domain waveform values Waveforms are acquired and averaged within the time domain. After averaging, FFT calculation is performed. When the trigger mode is [Auto]: Data is acquired when the START key is pressed, even if trigger criteria are not met after a certain interval. So if averaging is applied to an asynchronous signal, the resulting data is meaningless.
60 3.4 Setting FFT Analysis Conditions Trigger Modes and Averaging ____________________________________ When the trigger mode is [Single] Measurements continue until the specified number of averaging points is acquired. (Spectrum averaging) (Waveform averaging) Start Measurement START key Input Signal Trigger criteria met Awaiting Trigger FFT analysis Waveform acquisition (specified no. of points) FFT analysis Display Averaging End *2 When the acquired count < the specified count *1 *1.
61 3.4 Setting FFT Analysis Conditions 3.4.7 Emphasizing Analysis Results (phase spectra only) By specifying a setting factor (rate) to be applied to the input signal, the display of data exceeding the resulting threshold can be emphasized. This feature is useful for viewing waveforms that may otherwise be obscured by noise. The reliability of phase spectrum values is poor when discrete Fourier transform values are extremely small.
62 3.4 Setting FFT Analysis Conditions 3.4.8 Analysis Mode Settings Select the type of FFT analysis, channel(s), waveform display color and x and y axes. Analysis Content Settings To open the screen: Press the SET key → Select with the SUB MENU keys →Status Settings screen See Screen Layout (⇒ p. 40), To set from the Waveform screen (⇒ p. 67) Operating Key 1 Procedure Open the [Analyze] page. SHEET/PAGE Select the [Analyze] page. 1 Analysis Setting Contents Analysis No.
63 3.4 Setting FFT Analysis Conditions 4 Operating Key 4 5 6 Procedure When [Parameter] setting contents are displayed Set the parameter. CURSOR Move the cursor to the [Parameter] column of the Analysis No. to set. F1 to F8 Select the desired type of analysis or display. Analyze mode Parameter Setting Contents Linear Spectrum, Transfer Function, Cross Power Spectrum Normal Analysis results are displayed as amplitude vs. frequency. Nyquist Analysis results are displayed as imaginary vs.
64 3.4 Setting FFT Analysis Conditions Octave Filter Setting____________________________________________ Filter characteristics comply with tolerance standards for IEC61260 filters. Normal Sharp Filter characteristics approximate those of an analog filter. Only those spectral component within the octave band are used for analysis. Spectral components outside of the octave band are totally ignored.
65 3.4 Setting FFT Analysis Conditions To Set from a Dialog ____________________________________________ Move the cursor to the [No.] column of the Analysis to set, and press F1 [All Settings]. A dialog box appears. Items that cannot be set for the particular analysis mode are grayed out. Move the cursor to each item, and select with the F1 to F8 keys. These are the same as the setting contents on the [Analyze] page. Parameter Settings These are the same as the setting contents on the [Scale] page.
66 3.4 Setting FFT Analysis Conditions 3.4.9 Setting the Display Range of the Vertical Axis (Scaling) The display range of the vertical (y) axis can be set to automatically suit analysis results, and can be freely expanded and compressed. Vertical Axis (Scaling) Setting To open the screen: Press the SET key → Select with the SUB MENU keys →Status Settings screen See Screen Layout (⇒ p. 40) Operating Key 1 Procedure Open the [Scale] page. SHEET/PAGE Select the [Scale] page.
67 3.4 Setting FFT Analysis Conditions 3.4.10 Setting and Changing Analysis Conditions on the Waveform Screen The following settings can be made on the Waveform screen. Press the SUB MENU keys to switch the displayed measurement items. Changes to the displayed analysis results become effective when the settings are changed.
68 3.4 Setting FFT Analysis Conditions Changing analysis number, analysis mode, waveform color, analysis channel and x/y axis display type 1 Press the SUB MENU key to display Analysis Number (⇒ p. 62) 2 Use the CURSOR keys to move the cursor to each setting item, and select your choice with the F keys. [FFT(2/2]. This is linked to the setting on the [Analyze] page of the Status Settings screen.
69 3.5 Selecting Channels 3.5 Selecting Channels Channel selection is the same for all functions. The setting examples here describe operation with the Model 8957 High Resolution Unit. Channel Settings To open the screen: Press the SET key → Select with the SUB MENU keys →Channel Settings screen See Screen Layout (⇒ p. 41) Operating Key Procedure 1 SHEET/PAGE Select the [One Ch] page. 2 Select the module (Unit) and channel number to be set. 3 CURSOR Move the cursor to each [Unit (no.
70 3.5 Selecting Channels Operating Key 6 Procedure Set low-pass filtering (as occasion demands). CURSOR Move the cursor to the [LPF] item. F1 to F8 Set the low-pass filter in the input module. (For Model 8957) OFF, 5Hz, 50Hz, 500Hz, 5kHz, 50Hz 7 8 9 10 6 9 10 Select the probe attenuation. CURSOR Move the cursor to the [Probe] item. F1 to F8 Select according to the connection cables being used. 1:1 Select when measuring using Model 9197, 9198 or 9217 Connection Cords.
71 3.5 Selecting Channels Scaling _______________________________________________________ The scaling setting allows values displayed on this instrument to match the actual values read directly on a sound level meter or vibration meter. Without Scaling With Scaling Setting example: To display measurement data on this instrument so that it corresponds to that on a sound level meter.
72 3.6 Setting the Screen Layout of the Waveform Screen 3.6 Setting the Screen Layout of the Waveform Screen Measurement data can be split and displayed on up to 16 sheets on the Waveform screen. Assigning the Results of FFT Analysis to a Sheet To open the screen: Press the SET key → Select with the SUB MENU keys →Sheet Settings screen See Screen Layout (⇒ p. 42) Operating Key 1 2 1 Sheet Assignment. CURSOR F1 to F8 Move the cursor to the [Sheet 1] item. Select the number of the Sheet to set.
73 3.6 Setting the Screen Layout of the Waveform Screen Operating Key 5 5 Procedure Select the data to display on the Sheet. SHEET/PAGE Select the [FFT] page. CURSOR F1 to F8 Move the cursor to the [Analyze] column. Select the desired calculation number for display. (This becomes the Analysis No. setting on the Status Settings screen.) The analysis mode is displayed. (When using split-screen display) CURSOR F1 to F8 Move the cursor to the [Graph] column. Select the Graph number to be displayed.
74 3.6 Setting the Screen Layout of the Waveform Screen Display Types and Split-Screen Settings ___________________________ Fourteen display arrangements are available.
75 3.7 Saving Analysis Results 3.7 Saving Analysis Results The saving procedure is the same as for the Memory and Recorder functions. See "Chapter 10 Saving/Loading Data & Managing Files" in the Instruction Manual The size of saved files depends on the file format. See "Appendix 2.2 Waveform File Sizes" in the Instruction Manual When FFT Analysis Results are Saved as Text ______________________ A file is created for each analysis mode. One of the following text strings is appended to the file name.
76 3.8 Printing Analysis Results 3.8 Printing Analysis Results The printing procedure is the same as for the Memory and Recorder functions.
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78 3.9 Analysis with the Waveform Screen 3.9 Analysis with the Waveform Screen 3.9.1 Selecting the Display Method The display of FFT analysis data can be switched between waveform and numerical views. Press the DISP key repeatedly to change the display method. Pressing the DISP key opens the Display dialog in which to select a display method. Selections in this dialog are available using the F keys. Press the ESC key or an F key to close the dialog.
79 3.9 Analysis with the Waveform Screen 3.9.2 Selecting Gauges and Values Display of upper and lower limits and peak values [maximal/ maximum] can be selected by analysis number. However, selection is not possible when Nyquist display is enabled. Press the FUNCTION MODE key to enable the FN mode, then press F2 [Gauge & Value]. The Gauge dialog appears. Select an analysis number as occasion demands to display gauge and measurement values. Press the ESC key or the F8 [Close] key to close the dialog.
80 3.9 Analysis with the Waveform Screen 3.9.3 Analyzing after Specifying an Analysis Starting Point A starting point for FFT analysis can be specified on an existing memory waveform before analyzing. The procedure depends on the Trigger Mode setting. See "Trigger Modes and Averaging" (⇒ p. 60) • When the Trigger Mode is [Single] Analysis is performed once on the specified number of analysis points beginning with the specified starting point, and analysis results are displayed.
81 3.9 Analysis with the Waveform Screen Procedure 1. Verifying the analysis starting point while viewing analysis data 1 Display the waveform to be analyzed. 2 Select the FFT function (F3 [FFT]) to display the Status Settings screen. 3 Set the analysis input data source to [From Mem]. Set analysis conditions such as the analysis mode and number of analysis points (these can also be set on the Waveform screen). 4 Press the SUB MENU keys to display the Sheet Settings screen.
82 3.9 Analysis with the Waveform Screen Memory Waveform Analysis segment for one pass (the number of analysis points) 7 Specify the location of the analysis input data using the jog and shuttle controls. Jog Moves the analysis starting point. The analysis segment of the memory waveform for one pass is displayed. Shuttle Scrolls the Memory waveform. Cursor Speed: HIGH 8 Select analysis conditions as occasion demands. Press the SPEED key to adjust the movement and scrolling speed.
83 3.9 Analysis with the Waveform Screen Procedure 2. Performing FFT analysis after specifying a starting point on an existing memory waveform using the A/B cursors 1 Display the waveform with the Memory function. 2 Press the TYPE key and select [Vertical] or [Trace]. TYPE key A/B knob 3 Specify the analysis starting point with the A/B knobs. When both A/B cursors are enabled, the analysis starting point is determined by the earliest (leftmost) cursor.
84 3.9 Analysis with the Waveform Screen 7 Make other settings as occasion demands, then press the START key to begin analyzing.
85 3.10 FFT Analysis Modes 3.10 FFT Analysis Modes 3.10.1 Analysis Modes and Display Examples For the functions of each analysis mode, see "3.10.2 Analysis Mode Functions" (⇒ p. 102). Storage STR Displays the time axis waveform of the input signal. When the window function setting is other than rectangular, the window function is applied to the waveform and displayed.
86 3.10 FFT Analysis Modes Linear Spectrum LIN The linear spectrum plots the input signal frequency. It can be displayed as a Nyquist plot. Main uses: • To inspect the peak frequency contents of a waveform • To inspect signal amplitudes at each frequency See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p.
87 3.10 FFT Analysis Modes RMS Spectrum RMS Amplitudes (RMS values) are calculated along the frequency axis from the input signal waveform. RMS and power spectra displays use the same analysis results displayed logarithmically (amplitude in dB). Main uses: • To inspect the peak frequency contents of a waveform • To inspect the RMS value at each frequency See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p.
88 3.10 FFT Analysis Modes Power Spectrum PSP Displays input signal power as the amplitude component. Main uses: • To inspect the peak frequency contents of a waveform • To inspect the power level at each frequency See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p.
89 3.10 FFT Analysis Modes Power Spectrum Density PSD Indicates the power spectrum density of the input signal with only the amplitude component included. This is the power spectrum divided by the frequency resolution. Not available with external sampling enabled. Main uses: To acquire a power spectrum with 1-Hz resolution for highly irregular waveforms such as white noise See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p.
90 3.10 FFT Analysis Modes Auto Correlation Function ACR Shows the correlation of two points on the input signal at time differential t. Main uses: • To detect periodicy in irregular signals (improving and detecting SNR) • To inspect periodic components in a noisy waveform. See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p. 102) Axis Display Type Description X axis Linear Time display The center (t = 0) is the reference.
91 3.10 FFT Analysis Modes 1/1 and 1/3 Octave Analysis OCT The sound pressure level of the spectrum of a signal such as noise is displayed through a fixed-width one- or one-third octave band-pass filter. Not available with external sampling enabled. Main uses: To analyze frequency components of noise See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p. 102), "Octave Filter Characteristics" (⇒ p. 114) Axis Display Type Description X axis Log Displays the center frequency of each band.
Timebase Period [s] Sampling frequency [Hz] Frequency range [Hz] Center frequency [Hz] ( : 1/1 OCT, : 1/3 OCT) 92 3.
Timebase Period [s] Sampling frequency [Hz] Frequency range [Hz] Center frequency [Hz] ( : 1/1 OCT, : 1/3 OCT) 93 3.
Timebase Period [s] Sampling frequency [Hz] Frequency range [Hz] Center frequency [Hz] ( : 1/1 OCT, : 1/3 OCT) 94 3.
95 3.10 FFT Analysis Modes Phase Spectrum PHA Shows the phase characteristics of the input signal. Main uses: • To inspect the phase spectrum of channel 1. Displays the phase of a cosine waveform as a reference (0º). • To inspect the phase difference between channels 1 and 2. See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p. 102) 1 Ch FFT: Displays the phase of the signal on channel 1. Displays the phase of a cosine waveform as a reference (0º).
96 3.10 FFT Analysis Modes Transfer Function TRF From the input and output signals, the transfer function (frequency characteristic) of a measurement system can be obtained. It can also be displayed as a Nyquist plot. Main uses: • To inspect a filter’s frequency characteristic • To inspect the stability of a feedback control system (using the Nyquist plot) • To inspect the resonance characteristic of an object using an impulse hammer and pick-up sensor See About the Functions "3.10.
97 3.10 FFT Analysis Modes Cross Power Spectrum CSP The product of the spectra of two input signals can be obtained. The common frequency components of two signals can be obtained. Using the voltage and current waveforms as input signals, active power, reactive power and apparent power can be obtained at each frequency. Main uses: To inspect common frequency components of two signals See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p.
98 3.10 FFT Analysis Modes Cross-Correlation Function CCR Using two input signals, shows the correlation of two points on the input signal at time differential t. Output is displayed as a function of differential time t. Main uses: • To determine the phase shift of two signals per unit of time • To determine the speed and distance of time lag between two signals See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p.
99 3.10 FFT Analysis Modes Impulse Response IMP The transfer characteristic of a system is obtained as a time-domain waveform. Utilizing both output and input signals of the measurement system, a unit impulse is applied to the system and the corresponding response waveform is obtained. Main uses: To inspect circuit time constants See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p. 102), "Linear Time-Invariant Systems" (⇒ p.
100 3.10 FFT Analysis Modes Coherence Function COH This function gives a measure of the correlation (coherence) between input and output signals. Values obtained are between 0 and 1. With a single measurement, the coherence function gives a value of one for all frequencies. Spectrum (frequency-domain) averaging should always be performed before measurement (analysis is not available with time-domain averaging).
101 3.10 FFT Analysis Modes Power Spectrum Density (Linear Predictive Coding) LPC When the spectrum shape is complex and hard to comprehend with either linear or power spectra, a rough spectrum structure can be obtained. Not available with external sampling enabled. Main uses: To obtain a spectral envelope using statistical methods See About the Functions "3.10.2 Analysis Mode Functions" (⇒ p.
102 3.10 FFT Analysis Modes 3.10.2 Analysis Mode Functions Analysis Mode Internal analysis formula (linear, real, imag [imaginary], log [logarithm]) No Analysis No analysis. Storage Waveform A waveform obtained by applying the window function to a time-domain waveform.
103 3.11 FFT Definitions 3.11 FFT Definitions What is FFT? __________________________________________________ FFT is the abbreviation for Fast Fourier Transform, an efficient method to calculate the DFT (Discrete Fourier Transform) from a time-domain waveform. Also, the reverse process of transforming frequency data obtained by the FFT back into its original time-domain waveform is called the IFFT (Inverse FFT). The FFT functions perform various types of analysis using FFT and IFFT.
104 3.11 FFT Definitions Imaginary component F( k) 虚数部 Representing the above relationship on a complex flat surface produces the following figure. F (k ) φ (k ) 実数部 Real component Linear Time-Invariant Systems __________________________________ Consider a linear time-invariant (LTI) system y(n) that is a response to discrete time-domain signal x(n). In such an LTI system, the following expression applies to any integer Ai when the response to xi(n) is yi(n) = L[xi(n)].
105 3.11 FFT Definitions Number of Analysis Points_______________________________________ The FFT functions of this instrument can perform frequency analysis of timedomain waveforms consisting of 1000, 2000, 5000 or 10,000 points. However, when the following conditions are satisfied, previously analyzed data can be reanalyzed with a different number of analysis points. A. When measurements are made with the averaging function disabled (Off) B.
106 3.11 FFT Definitions Aliasing ______________________________________________________ When the frequency of a signal to be measured is higher than the sampling rate, the observed frequency is lower than that of the actual signal, with certain frequency limitations. This phenomena occurs when sampling occurs at a lower frequency than that defined by the Nyquist-Shannon sampling theorem, and is called aliasing.
107 3.11 FFT Definitions Anti-Aliasing Filters ____________________________________________ When the maximum frequency component of the input signal is higher than onehalf of the sampling frequency, aliasing distortion occurs. To eliminate aliasing distortion, a low-pass filter can be used that cuts frequencies higher than onehalf of the sampling frequency. Such a low-pass filter is called an anti-aliasing filter.
108 3.11 FFT Definitions Imaging ______________________________________________________ When the instrument is set to a measurement frequency range that requires a higher sampling rate than the maximum capability of the input module, intermediate data points are interpolated between successive data samples. In this case, the time-domain waveform exhibits a stair-step shape. When FFT analysis is performed in this situation, non-existent high frequency spectral components appear.
109 3.11 FFT Definitions Averaging_____________________________________________________ With the FFT function, averaging is performed according to the following analytical expressions. Averaging in the time domain produces meaningless data if performed with inconsistent trigger criteria. 1. Simple Averaging (Time and Frequency Domains) Sequences of acquired data are summed and divided by the number of acquisitions.
110 3.11 FFT Definitions Window Function ______________________________________________ The Fourier transform of a continuous system is defined by the integral Calculus in expression (14) for the time range from minus infinity to plus infinity. ∞ X ( f ) = ∫ x (t )ε − 2πft dt (14) −∞ However, because expression (14) cannot be calculated with actual measurements, the Analysis is performed on a segment between finite limits. Processing the waveform segment within these limits is called window processing.
111 3.11 FFT Definitions The following figure presents an example of spectral analysis by applying a window function to a time-domain waveform. Using the window function, discontinuous points on the time-domain waveform are eliminated, so the wave shape approaches a line spectrum. When a Blackman-Harris window function is applied to a time-domain waveform (⇒ p. 110) in which the number of analysis points is not an integer multiple of the input frequency 0 Magnitude [dB] Amplitude [V] 0.1 -100 0 -0.
112 3.11 FFT Definitions Exponential window 0 0.1% -20 50% 99.9% Gain [dB] Amplitude 0.1% 50% 99.
113 3.11 FFT Definitions Flat top window 0 Gain [dB] Amplitude -20 -40 -60 0 0 N-1 -80 0 Time-Domain Waveform 2 4 6 Frequency (1/W) 8 10 Spectrum The following example shows input sine waves of 1050 and 1150 Hz analyzed with different window functions.
114 3.11 FFT Definitions Octave Filter Characteristics _____________________________________ Octave filter characteristics are determined according to IEC61260 standards. The figures below show these standards and the filter characteristics of this instrument.
115 3.11 FFT Definitions Linear Predictive Coding (LPC) ___________________________________ In the following figure, linear predictive coding is implemented by passing a sample of the input signal through the prediction filter while altering the filter so as to minimize errors in the original signal.
116 3.
Index 1 Index Index A E A/B cursor .....................................................80, 83 Acquisition interval ..............................................55 ACR ....................................................................90 Aliasing .............................................................106 Analysis modes ...............................59, 62, 64, 102 Analysis starting point .........................................80 Analyze page ..................................................
Index 2 Index M Maximum value .................................................. 19 Measurable ranges with octave analysis ........... 92 Measurement End of measurement ...................................... 50 Start of measurement ..................................... 50 Measurement configuration settings .................. 47 Measurement range ........................................... 48 Memory waveform .............................................. 80 Minimum value ..................................
Index 3 Index Coefficient .......................................................56 Window function ....................................56, 67, 110 Multiplication ...................................................56 X X axis ..................................................................63 X-Y area ..............................................................20 Y Y axis ..................................................................63 Z Zero adjustment ..........................................
Index Index 4
HIOKI 8860/8861 MEMORY HiCORDER Analysis Supplement Publication date: July 2006 Revised edition 1 Edited and published by HIOKI E.E. CORPORATION Technical Support Section All inquiries to International Sales and Marketing Department 81 Koizumi, Ueda, Nagano, 386-1192, Japan TEL: +81-268-28-0562 / FAX: +81-268-28-0568 E-mail: os-com@hioki.co.jp URL http://www.hioki.co.
HEAD OFFICE 81 Koizumi, Ueda, Nagano 386-1192, Japan TEL +81-268-28-0562 / FAX +81-268-28-0568 E-mail: os-com@hioki.co.jp / URL http://www.hioki.co.
