User`s guide

Wavelet Analysis
5-529
5Wavelet Analysis
Purpose Decompose a signal into components of logarithmically decreasing frequency
intervals and sample rates (requires the Wavelet Toolbox).
Library Filtering / Multirate Filters
Description The Wavelet Analysis block uses the wfilters function from the Wavelet
Toolbox to construct a dyadic analysis filter bank that decomposes a broadband
signal into a collection of successively more bandlimited components. An
n-level filter bank structure is shown below, where n is specified by the
Number of levels parameter.
At each level, the low-frequency output of the previous level is decomposed into
adjacent high- and low-frequency subbands by a highpass (HP) and lowpass
(LP) filter pair. Each of the two output subbands is half the bandwidth of the
input to that level. The bandlimited output of each filter is maximally
decimated by a factor of 2 to preserve the bit rate of the original signal.
HP
LP
↓2
↓2
HP
↓2
LP
↓2
HP
↓2
LP
↓2
u
HP: highpass filter with f
c
≈ 1/2 Nyquist
LP: lowpass filter with
f
c
≈ 1/2 Nyquist
↓2: downsample by 2
y
1
y
2
y
3
y
n
HP
↓2
LP
↓2
. . .
y
n +1
Wave
l
et Ana
l
ysis Fi
l
ter Ban
k
, n Leve
l
s
T
si
=T
s
T
so
=(2
k
)T
s
for output y
k
, 1 ≤ k ≤ n
T
so
=(2
n
)T
s
for output y
n
+1
2T
s
4T
s
8T
s