User`s guide

Dyadic Synthesis Filter Bank
5-159
5Dyadic Synthesis Filter Bank
Purpose Reconstruct a signal from its multirate bandlimited components.
Library Filtering / Multirate Filters
Description The Dyadic Synthesis Filter Bank block typically reconstructs a signal that
was decomposed by the Dyadic Analysis Filter Bank block. The reconstruction
or synthesis process is the inverse of the analysis process, and restores the
original signal by upsampling, filtering, and summing the bandlimited inputs
in stages corresponding to the analysis process. The typical (asymmetric)
n-level filter bank structure is shown below.
At each level, the two bandlimited inputs (one low-frequency, one
high-frequency, both with the same sample rate) are upsampled by a factor of 2
to match the sample rate of the input to the next stage. They are then filtered
by a highpass (HP) and lowpass (LP) filter pair with coefficients calculated to
cancel (in the subsequent summation) the aliasing introduced in the
corresponding dyadic analysis filter stage. The output from each
(upsample-filter-sum) level has twice the bandwidth and twice the sample rate
of the input to that level (hence “dyadic”).
The
Lowpass FIR filter coefficients and Highpass FIR filter coefficients
parameters specify (respectively) the filter coefficients to be used for every
HP
LP
↑2
↑2
HP
↑2
LP
↑2
HP
↑2
LP
↑2
y
HP: highpass filter with f
c
≈ 1/2 Nyquist
LP: lowpass filter with
f
c
≈ 1/2 Nyquist
↑2: upsample by 2
u
1
u
2
u
3
u
n
HP
↑2
LP
↑2
. . .
u
n +1
Asymmetric Fi
l
ter Ban
k
, n Leve
l
s
Σ
Σ
Σ
Σ
2T
s
4T
s
8T
s
T
si
=(2
k
)T
s
for input u
k
, 1 ≤ k ≤ n
T
si
=(2
n
)T
s
for input u
n
+1
T
so
=T
s