Digital Signal Processing Reference
In-Depth Information
In the
synthesis stage,
the wavelet coefficients are repeatedly
upsampled
and fil-
tered to reconstruct the input signal. This problem will demonstrate that the filtering
and upsampling steps of the wavelet transform can be interchanged.
To upsample a signal
x
[
n
], we form
x[
M
],
if n is an integer-multiple of M
b
x
M
[n] =
.
0,
otherwise.
(a)
A filter with impulse response
h
[
n
] is applied to a signal
x
[
n
] to form
y
[
n
]. The sig-
nal
y
[
n
] is then upsampled by a factor of
M
to form
y
M
[n].
Find
Y
M
(z).
(b)
Next the input signal
x
[
n
] is first upsampled by
M
to form
x
M
[n].
The filter
h
[
n
] is
also upsampled by
M
to form
h
M
[n]
and is then applied to
x
M
[n].
Find the
-transform of x
M
[n]
…
h
M
[n].
z
