Digital Signal Processing Reference
In-Depth Information
(0.7)
-n
u[n + 7]
(e)
(f)
0.7
n
u[-n]
11.27. (a)
Find the inverse of the bilateral
z
-transform
.6z
(z - 1)(z - .6)
F
b
(z) =
for the following regions of convergence:
(i)
(ii)
(iii)
(b)
Give the final values of the functions of parts (i) through (iii).
ƒ z ƒ 6 .6
ƒ z ƒ 7 1
.6 6 ƒ z ƒ 6 1
11.28. (a)
Given the discrete-time function
(
2
)
n
,
-10 F n F 20
f[n] =
b
,
0,
otherwise
express the bilateral
z
-transform of this function in closed form (not as a power
series).
(b)
Find the region of convergence of the transform of part (a).
(c)
Repeat parts (a) and (b) for the discrete-time function
(
2
)
n
,
-10 F n F 10
(
4
)
n
,
f[n] =
c
n G 21
.
0,
otherwise
(d)
Repeat parts (a) and (b) for the discrete-time function
(
2
)
n
,
-10 F n F 0
(
4
)
n
,
f[n] =
c
1F n F 10
.
0,
otherwise
11.29.
Consider the bilateral
z
-transform
3z
z - 1
+
z
z - 12
-
z
z - .6
.
F(z) =
(a)
Find all possible regions of convergence for this function.
(b)
Find the inverse transform for each region of convergence found in part (a).
11.30.
The
wavelet transform
[4] is popular for various signal-processing operations. The
analysis step
involves applying a series of low-pass filters to the input signal. After each
application of the filter, the signal is
downsampled
to retain only every other sample
point so that the number of wavelet transform coefficients that remains is equal to the
number of points in the input function.
