Digital Signal Processing Reference
In-Depth Information
(d)
Repeat part (a) for
(e)
Repeat part (a) for
(f)
y[n] = log(x[n]).
y[n] = log(nx[n]).
Repeat part (a) for
y[n] = 4x[n - 3] + 3.
n+ 2
(g)
y[n] =
cos(x[k])
a
k=-
q
9.24.
The system described by the linear difference equation
y[n] - 2y[n - 1] + y[n - 2] = x[n],
n G 0,
with constant coefficients can be shown to be invertible and unstable. Determine
whether this system is
(a)
memoryless;
(b)
time invariant;
(c)
linear.
9.25.
(a)
Determine whether the summation operation, defined by
n
y[n] =
a
x[k + a],
is
k=-n
where
a
is an integer.
(i)
memoryless;
(ii)
invertible;
(iii)
causal;
(iv)
stable;
(v)
time invariant;
(vi)
linear.
(b)
Repeat part (a) for the averaging filter
1
2
[x[n] + x[n - 1]]
y[n] =
(c)
Repeat part (a) for the running average filter (
M 7 0
is an integer)
M- 1
1
M
a
y[n] =
x[n - k].
k= 0
9.26.
For the system of Example 9.10, show that for
ƒ x[n] ƒ F M,
ƒ y[n] ƒ F 9M.
9.27.
(a)
Sketch the characteristic
y
versus
x
for the system
y[n] =-3 ƒ x[n] ƒ .
Determine
whether this system is
(i)
memoryless;
(ii)
invertible;
(iii)
causal;
(iv)
stable;
(v)
time invariant;
(vi)
linear.
(b)
Repeat part (a) for
3x[n],
x[n] 6 0
y[n] =
b
0,
x[n] G 0.
