Digital Signal Processing Reference
In-Depth Information
(b)
Repeat part (a) for
y
b
[n] = y
a
[n] + x[n].
9.21.
(a)
Consider the feedback system of Figure P9.21. Express the output signal as a func-
tion of the transformation of the input signal, in the form of (9.61).
(b)
Draw a block diagram, as in Figure P9.21, for a system described by
y[n] = T
2
(T
1
(x[n] - y[n]) - y[n]).
1
x
[
n
]
m
[
n
]
y
[
n
]
2
3
4
Figure P9.21
9.22.
The trapezoidal rule for numerical integration is defined in Figure P9.22. The value of the
integral at is equal to its value at plus the trapezoidal area shown.
(a)
Write a difference equation relating
y
[
k
], the numerical integral of
t = kT
t = (k - 1)T
x(t),
to
x
[
k
] for
this integrator.
(b)
Write a MATLAB program that integrates
e
-t
, 0 F t
F 5 s,
with
T = 0.1 s,
using
trapezoidal integration.
(c)
Run the program in part (b), and verify the result.
x
(
t
)
(
k
1)
T
kT
t
Figure P9.22
9.23.
(a)
Determine whether the system described by
y[n] = nx[an + 1] + 5,
where
a
is an integer and
ƒ a ƒ 7 1,
is
(i)
memoryless;
(ii)
invertible;
(iii)
causal;
(iv)
stable;
(v)
time invariant;
(vi)
linear.
(b)
Repeat part (a) for
(c)
Repeat part (a) for
y[n] = x[-n + 2]
y[n] = cos(x[n]).
