Digital Signal Processing Reference
In-Depth Information
sinc(x)
. What kind of filter impulse response results from the functions below? What effect does the
parameter
c
have, and what effect does the length of the vector
n
have?
(a)
n =-9:1:9; c = 0.8; y = sinc(c*n);
(b)
n =-9:1:9; c = 0.4; y = sinc(c*n);
(c)
n =-9:1:9; c = 0.2; y = sinc(c*n);
(d)
n =-9:1:9; c = 0.1; y = sinc(c*n);
(e)
n =-39:1:39; c = 0.8; y = sinc(c*n);
(f )
n =-39:1:39; c = 0.4; y = sinc(c*n);
(g)
n =-39:1:39; c = 0.2; y = sinc(c*n);
(h)
n =-39:1:39; c = 0.1; y = sinc(c*n);
(i)
n =-139:1:139; c = 0.8.; y = sinc(c*n);
(j)
n =-139:1:139; c = 0.4.; y = sinc(c*n);
(k)
n =-139:1:139; c = 0.2.; y = sinc(c*n);
(l)
n =-139:1:139; c = 0.1.; y = sinc(c*n);
5. Compute and plot the magnitude and phase of the DTFT of the following impulse responses
x
. Note
the effect of the frequency parameter
f
and the difference in impulse responses and especially phase
responses between (a)-(e) and (f )-(j).
(a)
n = -10:1:10; f = 0.05; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(b)
n = -10:1:10; f = 0.1; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(c)
n = -10:1:10; f = 0.2; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(d)
n = -10:1:10; f = 0.4; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(e)
n = -10:1:10; f = 0.8; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(f )
n = 0:1:20; f = 0.05; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(g)
n = 0:1:20; f = 0.1; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(h)
n = 0:1:20; f = 0.2; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(i)
n = 0:1:20; f = 0.4; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
(j)
n = 0:1:20; f = 0.8; x = ((0.9).ˆ(abs(n))).*cos(f*pi*n)
6. An ideal lowpass filter should have unity gain for
>ω
c
, and a linear
phase factor or constant sample delay equal to
e
−
jωM
where
M
represents the number of samples of delay.
Use the inverse DTFT to determine the impulse response that corresponds to this frequency specification.
That is to say, perform the following integration
|
ω
| ≤
ω
c
and zero gain for
|
ω
|
π
1
2
π
X(e
jω
)e
jwn
dω
[
]=
x
n
−
π
where
1
e
−
jωM
|
|
·
ω
≤
ω
c
X(e
jω
)
=
>ω
c
After performing the integration and obtaining an expression for
x
0
|
ω
|
[
]
, use
n
= -20:1:20 and
M
=
10, and obtain four impulse responses corresponding to the following values of
ω
c
:
(a) 0.1
π
(b) 0.25
π
(c) 0.5
π
(d) 0.75
π
n
