matel
June 20, 2015 Name:
Section:
Laboratory Exercise 7
LINEAR, TIME-INVARIANT DISCRETE-TIME SYSTEMS:
FREQUENCY-DOMAIN REPRESENTATIONS
Q4.19 A copy of Program P4_3 is given below:
< Insert program code here. Copy from m-file(s) and paste. >
The plots of the impulse responses of the four FIR filters generated by running Program P4_3 are given
below:
< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. > From the plots we make the following observations:
Filter #1 is of length ____9______ with a_对称_________ impulse response and is therefore a Type _1_ linear-phase FIR filter.
Filter #2 is of length ____10______ with a____对称______ impulse response and is therefore a Type _2_ linear-phase FIR filter.
Filter #3 is of length ________9__ with a____反对称______ impulse response and is therefore a Type _3_ linear-phase FIR filter.
Filter #4 is of length _________10_ with a________反对称__ impulse response and is therefore a Type _4_ linear-phase FIR filter.
From the zeros of these filters generated by Program P4_3 we observe that:
Filter #1 has zeros at z = 2.9744, 2.0888, 0.9790 + 1.4110i, 0.9790 - 1.4110i,
0.3319 + 0.4784i, 0.3319 - 0.4784i, 0.4787, 0.3362
Filter #2 has zeros at z = 3.7585 + 1.5147i, 3.7585 - 1.5147i, 0.6733 + 2.6623i,
0.6733 - 2.6623i, -1.0000, 0.0893 + 0.3530i, 0.0893 - 0.3530i, 0.2289 + 0.0922i,
0.2289 - 0.0922i
Filter #3 has zeros at z = 4.7627, 1.6279 + 3.0565i, 1 .6279 - 3.0565i, -1.0000,
1.0000, 0.1357 + 0.2549i, 0.1357 - 0.2549i, 0.2100
Filter #4 has zeros at z = 3.4139, 1.6541 + 1.5813i, 1.6541 - 1.5813i,
-0.0733 + 0.9973i, -0.0733 - 0.9973i, 1.0000, 0.3159 + 0.3020i, 0.3159 - 0.3020i,
0.2929
Plots of the phase response of each of these filters obtained using MATLAB are shown below:
< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. >
From these plots we conclude that each of these filters have ______线性____ phase.
The group delay of Filter # 1 is - 4.0000
The group delay of Filter # 2 is - 4.5000
The group delay of Filter # 3 is - 4
The group delay of Filter # 4 is - 4.5000
Q4.20 The plots of the impulse responses of the four FIR filters generated by running Program P4_3 are given
below:
< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. > From the plots we make the following observations:
Filter #1 is of length _______9___ with a______对称____ impulse response and is therefore a Type _1_ linear-phase FIR filter.
Filter #2 is of length ______10____ with a______对称____ impulse response and is therefore a Type 2__ linear-phase FIR filter.
Filter #3 is of length _______9___ with a____反对称______ impulse response and is therefore a Type 3__ linear-phase FIR filter.
Filter #4 is of length _______10___ with a_______反对称___ impulse response and is therefore a Type 4__ linear-phase FIR filter.
From the zeros of these filters generated by Program P4_3 we observe that:
Filter #1 has zeros at z = 2.3273 + 2.0140i
2.3273 - 2.0140i
-1.2659 + 2.0135i
-1.2659 - 2.0135i
-0.2238 + 0.3559i
-0.2238 - 0.3559i
0.2457 + 0.2126i
0.2457 - 0.2126i
Filter #2 has zeros at z = 2.5270 + 2.0392i
2.5270 - 2.0392i
-1.0101 + 2.1930i
-1.0101 - 2.1930i
-1.0000
-0.1733 + 0.3762i
-0.1733 - 0.3762i
0.2397 + 0.1934i
0.2397 - 0.1934i
Filter #3 has zeros at z = -1.0000
0.2602 + 1.2263i
0.2602 - 1.2263i
1.0000
0.6576 + 0.7534i
0.6576 - 0.7534i
0.1655 + 0.7803i
0.1655 - 0.7803i Filter #4 has zeros at z = 2.0841 + 2.0565i
2.0841 - 2.0565i
-1.5032 + 1.9960i
-1.5032 - 1.9960i
1.0000
-0.2408 + 0.3197i
-0.2408 - 0.3197i
0.2431 + 0.2399i
0.2431 - 0.2399i
Plots of the phase response of each of these filters obtained using MATLAB are shown
below:
< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. > From these plots we conclude that each of these filters have ____线性______ phase.
The group delay of Filter # 1 is - 4.0000
The group delay of Filter # 2 is - 4.5000
The group delay of Filter # 3 is - 4.0000
The group delay of Filter # 4 is - 4.5000
Answers:
Q4.21 A plot of the magnitude response of H1(z) obtained using MATLAB is shown
below:
< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. > From this plot we observe that the magnitude response has a maximum at = 0.5049
with a value = 0.3289
Using zplane we observe that the poles of H1(z) are __外________ the unit circle and hence the transfer function is/is not stable.
Q4.22 A plot of the magnitude response of G1(z) obtained using MATLAB is shown below:
< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. >
From this plot we observe that the magnitude response has a maximum at = 0.4599
with a value = 1.7854
Using zplane we observe that the poles of G1(z) are ___内_______ the unit circle and hence the transfer function is/is not stable.
Since the maximum value of the magnitude response of G1(z) is = 1.7854, we scale
G1(z) by __1/1.7854___ and arrive at a bounded-real transfer function
4.3
STABILITY TEST
A copy of Program P4_4 is given below: % Program P4_4
% Stability Test
clf;
den = input('Denominator coefficients = ');
ki = poly2rc(den);
disp('Stability test parameters are');
disp(ki);
< Insert program code here. Copy from m-file(s) and paste. >
Answers:
Q4.23 The pole-zero plots of H1(z) and H2(z) obtained using zplane are shown below:
< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. >
From the above pole-zero plots we observe that ::H1（Z）是稳定的 2H2（Z）是不稳
定的
Q4.24 Using Program P4_4 we tested the stability of H1(z) and arrive at the following stability test parameters {k i}:-0.9989, 0.8500
From these parameters we conclude that H1(z) is ________稳定的_____ .
Using Program P4_4 we tested the stability of H2(z) and arrive at the following stability test parameters {k i}:-1.0005, 0.8500
From these parameters we conclude that H2(z) is _______不稳定的______ .
Q4.25 Using Program P4_4 we tested the root locations of D(z) and arrive at the following
stability test parameters {k i}:0.9630
0.8726
0.6225
0.2346
0.0313
From these parameters we conclude that all roots of D(z) are ___内_____ the unit circle.
Q4.26Using Program P4_4 we tested the root locations of D(z) and arrive at the following
stability test parameters {k i}:-0.6087
0.7958
0.6742
0.5938
0.6000
From these parameters we conclude that all roots of D(z) are ____内____ the unit circle. Date:2015-12-10 Signature: