Matlab: MUST SHOW ANSwER TYPED (copy & paste code or screenshot). DO NOT SUBMIT handwritten code, cannot read it.
Recursive Digital Filters:
Homework Answers
MATLAB CODE
%% Low Pass Chebyshev Type I filter
clc
N=input('Enter Order of Low Pass Filer : ');
Rp=input('Enter Passband Gain of Low Pass Filer in dB : ');
Wp=input('Enter Passband Edge of Low Pass Filer '); % Cut off
frequency
[b,a] = cheby1(N,Rp,Wp,'low')
freqz(b,a); % Frequency Response
[z,p,k] =cheby1(N,Rp,Wp,'low') % To know zeros (z)
position ,poles position (p) and gain k
TF=tf(b,a,1000) % Transfer function for Sampling frequency 1000
Hz
Result:
Enter Order of Low Pass Filer : 20
Enter Passband Gain of Low Pass Filer in dB : 15
Enter Passband Edge of Low Pass Filer 0.4
b =
1.0e-04 *
Columns 1 through 12
0.0000 0.0000 0.0001 0.0007 0.0028 0.0090 0.0224 0.0448 0.0729
0.0972 0.1069 0.0972
Columns 13 through 21
0.0729 0.0448 0.0224 0.0090 0.0028 0.0007 0.0001 0.0000
0.0000
a =
1.0e+04 *
Columns 1 through 12
0.0001 -0.0012 0.0076 -0.0318 0.0994 -0.2461 0.4996 -0.8501 1.2297
-1.5256 1.6314 -1.5060
Columns 13 through 21
1.1981 -0.8174 0.4740 -0.2303 0.0918 -0.0290 0.0068 -0.0011
0.0001
z =
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
p =
0.9807 + 0.1122i
0.9807 - 0.1122i
0.9325 + 0.3257i
0.9325 - 0.3257i
0.8469 + 0.5105i
0.8469 - 0.5105i
0.7408 + 0.6572i
0.7408 - 0.6572i
0.6306 + 0.7656i
0.6306 - 0.7656i
0.5288 + 0.8411i
0.5288 - 0.8411i
0.3116 + 0.9495i
0.3116 - 0.9495i
0.3334 + 0.9406i
0.3334 - 0.9406i
0.3774 + 0.9223i
0.3774 - 0.9223i
0.4431 + 0.8910i
0.4431 - 0.8910i
k =
5.7847e-11
TF =
5.785e-11 z^20 + 1.157e-09 z^19 + 1.099e-08 z^18 + 6.595e-08 z^17 +
2.803e-07 z^16 + 8.969e-07 z^15
+ 2.242e-06 z^14 + 4.484e-06 z^13 + 7.287e-06 z^12 + 9.716e-06 z^11
+ 1.069e-05 z^10 + 9.716e-06 z^9
+ 7.287e-06 z^8 + 4.484e-06 z^7 + 2.242e-06 z^6 + 8.969e-07 z^5 +
2.803e-07 z^4 + 6.595e
-08 z^3 + 1.099e-08 z^2 + 1.157e-09 z + 5.785e-11
-------------------------------------------------------------------------------------------------------------
z^20 - 12.25 z^19 + 76.27 z^18 - 318.3 z^17 + 994.3 z^16 - 2461
z^15 + 4996 z^14 - 8501 z^13 + 1.23e04 z^12
- 1.526e04 z^11 + 1.631e04 z^10 - 1.506e04 z^9 + 1.198e04 z^8 -
8174 z^7 + 4740 z^6 - 2303 z^5
+ 917.6 z^4 - 289.5 z^3 + 68.32 z^2 - 10.8 z + 0.866
Sample time: 1000 seconds
Discrete-time transfer function.
>>
plot:
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