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EE 448 Homework #6 1. Determine the impulse response, h(n), and plot the magnitude frequency response of each of the followin

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Answer #1

Below is matlab Code

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

close all,
clear all,
clc,

Wn = pi/5;
M=25;

ProjectPath = pwd;
FilePath = strcat(ProjectPath,'\Tables.txt');
fpt = fopen(FilePath,'wt');


figure,
win1 = rectwin(M+1)';
b = fir1(M,Wn,'low',win1,'noscale');
subplot(2,1,1); freqz(b,1,512); title('Low Pass FIR Filter - Mag. Response using Rectangular Window, Fc1 = pi/5');
subplot(2,1,2); impz(b); title('Impulse Response using Rectangular Window, Fc1 = pi/5');

fprintf(fpt,'Low Pass FIR Filter - Mag. Response using Rectangular Window, Fc1 = pi/5\n');
fprintf(fpt,' n b(n) w(n)\n');
for r=1:length(win1)
fprintf(fpt,'%5d%10.4f%10.4f\n',(r-1),win1(r),b(r));
end

figure,
win1 = bartlett(M+1)';
b = fir1(M,Wn,'low',win1,'noscale');
subplot(2,1,1); freqz(b,1,512); title('Low Pass FIR Filter - Mag. Response using bartlett Window, Fc1 = pi/5');
subplot(2,1,2); impz(b); title('Impulse Response using bartlett Window, Fc1 = pi/5');
fprintf(fpt,'\n\n\nLow Pass FIR Filter - Mag. Response using bartlett Window, Fc1 = pi/5\n');
fprintf(fpt,' n b(n) w(n)\n');
for r=1:length(win1)
fprintf(fpt,'%5d%10.4f%10.4f\n',(r-1),win1(r),b(r));
end


figure,
win1 = hamming(M+1)';
b = fir1(M,Wn,'low',win1,'noscale');
subplot(2,1,1); freqz(b,1,512); title('Low Pass FIR Filter - Mag. Response using Hamming Window, Fc1 = pi/5');
subplot(2,1,2); impz(b); title('Impulse Response using Hamming Window, Fc1 = pi/5');
fprintf(fpt,'\n\n\nLow Pass FIR Filter - Mag. Response using Hamming Window, Fc1 = pi/5\n');
fprintf(fpt,' n b(n) w(n)\n');
for r=1:length(win1)
fprintf(fpt,'%5d%10.4f%10.4f\n',(r-1),win1(r),b(r));
end


figure,
win1 = hamming(M+1)';
b = fir1(M,[pi/10 pi/5],'bandpass',win1,'noscale');
subplot(2,1,1); freqz(b,1,512); title('Band Pass FIR Filter - Mag. Response using bartlett Window, Fc1 = [pi/5 3.pi/5]');
subplot(2,1,2); impz(b); title('Impulse Response using bartlett Window, Fc1 = pi/5');
fprintf(fpt,'\n\n\nBand Pass FIR Filter - Mag. Response using bartlett Window, Fc1 = [pi/5 3.pi/5\n');
fprintf(fpt,' n b(n) w(n)\n');
for r=1:length(win1)
fprintf(fpt,'%5d%10.4f%10.4f\n',(r-1),win1(r),b(r));
end
fclose(fpt);

winopen(FilePath);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Mag Response using Rectangular Window, Fc1 pi5 20 20 40 -60 100 09 08 0.7 05 0.4 120 0.3 0.2 0.1 Normalized Frequency (xn radpi/5 Mag. Response using bartlett Window, Fc1 10 20 30 40 50 09 08 07 05 70 0.4 0.3 0.2 0.1 Normalized Frequency (xn rad/sampMag Response using Hamming Window, Fc1 pi/5 20 0 20 40 60 80 09 08 n 7 05 -100 0.4 0.3 0.2 0.1 Normalized Frequency (xn rad/sBand Pass FIR Filter Mag. Response using bartlett Window, Fc1 Ipi/5 3.pi/5] 50 100 0.9 08 0.7 0.5 150 04 03 0.2 0.1 Normalize

Below is Text File

Low Pass FIR Filter - Mag. Response using Rectangular Window, Fc1 = pi/5
n b(n) w(n)
0 1.0000 -0.0113
1 1.0000 -0.0180
2 1.0000 0.0289
3 1.0000 -0.0033
4 1.0000 -0.0329
5 1.0000 0.0333
6 1.0000 0.0128
7 1.0000 -0.0573
8 1.0000 0.0365
9 1.0000 0.0533
10 1.0000 -0.1242
11 1.0000 0.0381
12 1.0000 0.5312
13 1.0000 0.5312
14 1.0000 0.0381
15 1.0000 -0.1242
16 1.0000 0.0533
17 1.0000 0.0365
18 1.0000 -0.0573
19 1.0000 0.0128
20 1.0000 0.0333
21 1.0000 -0.0329
22 1.0000 -0.0033
23 1.0000 0.0289
24 1.0000 -0.0180
25 1.0000 -0.0113

Low Pass FIR Filter - Mag. Response using bartlett Window, Fc1 = pi/5
n b(n) w(n)
0 0.0000 -0.0000
1 0.0800 -0.0014
2 0.1600 0.0046
3 0.2400 -0.0008
4 0.3200 -0.0105
5 0.4000 0.0133
6 0.4800 0.0061
7 0.5600 -0.0321
8 0.6400 0.0234
9 0.7200 0.0383
10 0.8000 -0.0994
11 0.8800 0.0336
12 0.9600 0.5099
13 0.9600 0.5099
14 0.8800 0.0336
15 0.8000 -0.0994
16 0.7200 0.0383
17 0.6400 0.0234
18 0.5600 -0.0321
19 0.4800 0.0061
20 0.4000 0.0133
21 0.3200 -0.0105
22 0.2400 -0.0008
23 0.1600 0.0046
24 0.0800 -0.0014
25 0.0000 -0.0000

Low Pass FIR Filter - Mag. Response using Hamming Window, Fc1 = pi/5
n b(n) w(n)
0 0.0800 -0.0009
1 0.0945 -0.0017
2 0.1369 0.0040
3 0.2047 -0.0007
4 0.2935 -0.0096
5 0.3979 0.0133
6 0.5111 0.0065
7 0.6262 -0.0359
8 0.7359 0.0269
9 0.8332 0.0444
10 0.9121 -0.1133
11 0.9677 0.0369
12 0.9964 0.5292
13 0.9964 0.5292
14 0.9677 0.0369
15 0.9121 -0.1133
16 0.8332 0.0444
17 0.7359 0.0269
18 0.6262 -0.0359
19 0.5111 0.0065
20 0.3979 0.0133
21 0.2935 -0.0096
22 0.2047 -0.0007
23 0.1369 0.0040
24 0.0945 -0.0017
25 0.0800 -0.0009

Band Pass FIR Filter - Mag. Response using bartlett Window, Fc1 = [pi/5 3.pi/5
n b(n) w(n)
0 0.0800 -0.0004
1 0.0945 0.0007
2 0.1369 0.0073
3 0.2047 -0.0010
4 0.2935 -0.0191
5 0.3979 -0.0019
6 0.5111 0.0032
7 0.6262 -0.0085
8 0.7359 0.0770
9 0.8332 0.0677
10 0.9121 -0.1858
11 0.9677 -0.1676
12 0.9964 0.2288
13 0.9964 0.2288
14 0.9677 -0.1676
15 0.9121 -0.1858
16 0.8332 0.0677
17 0.7359 0.0770
18 0.6262 -0.0085
19 0.5111 0.0032
20 0.3979 -0.0019
21 0.2935 -0.0191
22 0.2047 -0.0010
23 0.1369 0.0073
24 0.0945 0.0007
25 0.0800 -0.0004

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