FIR BPF - Window Based

Senthilkumar March 22, 2011 Coded in Scilab
//PROGRAM TO DESIGN AND OBTAIN THE FREQUENCY RESPONSE OF FIR FILTER
//Band PASS FILTER - Window Based
clear all;
clc;
close;
M = 7            //Filter length = 7
Wc = [%pi/5,3*%pi/4];        //Digital Cutoff frequency
Wc2 = Wc(2)
Wc1 = Wc(1)
Tuo = (M-1)/2     //Center Value
hd = zeros(1,M);
W = zeros(1,M);
for n = 1:M
  if (n == Tuo+1)
     hd(n) = (Wc2-Wc1)/%pi;
  else
        n
     hd(n) = (sin(Wc2*((n-1)-Tuo)) -sin(Wc1*((n-1)-Tuo)))/(((n-1)-Tuo)*%pi);
  end
  if(abs(hd(n))<(0.00001))
    hd(n)=0;
  end
end
hd;
//Rectangular Window
for n = 1:M
  W(n) = 1;
end
//Windowing Fitler Coefficients
h = hd.*W;
disp(h,'Filter Coefficients are')
[hzm,fr]=frmag(h,256);
hzm_dB = 20*log10(hzm)./max(hzm);
plot(2*fr,hzm_dB)
xlabel('Normalized Digital Frequency W');
ylabel('Magnitude in dB');
title('Frequency Response 0f FIR BPF using Rectangular window M=7')
xgrid(1)

FIR - HPF - Window based in scilab

Senthilkumar March 22, 2011 Coded in Scilab
//PROGRAM TO DESIGN AND OBTAIN THE FREQUENCY RESPONSE OF FIR FILTER
//HIGH PASS FILTER -WINDOW BASED
clear all;
clc;
close;
M = 7             //Filter length = 7
Wc = %pi/4;        //Digital Cutoff frequency
Tuo = (M-1)/2     //Center Value
for n = 1:M
    if (n == Tuo+1)
      hd(n) = 1-Wc/%pi;
    else
      hd(n) = (sin(%pi*((n-1)-Tuo)) -sin(Wc*((n-1)-Tuo)))/(((n-1)-Tuo)*%pi);
  end
end
//Rectangular Window
for n = 1:M
  W(n) = 1;
end
//Windowing Fitler Coefficients
h = hd.*W;
disp('Filter Coefficients are')
h;
[hzm,fr]=frmag(h,256);
hzm_dB = 20*log10(hzm)./max(hzm);
plot(fr,hzm_dB)
xlabel('Normalized Digital Frequency W');
ylabel('Magnitude in dB');
title('Frequency Response 0f FIR HPF using Rectangular window M=7')

FIR - LPF -Window based in scilab

Senthilkumar March 22, 20114 comments Coded in Scilab
//Program to design a FIR Low Pass Filter- Window Based
//Technique
clear all;
clc;
close;
M = 7             //Filter length = 7
Wc = %pi/4;        //Digital Cutoff frequency
Tuo = (M-1)/2     //Center Value
for n = 1:M
    if (n == Tuo+1)
      hd(n) = Wc/%pi;
    else
      hd(n) =  sin(Wc*((n-1)-Tuo))/(((n-1)-Tuo)*%pi);
  end
end
//Rectangular Window
for n = 1:M
  W(n) = 1;
end
//Windowing Fitler Coefficients
h = hd.*W;
disp('Filter Coefficients are')
h;
[hzm,fr]=frmag(h,256);
hzm_dB = 20*log10(hzm)./max(hzm);
plot(fr,hzm_dB)
xlabel('Normalized Digital Frequency W');
ylabel('Magnitude in dB');
title('Frequency Response 0f FIR LPF using Rectangular window M=7')

FIR Band Pass Filter - Remez Algorithm -Previous one for LPF

Senthilkumar March 22, 2011 Coded in Scilab
//Band Pass FIlter of length M = 16
//Lower Cutoff frequency fp = 0.2 and Upper Cutoff frequency fs = 0.3
// Choose the number of cosine functions and create a dense grid 
// in [0,0.1) and [0.2,0.35] and [0.425,0.5]
//magnitude for pass band = 1 & stop band = 0 (i.e) [0 1 0]
//Weighting function =[10 1 10]
clear all;
clc;
close;
hn = 0;
hm = 0;
hn=eqfir(16,[0 .1;.2 .35;.425 .5],[0 1 0],[10 1 10]);
[hm,fr]=frmag(hn,256);
disp(hn,'The Filter Coefficients are:')
figure
plot(.5*(0:255)/256,20*log10(frmag(hn,256)));
a = gca();
xlabel('Normalized Digital Frequency fr');
ylabel('Magnitude in dB');
title('Frequency Response of FIR BPF using REMEZ algorithm M=16')
xgrid(2)

FIR Band Pass Filter - Remez Algorithm Based

Senthilkumar March 22, 2011 Coded in Scilab
//Low Pass FIlter of length M = 11
//Pass band Edge frequency fp = 0.1 and a Stop edge frequency fs = 0.15
// Choose the number of cosine functions and create a dense grid 
// in [0,0.2) and [0.25,0.5)
//magnitude for pass band = 1 & stop band = 0 (i.e) [1 0]
//Weighting function =[1 1]
clear all;
clc;
close;
M =11;
hn=eqfir(11,[0,0.2;0.25,0.5],[1 0],[1 1]);
[hm,fr]=frmag(hn,256);
disp(hn,'The Filter Coefficients are:')
figure
plot(.5*(0:255)/256,20*log10(frmag(hn,256)));
xlabel('Normalized Digital Frequency fr');
ylabel('Magnitude in dB');
title('Frequency Response of FIR LPF using REMEZ algorithm M=11')
xgrid(2)

Analog IIR to Digital IIR -Bilinear Transformation

Senthilkumar March 21, 20111 comment Coded in Scilab
//Program To convert analog IIR filter into digital IIR filter using
//Bilinear Transformation
clear all;
clc;
close;
s = poly(0,'s');
H = (s+0.1)/((s+0.1)^2+16);
T = 0.5;
z = poly(0,'z');
Hz = horner(H,(2/T)*((z-1)/(z+1)))

Analog IIR filter to Digital IIR Filter - Backward Difference

Senthilkumar March 21, 20113 comments Coded in Scilab
//Program To convert analog filter into digital filter using
//mapping = (z-(z^-1))/T - Backward Difference  
clear all;
clc;
close;
s = poly(0,'s');
H = 1/((s+0.1)^2+9)
T =1;//Sampling period T = 1 Second
z = poly(0,'z');
Hz = horner(H,(1/T)*(z-(z^-1)))

Frequency response of window functions for FIR Filter

Senthilkumar March 21, 20112 comments Coded in Scilab
//Program to find and plot the frequency response of
//(1) Hanning window (2)Hamming window for M = 11 
clear all;
close;
clc
M = 11;
for n = 1:M
  h_hann_11(n) = 0.5-0.5*cos(2*%pi*(n-1)/(M-1));
  h_hamm_11(n) = 0.54-0.46*cos(2*%pi*(n-1)/(M-1));
end
subplot(2,1,1)
[h_hann_11_M,fr]=frmag(h_hann_11,512);
h_hann_11_M = 20*log10(h_hann_11_M./max(h_hann_11_M));
plot2d(fr,h_hann_11_M,2);
title('Frequency Response 0f Hanning window Filter length M =11')
subplot(2,1,2)
[h_hamm_11_M,fr]=frmag(h_hamm_11,512);
h_hamm_11_M = 20*log10(h_hamm_11_M./max(h_hamm_11_M));
plot2d(fr,h_hamm_11_M,2);
title('Frequency Response of Hamming window Filter length M =11')

Window Functions for FIR Filter design

Senthilkumar March 21, 2011 Coded in Scilab
//Program to generate different window functions
//For FIR Filter design based on windowing techniques
clear all;
close;
clc
M =11 ;
for n = 1:M
  h_Rect(n) = 1;
  h_hann(n) = 0.5-0.5*cos(2*%pi*(n-1)/(M-1));
  h_hamm(n) = 0.54-0.46*cos(2*%pi*(n-1)/(M-1));
  h_balckmann(n) = 0.42-0.5*cos(2*%pi*n/(M-1))+0.08*cos(4*%pi*n/(M-1));
end
plot2d(1:M,[h_Rect,h_hann,h_hamm,h_balckmann],[2,5,7,9]); 
legend(['Rectangular Window';'Hanning';'Hamming';'Balckmann']);
title('Window Functions for Length M = 11')

Interpolation or upsampling in scilab

Senthilkumar March 21, 2011 Coded in Scilab
//Multirate Signal Processing in scilab
//Upsampling a sinusoidal signal by a factor of 2
clear;
clc;
n = 0:%pi/200:2*%pi;
x = sin(%pi*n);   //original signal
upsampling_x = zeros(1,2*length(x)); //upsampled by a factor of 2
upsampling_x(1:2:2*length(x)) = x;
subplot(2,1,1)
plot(1:length(x),x);
xtitle('original singal')
subplot(2,1,2)
plot(1:length(upsampling_x),upsampling_x);
xtitle('Upsampled Signal by a factor of 2');