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Constellation for Binary FSK
function[y]= Constellation_BFSK()
M =2;
y = [1,0;0,1];
annot = dec2bin([M-1:-1:0],log2(M));
disp(y,'coordinates of message points')
disp(annot,'Message points')
figure;
a =gca();
a.data_bounds = [-2,-2;2,2];
a.x_location = "origin";
a.y_location = "origin";
plot2d(y(1,1),y(1,2),-9)
plot2d(y(2,1),y(2,2),-5)
xlabel(' In-Phase');
ylabel(' Quadrature');
title('Constellation for BFSK')
legend(['message point 1 (binary 1)';'message point 2 (binary 0)'],5)
endfunction
//Result
//coordinates of message points
//
// 1. 0.
// 0. 1.
//
// Message points
//
//!1 0 !PSD estimation window based-scilab code
//Caption:Determination of spectrum of a signal
//With maximum normalized frequency f = 0.1
//using Rectangular window and Blackmann window
clear all;
close;
clc;
N = 61;
cfreq = [0.1 0];
[wft,wfm,fr]=wfir('lp',N,cfreq,'re',0);
disp(wft,'Time domain filter coefficients hd(n)=');
disp(wfm,'Frequency domain filter values Hd(w)=');
WFM_dB = 20*log10(wfm);//Frequency response in dB
for n = 1:N
h_balckmann(n)=0.42-0.5*cos(2*%pi*n/(N-1))+0.08*cos(4*%pi*n/(N-1));
end
wft_blmn = wft'.*h_balckmann;
disp(wft_blmn,'Blackmann window based Filter output h(n)=')
wfm_blmn = frmag(wft_blmn,length(fr));
WFM_blmn_dB =20*log10(wfm_blmn);
subplot(2,1,1)
plot2d(fr,WFM_dB)
xgrid(1)
xtitle('Power Spectrum with Rectangular window Filtered M = 61','Frequency in cycles per samples f','Energy density in dB')
subplot(2,1,2)
plot2d(fr,WFM_blmn_dB)
xgrid(1)
xtitle('Power Spectrum with Blackmann window Filtered M = 61','Frequency in cycles per samples f','Energy density in dB')PSD estimation using N-point DFT -scilab code
//Caption: Evaluating power spectrum of a discrete sequence
//Using N-point DFT
clear all;
clc;
close;
N =16; //Number of samples in given sequence
n =0:N-1;
delta_f = [0.06,0.01];//frequency separation
x1 = sin(2*%pi*0.315*n)+cos(2*%pi*(0.315+delta_f(1))*n);
x2 = sin(2*%pi*0.315*n)+cos(2*%pi*(0.315+delta_f(2))*n);
L = [8,16,32,128];
k1 = 0:L(1)-1;
k2 = 0:L(2)-1;
k3 = 0:L(3)-1;
k4 = 0:L(4)-1;
fk1 = k1./L(1);
fk2 = k2./L(2);
fk3 = k3./L(3);
fk4 = k4./L(4);
for i =1:length(fk1)
Pxx1_fk1(i) = 0;
Pxx2_fk1(i) = 0;
for m = 1:N
Pxx1_fk1(i)=Pxx1_fk1(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk1(i));
Pxx2_fk1(i)=Pxx1_fk1(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk1(i));
end
Pxx1_fk1(i) = (Pxx1_fk1(i)^2)/N;
Pxx2_fk1(i) = (Pxx2_fk1(i)^2)/N;
end
for i =1:length(fk2)
Pxx1_fk2(i) = 0;
Pxx2_fk2(i) = 0;
for m = 1:N
Pxx1_fk2(i)=Pxx1_fk2(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk2(i));
Pxx2_fk2(i)=Pxx1_fk2(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk2(i));
end
Pxx1_fk2(i) = (Pxx1_fk2(i)^2)/N;
Pxx2_fk2(i) = (Pxx1_fk2(i)^2)/N;
end
for i =1:length(fk3)
Pxx1_fk3(i) = 0;
Pxx2_fk3(i) = 0;
for m = 1:N
Pxx1_fk3(i) =Pxx1_fk3(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk3(i));
Pxx2_fk3(i) =Pxx1_fk3(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk3(i));
end
Pxx1_fk3(i) = (Pxx1_fk3(i)^2)/N;
Pxx2_fk3(i) = (Pxx1_fk3(i)^2)/N;
end
for i =1:length(fk4)
Pxx1_fk4(i) = 0;
Pxx2_fk4(i) = 0;
for m = 1:N
Pxx1_fk4(i) =Pxx1_fk4(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk4(i));
Pxx2_fk4(i) =Pxx1_fk4(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk4(i));
end
Pxx1_fk4(i) = (Pxx1_fk4(i)^2)/N;
Pxx2_fk4(i) = (Pxx1_fk4(i)^2)/N;
end
figure(1)
subplot(2,2,1)
plot2d3('gnn',k1,abs(Pxx1_fk1))
xtitle('8 point DFT')
subplot(2,2,2)
plot2d3('gnn',k2,abs(Pxx1_fk2))
xtitle('16 point DFT')
subplot(2,2,3)
plot2d3('gnn',k3,abs(Pxx1_fk3))
xtitle('32 point DFT')
subplot(2,2,4)
plot2d3('gnn',k4,abs(Pxx1_fk4))
xtitle('128 point DFT')
figure(2)
subplot(2,2,1)
plot2d3('gnn',k1,abs(Pxx2_fk1))
xtitle('8 point DFT')
subplot(2,2,2)
plot2d3('gnn',k2,abs(Pxx2_fk2))
xtitle('16 point DFT')
subplot(2,2,3)
plot2d3('gnn',k3,abs(Pxx2_fk3))
xtitle('32 point DFT')
subplot(2,2,4)
plot2d3('gnn',k4,abs(Pxx2_fk4))
xtitle('128 point DFT')Direct Sequence Spread Spectrum (DS-BPSK)
function[st,mt]= DS_Spread_Spectrum(bt,ct_polar)
//Caption:Direct Sequence Spread Coherent BPSK
//Generation of waveforms in DS/BPSK spread spectrum transmitter
//bt: Input Data Sequence (bipolar format)
//ct_polar: Spreading code (bipolar format)
Ft = 0:0.01:1;
//bt = [1*ones(1,N) -1*ones(1,N)];
t = 0:length(bt)-1;
//ct_polar = [-1,-1,1,1,1,-1,1,-1,-1,1,1,1,-1,1];
mt = bt.*ct_polar;
Carrier = 2*sin(Ft*2*%pi);
st = [];
for i = 1:length(mt)
st = [st mt(i)*Carrier];
end
//
figure
subplot(3,1,1)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot2d2(t,bt,5)
xlabel(' t')
title('Data b(t)')
subplot(3,1,2)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot2d2(t,ct_polar,5)
xlabel(' t')
title('Spreading code c(t)')
subplot(3,1,3)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot2d2(t,mt,5)
xlabel(' t')
title('Product Signal m(t)')
//
figure
subplot(3,1,1)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot2d2(t,mt,5)
xlabel(' t')
title('Product Signal m(t)')
subplot(3,1,2)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot(Carrier)
xlabel(' t')
title('Carrier Signal')
subplot(3,1,3)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot(st)
xlabel(' t')
title('DS/BPSK signal s(t)')
endfunction
//Result
//->bt = [1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1]
// bt =
//
// 1. 1. 1. 1. 1. 1. 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1.
//
//-->ct_polar = [-1,-1,1,1,1,-1,1,-1,-1,1,1,1,-1,1]
// ct_polar =
//
// - 1. - 1. 1. 1. 1. - 1. 1. - 1. - 1. 1. 1. 1. - 1. 1.
//
//-->exec('C:\Users\SENTHILKUMAR\Desktop\Communication_Toolbox\Digital_Communication\DS_Spread_Spectrum.sci', -1)
//
//-->[st,mt]= DS_Spread_Spectrum(bt,ct_polar)
// mt =
//
// - 1. - 1. 1. 1. 1. - 1. 1. 1. 1. - 1. - 1. - 1. 1. - 1.auto correlation in scilab
//Autocorrelation of a given Input Sequence
//Finding out the period of the signal using autocorrelation technique
clear;
clc;
close;
x = input('Enter the given discrete time sequence');
L = length(x);
h = zeros(1,L);
for i = 1:L
h(L-i+1) = x(i);
end
N = 2*L-1;
Rxx = zeros(1,N);
for i = L+1:N
h(i) = 0;
end
for i = L+1:N
x(i) = 0;
end
for n = 1:N
for k = 1:N
if(n >= k)
Rxx(n) = Rxx(n)+x(n-k+1)*h(k);
end
end
end
disp('Auto Correlation Result is')
Rxx
disp('Center Value is the Maximum of autocorrelation result')
[m,n] = max(Rxx)
disp('Period of the given signal using Auto Correlation Sequence')
nConstellation diagram for Binary PSK
function[y]= Constellation_BPSK()
M =2;
i = 1:M;
y = cos(2*%pi+(i-1)*%pi);
annot = dec2bin([length(y)-1:-1:0],log2(M));
disp(y,'coordinates of message points')
disp(annot,'Message points')
figure;
a =gca();
a.data_bounds = [-2,-2;2,2];
a.x_location = "origin";
a.y_location = "origin";
plot2d(real(y(1)),imag(y(1)),-9)
plot2d(real(y(2)),imag(y(2)),-5)
xlabel(' In-Phase');
ylabel(' Quadrature');
title('Constellation for BPSK')
legend(['message point 1 (binary 1)';'message point 2 (binary 0)'],5)
endfunction
//Result
//coordinates of message points
//
// 1. - 1.
//
// Message points
//
//!1 0 !scilab program to speech signal information
//Caption: Reading a Speech Signal &
//[1]. Displaying its sampling rate
//[2]. Number of bits used per speech sample
//[3]. Total Time duration of the speech signal in seconds
clear;
clc;
[y,Fs,bits]=wavread("E:\4.wav");
a = gca();
plot2d(y);
a.x_location = 'origin';
title('Speech signal with Sampling Rate = 8 KHz, No. of Samples = 8360')
disp(Fs,'Sampling Rate in Hz Fs = ');
disp(bits,'Number of bits used per speech sample b =');
N = length(y);
T = N/Fs;
disp(N,'Total Number of Samples N =')
disp(T,'Duration of speech signal in seconds T=')
//Result
//Sampling Rate in Hz Fs =
// 8000.
//Number of bits used per speech sample b =
// 16.
//Total Number of Samples N =
// 8360.
//Duration of speech signal in seconds T=
// 1.045Subband coding speech signal-scilab code
//Caption: write a program for subband coding of speech signal
clear;
clc;
[x,Fs,bits]=wavread("E:\4.wav");
n = length(x)
//Low Pass Filter of Length = 19, Wc = 0.5, Hamming Window
[wft_LPF,wfm_LPF,fr_LPF]=wfir('lp',18,[0.25,0],'hm',[0,0])
//High Pass Filter of Length = 19, Wc = 0.5, Hamming Window
[wft_HPF,wfm_HPF,fr_HPF]=wfir('hp',18,[0.25,0],'hm',[0,0])
//LPF output
Y_lpf = convol(x,wft_LPF)
//HPF output
Y_hpf = convol(x,wft_HPF)
//Downsampling by a factor of 2
Downsampling_XLPF = Y_lpf(1:2:length(Y_lpf));
Downsampling_XHPF = Y_hpf(1:2:length(Y_hpf));
figure(1)
subplot(3,1,1)
plot([1:n],x)
xtitle("ORIGINAL Speech SIGNAL");
subplot(3,1,2)
plot([1:length(Y_lpf)],Y_lpf)
xtitle("Low Pass Filtered Speech SIGNAL");
subplot(3,1,3)
plot([1:length(Y_hpf)],Y_hpf)
xtitle("High Pass Filtered Speech SIGNAL");
figure(2)
subplot(2,1,1)
plot([1:length(Y_lpf)],Y_lpf)
xtitle("Low Pass Filtered Speech SIGNAL");
subplot(2,1,2)
plot([1:length(Downsampling_XLPF)],Downsampling_XLPF,'r')
xtitle("LPF Output Downsampled by 2");
figure(3)
subplot(2,1,1)
plot([1:length(Y_hpf)],Y_hpf)
xtitle("High Pass Filtered Speech SIGNAL");
subplot(2,1,2)
plot([1:length(Downsampling_XHPF)],Downsampling_XHPF,'r')
xtitle("HPF Output Downsampled by 2");Repetition code
function [G,H,x]=RepetitionCode(n,k,m)
//Repetition Codes
//n =block of identical 'n' bits
//k =1 one bit
//m = 1;// bit value = 1
I = eye(n-k,n-k);//Identity matrix
P = ones(1,n-k);//coefficient matrix
H = [I P'];//parity-check matrix
G = [P 1];//generator matrix
x = m.*G; //code word
disp(G,'generator matrix');
disp(H,'parity-check matrix');
disp(x,'code word for binary one input');
endfunction
//Result
//-->exec('C:\Users\SENTHILKUMAR\Desktop\Communication_Toolbox\Digital_Communication\RepetitionCode.sci', -1)
//
//-->n = 5
// n =
//
// 5.
//
//-->k =1
// k =
//
// 1.
//
//-->m =1
// m =
//
// 1.
//
//-->[G,H,x]=RepetitionCode(n,k,m)
//
// generator matrix
//
// 1. 1. 1. 1. 1.
//
// parity-check matrix
//
// 1. 0. 0. 0. 1.
// 0. 1. 0. 0. 1.
// 0. 0. 1. 0. 1.
// 0. 0. 0. 1. 1.
//
// code word for binary one input
//
// 1. 1. 1. 1. 1.
// x =
//
// 1. 1. 1. 1. 1.
// H =
//
// 1. 0. 0. 0. 1.
// 0. 1. 0. 0. 1.
// 0. 0. 1. 0. 1.
// 0. 0. 0. 1. 1.
// G =
//
// 1. 1. 1. 1. 1.Continuous Time Fourier Series of sine signal
//Continuous Time Fourier Series Spectral Coefficients of
//a periodic sine signal x(t) = sin(Wot)
clear;
close;
clc;
t = 0:0.01:1;
T = 1;
Wo = 2*%pi/T;
xt = sin(Wo*t);
for k =0:5
C(k+1,:) = exp(-sqrt(-1)*Wo*t.*k);
a(k+1) = xt*C(k+1,:)'/length(t); //fourier series is done
if(abs(a(k+1))<=0.01)
a(k+1)=0;
end
end
a =a';
ak = [-a($:-1:1),a(2:$)];
disp(ak,'Continuous Time Fourier Series Coefficients are:')
//Result
//Continuous Time Fourier Series Coefficients are:
// column 1 to 11
// 0 0 0 0 -1.010D-18+0.4950495i 0 1.010D-18-0.4950495i 0 0 0 0Direct Sequence Spread Spectrum (DS-BPSK)
function[st,mt]= DS_Spread_Spectrum(bt,ct_polar)
//Caption:Direct Sequence Spread Coherent BPSK
//Generation of waveforms in DS/BPSK spread spectrum transmitter
//bt: Input Data Sequence (bipolar format)
//ct_polar: Spreading code (bipolar format)
Ft = 0:0.01:1;
//bt = [1*ones(1,N) -1*ones(1,N)];
t = 0:length(bt)-1;
//ct_polar = [-1,-1,1,1,1,-1,1,-1,-1,1,1,1,-1,1];
mt = bt.*ct_polar;
Carrier = 2*sin(Ft*2*%pi);
st = [];
for i = 1:length(mt)
st = [st mt(i)*Carrier];
end
//
figure
subplot(3,1,1)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot2d2(t,bt,5)
xlabel(' t')
title('Data b(t)')
subplot(3,1,2)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot2d2(t,ct_polar,5)
xlabel(' t')
title('Spreading code c(t)')
subplot(3,1,3)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot2d2(t,mt,5)
xlabel(' t')
title('Product Signal m(t)')
//
figure
subplot(3,1,1)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot2d2(t,mt,5)
xlabel(' t')
title('Product Signal m(t)')
subplot(3,1,2)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot(Carrier)
xlabel(' t')
title('Carrier Signal')
subplot(3,1,3)
a =gca();
a.x_location = "origin";
a.y_location = "origin";
a.data_bounds = [0,-2;20,2];
plot(st)
xlabel(' t')
title('DS/BPSK signal s(t)')
endfunction
//Result
//->bt = [1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1]
// bt =
//
// 1. 1. 1. 1. 1. 1. 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1.
//
//-->ct_polar = [-1,-1,1,1,1,-1,1,-1,-1,1,1,1,-1,1]
// ct_polar =
//
// - 1. - 1. 1. 1. 1. - 1. 1. - 1. - 1. 1. 1. 1. - 1. 1.
//
//-->exec('C:\Users\SENTHILKUMAR\Desktop\Communication_Toolbox\Digital_Communication\DS_Spread_Spectrum.sci', -1)
//
//-->[st,mt]= DS_Spread_Spectrum(bt,ct_polar)
// mt =
//
// - 1. - 1. 1. 1. 1. - 1. 1. 1. 1. - 1. - 1. - 1. 1. - 1.Convolutional coding using transform domain approach
function [x1D,x2D]= ConvolutionCode_TransDomain()
//Convolutional code - Transform domain approach
//g1D = generator polynomial 1
//g2D = generator polynomial 2
//x1D = top output sequence polynomial
//x2D = bottom output sequence polynomial
D = poly(0,'D');
g1D = input('Enter the generator polynomial 1=') //generator polynomial 1
g2D = input('Enter the generator polynomial 2=') //generator polynomial 2
mD = input('Enter the message sequence')//message sequence polynomial representation
x1D = g1D*mD; //top output polynomial
x2D = g2D*mD; //bottom output polynomial
x1 = coeff(x1D);
x2 = coeff(x2D);
disp(modulo(x1,2),'top output sequence')
disp(modulo(x2,2),'bottom output sequence')
endfunction
//Result
//Enter the generator polynomial 1 = 1+D+D^2
//Enter the generator polynomial 2 = 1+D^2;
//Enter the message sequence = 1+0+0+D^3+D^4;
//top output sequence
//
// 1. 1. 1. 1. 0. 0. 1.
//bottom output sequence
//
// 1. 0. 1. 1. 1. 1. 1.
//x2D =
//
// 2 3 4 5 6
// 1 + D + D + D + D + D
//x1D =
//
// 2 3 4 5 6
// 1 + D + D + D + 2D + 2D + DConstellation Diagram for Binary QPSK
function[y] = Constellation_QPSK()
M =4;
i = 1:M;
y = cos((2*i-1)*%pi/4)-sin((2*i-1)*%pi/4)*%i;
annot = dec2bin([0:M-1],log2(M));
disp(y,'coordinates of message points')
disp(annot,'dibits value')
figure;
a =gca();
a.data_bounds = [-1,-1;1,1];
a.x_location = "origin";
a.y_location = "origin";
plot2d(real(y(1)),imag(y(1)),-2)
plot2d(real(y(2)),imag(y(2)),-4)
plot2d(real(y(3)),imag(y(3)),-5)
plot2d(real(y(4)),imag(y(4)),-9)
xlabel(' In-Phase');
ylabel(' Quadrature');
title('Constellation for QPSK')
legend(['message point 1 (dibit 10)';'message point 2 (dibit 00)';'message point 3 (dibit 01)';'message point 4 (dibit 11)'],5)
endfunction
//Result
//coordinates of message points
// 0.7071068 - 0.7071068i - 0.7071068 - 0.7071068i - 0.7071068 + 0.7071068i 0.7071068 + 0.7071068i
//
// dibits value
//
//!00 01 10 11 !Constellation diagram for Binary PSK
function[y]= Constellation_BPSK()
M =2;
i = 1:M;
y = cos(2*%pi+(i-1)*%pi);
annot = dec2bin([length(y)-1:-1:0],log2(M));
disp(y,'coordinates of message points')
disp(annot,'Message points')
figure;
a =gca();
a.data_bounds = [-2,-2;2,2];
a.x_location = "origin";
a.y_location = "origin";
plot2d(real(y(1)),imag(y(1)),-9)
plot2d(real(y(2)),imag(y(2)),-5)
xlabel(' In-Phase');
ylabel(' Quadrature');
title('Constellation for BPSK')
legend(['message point 1 (binary 1)';'message point 2 (binary 0)'],5)
endfunction
//Result
//coordinates of message points
//
// 1. - 1.
//
// Message points
//
//!1 0 !Constellation for Binary FSK
function[y]= Constellation_BFSK()
M =2;
y = [1,0;0,1];
annot = dec2bin([M-1:-1:0],log2(M));
disp(y,'coordinates of message points')
disp(annot,'Message points')
figure;
a =gca();
a.data_bounds = [-2,-2;2,2];
a.x_location = "origin";
a.y_location = "origin";
plot2d(y(1,1),y(1,2),-9)
plot2d(y(2,1),y(2,2),-5)
xlabel(' In-Phase');
ylabel(' Quadrature');
title('Constellation for BFSK')
legend(['message point 1 (binary 1)';'message point 2 (binary 0)'],5)
endfunction
//Result
//coordinates of message points
//
// 1. 0.
// 0. 1.
//
// Message points
//
//!1 0 !PSD estimation window based-scilab code
//Caption:Determination of spectrum of a signal
//With maximum normalized frequency f = 0.1
//using Rectangular window and Blackmann window
clear all;
close;
clc;
N = 61;
cfreq = [0.1 0];
[wft,wfm,fr]=wfir('lp',N,cfreq,'re',0);
disp(wft,'Time domain filter coefficients hd(n)=');
disp(wfm,'Frequency domain filter values Hd(w)=');
WFM_dB = 20*log10(wfm);//Frequency response in dB
for n = 1:N
h_balckmann(n)=0.42-0.5*cos(2*%pi*n/(N-1))+0.08*cos(4*%pi*n/(N-1));
end
wft_blmn = wft'.*h_balckmann;
disp(wft_blmn,'Blackmann window based Filter output h(n)=')
wfm_blmn = frmag(wft_blmn,length(fr));
WFM_blmn_dB =20*log10(wfm_blmn);
subplot(2,1,1)
plot2d(fr,WFM_dB)
xgrid(1)
xtitle('Power Spectrum with Rectangular window Filtered M = 61','Frequency in cycles per samples f','Energy density in dB')
subplot(2,1,2)
plot2d(fr,WFM_blmn_dB)
xgrid(1)
xtitle('Power Spectrum with Blackmann window Filtered M = 61','Frequency in cycles per samples f','Energy density in dB')PSD estimation using N-point DFT -scilab code
//Caption: Evaluating power spectrum of a discrete sequence
//Using N-point DFT
clear all;
clc;
close;
N =16; //Number of samples in given sequence
n =0:N-1;
delta_f = [0.06,0.01];//frequency separation
x1 = sin(2*%pi*0.315*n)+cos(2*%pi*(0.315+delta_f(1))*n);
x2 = sin(2*%pi*0.315*n)+cos(2*%pi*(0.315+delta_f(2))*n);
L = [8,16,32,128];
k1 = 0:L(1)-1;
k2 = 0:L(2)-1;
k3 = 0:L(3)-1;
k4 = 0:L(4)-1;
fk1 = k1./L(1);
fk2 = k2./L(2);
fk3 = k3./L(3);
fk4 = k4./L(4);
for i =1:length(fk1)
Pxx1_fk1(i) = 0;
Pxx2_fk1(i) = 0;
for m = 1:N
Pxx1_fk1(i)=Pxx1_fk1(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk1(i));
Pxx2_fk1(i)=Pxx1_fk1(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk1(i));
end
Pxx1_fk1(i) = (Pxx1_fk1(i)^2)/N;
Pxx2_fk1(i) = (Pxx2_fk1(i)^2)/N;
end
for i =1:length(fk2)
Pxx1_fk2(i) = 0;
Pxx2_fk2(i) = 0;
for m = 1:N
Pxx1_fk2(i)=Pxx1_fk2(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk2(i));
Pxx2_fk2(i)=Pxx1_fk2(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk2(i));
end
Pxx1_fk2(i) = (Pxx1_fk2(i)^2)/N;
Pxx2_fk2(i) = (Pxx1_fk2(i)^2)/N;
end
for i =1:length(fk3)
Pxx1_fk3(i) = 0;
Pxx2_fk3(i) = 0;
for m = 1:N
Pxx1_fk3(i) =Pxx1_fk3(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk3(i));
Pxx2_fk3(i) =Pxx1_fk3(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk3(i));
end
Pxx1_fk3(i) = (Pxx1_fk3(i)^2)/N;
Pxx2_fk3(i) = (Pxx1_fk3(i)^2)/N;
end
for i =1:length(fk4)
Pxx1_fk4(i) = 0;
Pxx2_fk4(i) = 0;
for m = 1:N
Pxx1_fk4(i) =Pxx1_fk4(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk4(i));
Pxx2_fk4(i) =Pxx1_fk4(i)+x1(m)*exp(-sqrt(-1)*2*%pi*(m-1)*fk4(i));
end
Pxx1_fk4(i) = (Pxx1_fk4(i)^2)/N;
Pxx2_fk4(i) = (Pxx1_fk4(i)^2)/N;
end
figure(1)
subplot(2,2,1)
plot2d3('gnn',k1,abs(Pxx1_fk1))
xtitle('8 point DFT')
subplot(2,2,2)
plot2d3('gnn',k2,abs(Pxx1_fk2))
xtitle('16 point DFT')
subplot(2,2,3)
plot2d3('gnn',k3,abs(Pxx1_fk3))
xtitle('32 point DFT')
subplot(2,2,4)
plot2d3('gnn',k4,abs(Pxx1_fk4))
xtitle('128 point DFT')
figure(2)
subplot(2,2,1)
plot2d3('gnn',k1,abs(Pxx2_fk1))
xtitle('8 point DFT')
subplot(2,2,2)
plot2d3('gnn',k2,abs(Pxx2_fk2))
xtitle('16 point DFT')
subplot(2,2,3)
plot2d3('gnn',k3,abs(Pxx2_fk3))
xtitle('32 point DFT')
subplot(2,2,4)
plot2d3('gnn',k4,abs(Pxx2_fk4))
xtitle('128 point DFT')Comparison of different power spectrum estimates
//Caption: Determination of Frequency Resolution of the
//[1]. Barlett [2]. Welch [3].Blackman Tukey Power Spectrum Estimation
//Methods
clear;
clc;
close;
Q = 10; //Quality factor
N = 1000; //Length of the sample sequence
//Bartlett Method
F_Bartlett = Q/(1.11*N);
disp(F_Bartlett,'Frequency Resolution of Bartlett Power Spectrum Estimation')
//Welch Method
F_Welch = Q/(1.39*N);
disp(F_Welch,'Frequency Resolution of Welch Power Spectrum Estimation')
//Blackmann-Tukey Method
F_Blackmann_Tukey = Q/(2.34*N);
disp(F_Blackmann_Tukey,'Frequency Resolution of Blackmann Tukey Power Spectrum Estimation')
//Result
//Frequency Resolution of Bartlett Power Spectrum Estimation
// 0.0090090
//Frequency Resolution of Welch Power Spectrum Estimation
// 0.0071942
//Frequency Resolution of Blackmann Tukey Power Spectrum Estimation
// 0.0042735PSD Estimation [Blackmann-Tukey Method]-scilab code
//Caption: PSD Estimation using Blackmann-Tukey Method
// of Given Discrete Sequence
//x(n) =(0.9)^n, 0<= n<=20
clear;
clc;
close;
N =16; //8-point DFT
n = 0:20;
x1 = (0.9.^n) //given discrete sequence
x = x1([1:16]);
X = dft(x,-1); //16-point DFT of given discrete sequence
Pxx = (1/N)*(abs(X).^2); //Peridogram Estimate
disp(x,'16 point input discrete sequence x(n)=')
disp(X,'DFT of x(n)is X(k)=')
disp(Pxx,'Peridogram of x(n) is Pxx(k/N)=')
figure(1)
a = gca();
a.data_bounds =[0,0;20,5];
plot2d3('gnn',[1:N],Pxx)
a.foreground = 5;
a.font_color = 5;
a.font_style = 5;
title('Peridogram Estimate')
xlabel('Discrete Frequency Variable K ----->')
ylabel('Periodogram Pxx (k /N) ---->')
//Result
//16 point input discrete sequence x(n)=
//column 1 to 9
//1. 0.9 0.81 0.729 0.6561 0.59049 0.531441 0.4782969 0.4304672
//column 10 to 16
//0.3874205 0.3486784 0.3138106 0.2824295 0.2541866 0.2287679 0.2058911
//DFT of x(n)is X(k)=
// 8.1469798
// 0.9337942 - 1.9085859i
// 0.5514204 - 0.9651212i
// 0.4763807 - 0.6042033i
// 0.4501094 - 0.4050984i
// 0.4383220 - 0.2710927i
// 0.4324549 - 0.1681821i
// 0.4296342 - 0.0807934i
// 0.4287884 - 1.159D-15i
// 0.4296342 + 0.0807934i
// 0.4324549 + 0.1681821i
// 0.4383220 + 0.2710927i
// 0.4501094 + 0.4050984i
// 0.4763807 + 0.6042033i
// 0.5514204 + 0.9651212i
// 0.9337942 + 1.9085859i
//
//Peridogram of x(n) is Pxx(k/N)=
// 4.14833
// 0.2821670
// 0.0772202
// 0.0370000
// 0.0229190
// 0.0166011
// 0.0134564
// 0.0119446
// 0.0114912
// 0.0119446
// 0.0134564
// 0.0166011
// 0.0229190
// 0.0370000
// 0.0772202
// 0.2821670Subband coding speech signal-scilab code
//Caption: write a program for subband coding of speech signal
clear;
clc;
[x,Fs,bits]=wavread("E:\4.wav");
n = length(x)
//Low Pass Filter of Length = 19, Wc = 0.5, Hamming Window
[wft_LPF,wfm_LPF,fr_LPF]=wfir('lp',18,[0.25,0],'hm',[0,0])
//High Pass Filter of Length = 19, Wc = 0.5, Hamming Window
[wft_HPF,wfm_HPF,fr_HPF]=wfir('hp',18,[0.25,0],'hm',[0,0])
//LPF output
Y_lpf = convol(x,wft_LPF)
//HPF output
Y_hpf = convol(x,wft_HPF)
//Downsampling by a factor of 2
Downsampling_XLPF = Y_lpf(1:2:length(Y_lpf));
Downsampling_XHPF = Y_hpf(1:2:length(Y_hpf));
figure(1)
subplot(3,1,1)
plot([1:n],x)
xtitle("ORIGINAL Speech SIGNAL");
subplot(3,1,2)
plot([1:length(Y_lpf)],Y_lpf)
xtitle("Low Pass Filtered Speech SIGNAL");
subplot(3,1,3)
plot([1:length(Y_hpf)],Y_hpf)
xtitle("High Pass Filtered Speech SIGNAL");
figure(2)
subplot(2,1,1)
plot([1:length(Y_lpf)],Y_lpf)
xtitle("Low Pass Filtered Speech SIGNAL");
subplot(2,1,2)
plot([1:length(Downsampling_XLPF)],Downsampling_XLPF,'r')
xtitle("LPF Output Downsampled by 2");
figure(3)
subplot(2,1,1)
plot([1:length(Y_hpf)],Y_hpf)
xtitle("High Pass Filtered Speech SIGNAL");
subplot(2,1,2)
plot([1:length(Downsampling_XHPF)],Downsampling_XHPF,'r')
xtitle("HPF Output Downsampled by 2");
