function [a] =ifft2d(a2)
//a2 = 2D-DFT of any real or complex 2D matrix
//a = 2D-IDFT of a2
m=size(a2,1)
n=size(a2,2)
//Inverse Fourier transform along the rows
for i=1:n
a1(:,i)=exp(2*%i*%pi*(0:m-1)'.*.(0:m-1)/m)*a2(:,i)
end
//Inverse fourier transform along the columns
for j=1:m
atemp=exp(2*%i*%pi*(0:n-1)'.*.(0:n-1)/n)*(a1(j,:)).'
a(j,:)=atemp.'
end
a = a/(m*n)
a = real(a)
endfunction
//Design of FIR Filter using Frquency Sampling Technique
//Low Pass Filter Design
//Cutoff Frequency Wc = pi/2
//M = Filter Lenth = 7
clear;
clc;
M = 7;
N = ((M-1)/2)+1
wc = %pi/2;
for k =1:M
w(k) = ((2*%pi)/M)*(k-1);
if (w(k)>=wc)
k-1
break
end
end
for i = 1:k-1
Hr(i) = 1;
G(i) = ((-1)^(i-1))*Hr(i);
end
for i = k:N
Hr(i) = 0;
G(i) = ((-1)^(i-1))*Hr(i);
end
h = zeros(1,M);
for n = 1:M
for k = 2:N
h(n) = G(k)*cos((2*%pi/M)*(k-1)*((n-1)+(1/2)))+h(n);
end
h(n) = (1/M)* (G(1)+2*h(n));
end
[hzm,fr]=frmag(h,256);
hzm_dB = 20*log10(hzm)./max(hzm);
plot(2*fr,hzm_dB)
xtitle('Frequency Response of LPF with Normalized cutoff =0.5','Normalized Frequency W ------>','Magnitude Response H(w)---->');
xgrid(1);
// Hamming Weight and Hamming Distance
//H(7,4)
//Code Word Length = 7, Message Word length = 4, Parity bits =3
close;
clc;
//Getting Code Words
code1 = input('Enter the first code word');
code2 = input('Enter the second code word');
Hamming_Distance = 0;
for i = 1:length(code1)
Hamming_Distance =Hamming_Distance+xor(code1(i),code2(i));
end
disp(Hamming_Distance,'Hamming Distance')
//Result
//Enter the first code word [0,1,1,1,0,0,1]
//Enter the second code word[1,1,0,0,1,0,1]
//Hamming Distance 4.
//Hamming Encoding
//H(7,4)
//Code Word Length = 7, Message Word length = 4, Parity bits =3
//clear;
close;
clc;
//Getting Message Word
m3 = input('Enter the 1 bit(MSb) of message word');
m2 = input('Enter the 2 bit of message word');
m1 = input('Enter the 3 bit of message word');
m0 = input('Enter the 4 bit(LSb) of message word');
//Generating Parity bits
for i = 1:(2^4)
b2(i) = xor(m0(i),xor(m3(i),m1(i)));
b1(i) = xor(m1(i),xor(m2(i),m3(i)));
b0(i) = xor(m0(i),xor(m1(i),m2(i)));
m(i,:) = [m3(i) m2(i) m1(i) m0(i)];
b(i,:) = [b2(i) b1(i) b0(i)];
end
C = [b m];
disp('___________________________________________________________')
for i = 1:2^4
disp(i)
disp(m(i,:),'Message Word')
disp(b(i,:),'Parity Bits')
disp(C(i,:),'CodeWord')
disp(" ");
disp(" ");
end
disp('___________________________________________________________')
//disp(m b C)
//Result
//Enter the 1 bit(MSb) of message word [0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1];
//Enter the 2 bit of message word [0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1];
//Enter the 3 bit of message word [0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1];
//Enter the 4 bit(LSb) of message word [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1];
function [E]=EqualizerFor_ApertureEff(Ts)
//Equalizer to Compensate for aperture effect
T_Ts = 0.01:0.01:Ts;
E(1) =1;
for i = 2:length(T_Ts)
E(i) = ((%pi/2)*T_Ts(i))/(sin((%pi/2)*T_Ts(i)));
end
a =gca();
a.data_bounds = [0,0.8;0.8,1.2];
plot2d(T_Ts,E,5)
xlabel('Duty cycle T/Ts')
ylabel('1/sinc(0.5(T/Ts))')
title('Normalized equalization (to compensate for aperture effect) plotted versus T/Ts')
endfunction
//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')
//Caption: Speech Noise Cancellation using LMS Adaptive Filter
clc;
//Reading a speech signal
[x,Fs,bits]=wavread("E:\4.wav");
order = 40; // Adaptive filter order
x = x';
N = length(x);
t = 1:N;
//Plot the speech signal
figure(1)
subplot(2,1,1)
plot(t,x)
title('Noise free Speech Signal')
//Generation of noise signal
noise = 0.1*rand(1,length(x));
//Adding noise with speech signal
for i = 1:length(noise)
primary(i)= x(i)+noise(i);
end
//Plot the noisy speech signal
subplot(2,1,2)
plot(t,primary)
title('primary = speech+noise (input 1)')
//Reference noise generation
for i = 1:length(noise)
ref(i)= noise(i)+0.025*rand(10);
end
//Plot the reference noise
figure(2)
subplot(2,1,1)
plot(t,ref)
title('reference noise (input 2)')
//Adaptive filter coefficients initialized to zeros
w = zeros(order,1);
Average_Power = pow_1(x,N)
mu = 1/(10*order*Average_Power); //Adaptive filter step size
//Speech noise cancellation
for k = 1:110
for i =1:N-order-1
buffer = ref(i:i+order-1); //current order points of reference
desired(i) = primary(i)-buffer'*w; // dot product the reference & filter
w = w+(buffer.*mu*desired(i)); //update filter coefficients
end
end
//Plot the Adaptive Filter output
subplot(2,1,2)
plot([1:length(desired)],desired)
title('Denoised Speech Signal at Adaptive Filter Output')
//Calculation of Mean Squarred Error between the original speech signal and
//Adaptive filter output
for i =1:N-order-1
err(i) = x(i)-desired(i);
square_error(i)= err(i)*err(i);
end
MSE = (sum(square_error))/(N-order-1);
MSE_dB = 20*log10(MSE);
//Playing the original speech signal
sound(x,Fs,16)
//Delay between playing sound signals
for i = 1:1000
j = 1;
end
/////////////////////////////////
//Playing Noisy Speech Signal
sound(primary,Fs,16)
//Delay between playing sound signals
for i = 1:1000
j = 1;
end
/////////////////////////////////
//Playing denoised speech signal (Adaptive Filter Output)
sound(desired,Fs,16)
//Caption: write a program for decimation and interpolation of given
//Speech Signal [ Multirate Signal Processing]
clear;
clc;
[x,Fs,bits]=wavread("E:\4.wav");
n = length(x)
DECIMATION_OF_X = x(1:2:length(x));
INTERPOLATION_OF_X = zeros(1,2*length(x));
INTERPOLATION_OF_X(1:2:2*length(x)) = x;
subplot(3,1,1)
plot([1:n],x)
xtitle("ORIGINAL Speech SIGNAL");
subplot(3,1,2)
plot([1:ceil((n/2))],DECIMATION_OF_X)
xtitle("DECIMATION BY A FACTOR OF 2")
subplot(3,1,3)
plot([1:2*n],INTERPOLATION_OF_X)
xtitle("INTERPOLATION BY A FACTOR OF 2")
//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=
// 1.045
function[y,M] = adapt_filt(xlms,B,h,delta,l,l1)
//x = the signal from the speaker directly
//B = the signal thorugh the echo path
//h = impulse response of adaptive filter
//l = length of signal 'x'
//l1 = length of adaptive filter order
for k = 1:150
for n = 1:l
xcap = xlms((n+l1-1):-1:(n+l1-1)-l1+1);
yout(n) = h*xcap;
e(n) = B(n)- yout(n);
xnorm = 0.001+(xcap*xcap');
h = h+((delta*e(n))*(xcap'));
end
eold = 0.0;
for i = 1:l
MSE = eold+(e(i)^2);
eold = MSE;
end
if MSE <= 0.0001 then
break;
end
end
y = zeros(1,length(e));
M = zeros(1,length(h));
y = e;
M = h;
endfunction
//Caption : FULL Band Echo Cnacellation using NLMS Adaptive Filter
clc;
//Reading a speech signal
[x,Fs,bits]=wavread("E:\4.wav");
order = 40; // Adaptive filter order
x = x';
N = length(x); //length of speech signal
//Delay introduced in echo path
delay = 100;
//Echo at same speaker
xdelayed = zeros(1,N+delay);
for i = delay+1:N+delay
xdelayed(i) = x(i-delay);
end
//Initialize the adaptive filter coefficients to zero
hcap = zeros(1,order);
//To avoid negative values generated during convolution
for i = 1:order-1
xlms(i) = 0.0;
end
for i = order:N+order-1
xlms(i) = x(i-order+1);
end
Power_X = pow_1(x,N); //Average power of speech signal
//Calculation of step size of adaptive filter
delta = 1/(10*order*Power_X);
[x_out,Adapt_Filter_IR] = adapt_filt(xlms,xdelayed,hcap,delta,N,order)
figure(1)
subplot(3,1,1)
plot([1:N],x)
title('Speech Signal Generated by some Speaker A')
sound(x,Fs,16)
subplot(3,1,2)
plot([1:length(xdelayed)],xdelayed)
title('Echo signal of speaker A received by speaker A')
sound(xdelayed,Fs,16)
subplot(3,1,3)
plot([1:length(x_out)],x_out)
title('Echo signal at speaker A after using NLMS Adaptive filter Echo Canceller')
figure(2)
plot2d3('gnn',[1:length(Adapt_Filter_IR)],Adapt_Filter_IR)
title('Adaptive Filter (Echo Canceller) Impulse response')
//Caption: Reading a Speech Signal &
//[1]. Write it in another file
//[2]. Changing the bit depth from 16 bits to 8 bits
clear;
clc;
[y,Fs,bits_y]=wavread("E:\4.wav");
wavwrite(y,Fs,8,"E:\4_8bit.wav");
[x,Fs,bits_x]=wavread("E:\4_8bit.wav");
Ny = length(y); //Number of samples in y (4.wav)
Nx = length(x); //Number of samples in x (4_8bit.wav)
Memory_y = Ny*bits_y; //memory requirement for 4.wav in bits
Memory_x = Nx*bits_x; //memory requirement for 4_8bit.wav in bits
disp(Memory_y,'memory requirement for 4.wav in bits =')
disp(Memory_x,'memory requirement for 4_8bit.wav in bits =')
//Result
//memory requirement for 4.wav in bits =
// 133760.
//
//memory requirement for 4_8bit.wav in bits =
// 66880.
//Generation of Differential Phase shift keying signal
clc;
bk = [1,0,1,1,0,1,1,1];//input digital sequence
for i = 1:length(bk)
if(bk(i)==1)
bk_not(i) =~1;
else
bk_not(i)= 1;
end
end
dk_1(1) = 1&bk(1); //initial value of differential encoded sequence
dk_1_not(1)=0&bk_not(1);
dk(1) = xor(dk_1(1),dk_1_not(1))//first bit of dpsk encoder
for i=2:length(bk)
dk_1(i) = dk(i-1);
dk_1_not(i) = ~dk(i-1);
dk(i) = xor((dk_1(i)&bk(i)),(dk_1_not(i)&bk_not(i)));
end
for i =1:length(dk)
if(dk(i)==1)
dk_radians(i)=0;
elseif(dk(i)==0)
dk_radians(i)=%pi;
end
end
disp(bk,'(bk)')
bk_not = bk_not';
disp(bk_not,'(bk_not)')
dk = dk';
disp(dk,'Differentially encoded sequence (dk)')
dk_radians = dk_radians';
disp(dk_radians,'Transmitted phase in radians')
