Understanding Spectrogram with DTMF Signals

This MATLAB tutorial explains the Spectrogram visualization using DTMF audio as input signal. The code reads, analyzes and plots the spectrogram of a DTMF signal. The time-frequency resolution problem is explained with different frame sizes.

Screen Display Specifications

%Measure screen size of the device
%Calculate position values of figure Windows

scrsz = get(0,'ScreenSize');
P1=[40 500 scrsz(3)/3 scrsz(4)/3];
P2=[40 80 scrsz(3)/3 scrsz(4)/3];
P3=[600 500 scrsz(3)/3 scrsz(4)/3];
P4=[600 80 scrsz(3)/3 scrsz(4)/3];
P5=[1000 500 scrsz(3)/3 scrsz(4)/3];
P6=[1000 80 scrsz(3)/3 scrsz(4)/3];

File Reading

[y, Fs] = audioread('C:\Users\SAJIL\Documents\MATLAB\DTMF1.wav');
L=length(y);
N = nextpow2(L);
T=1/Fs;

Signal Analysis Part

t=(0:T:(L-1)/Fs)';
NFFT = 2^nextpow2(L);
Y = fft(y,NFFT);%/L;
f = Fs/2*linspace(0,1,NFFT/2+1);
Mag=2*abs(Y(1:NFFT/2+1));

Plot Signal

figure('position', P1);
figure(1);
plot(t,y,'k');
grid on
title('Time Domain');
xlabel('Time in Seconds');
ylabel('Amplitude');
legend('DTMF Tone');

Plot single-sided Amplitude Spectrum.

figure('position',P2);
figure(2);
plot(f,Mag);
grid on
title('Magnitude Spectrum');
xlabel('Frequency (Hz)');
ylabel('|X(f)|');
legend('Frequency Spectrum');

DTMF Signal Table

I = imread('DTMF.png');
figure('position',P3);
figure(3);
image(I)
f=text(0.4,0.4,'Original Input is 0696675356','FontSize',12);
axis off

Spectrogram Display Part

figure('position',P4);
figure(4);
%spectrogram(x,window,noverlap,f,fs)
spectrogram(y,32);
text(0.4,28,'Frame Size 32','FontSize',12);
%colormap bone

figure('position',P5);
figure(5);
%spectrogram(x,window,noverlap,f,fs)
spectrogram(y,256);
text(0.4,28,'Frame Size 256','FontSize',12);

figure('position',P6);
figure(6);
%spectrogram(x,window,noverlap,f,fs)
spectrogram(y,512);
text(0.4,28,'Frame Size 512','FontSize',12);

  

Play back block

soundsc(y,Fs);

End of Program

An Intuitive Look Into Auto-Correlation

In this tutorial, we will take a look at the mathematical function called auto-correlation for various  common signals. The basic signals are generated and their respective auto-correlation output is plotted.

Screen Display Settings

%Measure Screen Size of the device
%Calculate position values of figure windows
scrsz = get(0,'ScreenSize');
P1 = [50 500 scrsz(3)/3 scrsz(4)/3];
P2 = [50 80 scrsz(3)/3 scrsz(4)/3];
P3 = [500 500 scrsz(3)/1.5 scrsz(4)/3];
P4 = [500 80 scrsz(3)/1.5 scrsz(4)/1.5];

Generate Basic Signals

figure('position', P4);
figure(1);

Sine Wave

t = 0:(1/1000):1;
x1 = sin(2*pi*1*t) ;
subplot(4,2,1);
plot(x1);
grid on
title('Sine Wave');
xlabel('Samples');
ylabel('Amplitude');

y1 = xcorr(x1,x1);
subplot(4,2,2);
plot(y1);
grid on
title('Sine Wave Autocorr');
xlabel('Samples');
ylabel('Amplitude');

Ramp

x2 = t;
subplot(4,2,3);
plot(t);
grid on
title('Ramp');
xlabel('Samples');
ylabel('Amplitude');

y2 = xcorr(x2,x2);
subplot(4,2,4);
plot(y2);
grid on
title('Ramp Autocorr');
xlabel('Samples');
ylabel('Amplitude');

Rectangular

x3 = ones(1,1500);
subplot(4,2,5);
plot(x3);
grid on
title('Rectangular');
xlabel('Samples');
ylabel('Amplitude');

y3 = xcorr(x3,x3);
subplot(4,2,6);
plot(y3);
grid on
title('Rect Autocorr');
xlabel('Samples');
ylabel('Amplitude');

1 minus x^2

x4 = 1- t.*t;
subplot(4,2,7);
plot(x4);
grid on
title('XSquare');
xlabel('Samples');
ylabel('Amplitude');

y4 = xcorr(x4,x4);
subplot(4,2,8);
plot(y4);
grid on
title('XSquare Autocorr');
xlabel('Samples');
ylabel('Amplitude');

End of Program

Sea Channel Simulation with MATLAB

The following MATLAB code simulates the effects happening to a signal transmitted over sea channel underwater cable. The changes happening to the signal is plotted at their respective stages.

19/05/2015 6:00 PM 'C:\Users\SAJIL\Documents\MATLAB\Seachannel.m'

%Version 1.0
%Sajil C. K., DCB, Uok.
%sajildcb@gmail.com
%This program Reads a speech wav file from Hard disk, then its applied
%though transformations in whcin it is attenuated and is affected by
%Gaussian noise. We can hear to the effects of these after each steps

Screen Display Specifications

%Measure screen size of PC
%Calculate position values of figure Windows

scrsz = get(0,'ScreenSize');
P1=[40 500 scrsz(3)/3 scrsz(4)/3];
P2=[40 80 scrsz(3)/3 scrsz(4)/3];
P3=[600 500 scrsz(3)/3 scrsz(4)/3];
P4=[600 80 scrsz(3)/3 scrsz(4)/3];
P5=[1000 500 scrsz(3)/3 scrsz(4)/3];
P6=[1000 80 scrsz(3)/3 scrsz(4)/3];
P =[P1;P2;P3;P4;P5;P6];
c=['m' 'c' 'r' 'g' 'b' 'k'];

File Reading

[x, Fs] = audioread('I Love You Daddy.wav');
x=x(:,1); % Discard one channel
N=length(x);
t=(0:(N-1))'/Fs;

Parameter specifications

A = 0.5; %Channel attenuation value
G = 6; %Specify Number of Gate Breaks here
i = 1;

Channel Model

while i<=G

Plot Signal

    figure('position', P(i,:));
    figure(i);
    plot(t,x,c(i));
    grid on
    title(strcat('Transmitted Signal at Gate ', num2str(i)));
    xlabel('Time in Seconds');
    ylabel('Amplitude');
    legend(strcat('Speech @ Gate ',num2str(i)));

     

Play back of Original

    p= audioplayer(x,Fs);
    play(p);
    pause(max(size(x))/Fs);

Generate Guassian Noise Model

    n= 0.5*rand(N,1)-0.5;

Signal Attenuation and Noise

    x=x*A;
    x=x+n;
    i=i+1;

end

End of Program

Echo Generation using Room Impulse Response Using MATLAB

The following code produces auralization effects to audio sounds saved in hard disk to add echo effect. The input will be a dry sound with no echo/reverberation but the output will sound like in a tunnel or Cathedral.

Screen Display Specifications

%Measure screen size of the device
%Calculate position values of figure Windows

scrsz = get(0,'ScreenSize');
P1=[40 500 scrsz(3)/3 scrsz(4)/3];
P2=[40 80 scrsz(3)/3 scrsz(4)/3];

Read Room Impulse Response File

[x1,Fs1]=audioread('tunnel_balloon_441k.wav');
[x2,Fs1]=audioread('carpark_balloon _441k.wav');

% Discard one channel
x1=x1(:,1);
x2=x2(:,1);

Plot Impulse Response of Tunnel

figure('position', P1);
figure(1);
plot(x1,'k');
grid on
title('IR of tunnel balloon 441k.wav');
xlabel('Samples');
ylabel('Amplitude');
legend('tunnel IR');

Plot Impulse Response of Underground Carpark

figure('position', P2);
figure(2);
plot(x2,'r');
grid on
title('carpark balloon 441k.wav');
xlabel('Samples');
ylabel('Amplitude');
legend('Carpark IR');

Read Input Signal

[y,Fs2]=audioread('Asianet.wav');
y=y(:,1);

Perform Convolution

o1 = conv(x1,y);
o2 = conv(x2,y);

Playback the Output Signal

%soundsc(o1,Fs1);
%soundsc(o2,Fs1);

End of Program