How would I plot signal energy of a .wav file making sure that time is the value of the x-axis?

When using the audioread function to read a .wav file, how would I plot the signal's energy making sure that the time domain is the value of the x-axis? This example was referenced but isn't working out. Assuming that if the .wav file is 30 seconds long, I wouldn't want the time domain to be t=0:0.01:1; considering that would only graph 1 sec of the 30 sec recording.

% time domain

t=0:0.01:1;

% signal x

x=sin(2*pi*t);

% signal's Energy

E=x.^2;

% plots

plotyy(t,x,t,E), grid on, axis([0 max(t) -2 2]) xlabel('t'), ylabel('x, E')

title('Signal and Energy')

Answer 1

[Star Strider]

The audioread function returns the signal amplitude matrices and the sampling frequency. To create a time vector for the ‘y’ data, use the linspace function with the values derived from the returned data.

Try this —

t=0:0.01:1; 
x=sin(2*pi*t); 
audiowrite('test.wav',x,1/t(2))

figure
plot(t,x)
grid
title('Input')

[y,Fs] = audioread('test.wav');

L = size(y,1);
t = linspace(0, L-1, L)/Fs;

figure
plot(t, y, 'DisplayName','Energy = y')
hold on
plot(t, y.^2, 'DisplayName','Power  = y^2')
hold off
grid
legend('Location','best')
title('Output')

.

[Andrew]

Do you have to use sin(2*pi*t) in order to plot the energy of a signal? Or could you use an fft function?

[Star Strider]

THe ‘sin(2*pi*t)’ here is the signalk that you defined in your code, so I used it. Measuring the contents of the signal recovered from the .wav file will be appropriate to that signal. The Fourier transform (fft) is another way of measuring the signal characteristics. Parseval’s theorem indicates that the results will be the same in the time and frequency domain.

Answer 2

[Paul]

Hi Andrew,

The energy in a signal is a single number, so it's not clear how one would plot that.

The instantaneous power is a function of time, so we can plot that.

load handel.mat
filename = 'handel.wav';
audiowrite(filename,y,Fs);
clear y Fs
[y,Fs] = audioread('handel.wav');

Assuming that the discrete time signal, y, is zero, for n <= 0 and n > numel(y) the instanteous power is

ipower = abs(y).^2;
plot(1:numel(y),ipower)

and the energy is

E = sum(ipower)

E = 2.8153e+03

If we want to treat the elements of y as samples of a continuous time signal, then the energy in the continuous time signal is approximated by

Ts = 1/Fs;
E = sum(ipower)*Ts

E = 0.3437

Here is a link to one Reference for these definitions.

Here is link to an Answer that may be of interest.