the error in x

clear all

close all

clc

t = 0:1/50:10-1/50;

x = 8*cos(120*pi*t)*pulse((t-2)/2);

plot(t,x)

y = fft(x);

f = (0:length(y)-1)*50/length(y);

plot(f,abs(y))

title('Magnitude')

n = length(x);

fshift = (-n/2:n/2-1)*(50/n);

yshift = fftshift(y);

plot(fshift,abs(yshift))

rng('default')

xnoise = x + 2.5*randn(size(t));

ynoise = fft(xnoise);

ynoiseshift = fftshift(ynoise);

power = abs(ynoiseshift).^2/n;

plot(fshift,power)

title('Power')

whaleFile = 'bluewhale.au';

[x,fs] = audioread(whaleFile);

whaleMoan = x(2.45e4:3.10e4);

t = 10*(0:1/fs:(length(whaleMoan)-1)/fs);

plot(t,whaleMoan)

xlabel('Time (seconds)')

ylabel('Amplitude')

xlim([0 t(end)])

m = length(whaleMoan);

n = pow2(nextpow2(m));

y = fft(whaleMoan,n);

f = (0:n-1)*(fs/n)/10; % frequency vector

power = abs(y).^2/n; % power spectrum

plot(f(1:floor(n/2)),power(1:floor(n/2)))

xlabel('Frequency')

ylabel('Power')