Applying Fourier to a real signal: guitar musical note B. Full article at http://www.firsttimeprogrammer.blogspot.com/2015/05/applying-fourier-to-real-signal-guitar.html

fourier_B_note.m

% Loading wav file
[ip fs] = wavread('B.wav');

% B tone
B = ip;

% Play the recording
sound(B,fs);

% Plot the recording
plot(B);
ylabel('Amplitude');
xlabel('samples');

% Take the FFT of the recording
n = length(B);
track = B(1:n-1);
FFT = fft(track);
ft_mod = abs(FFT);
bins = length(B)-1;

% Find the fundamental frequency
[max_value, max_location] = max(ft_mod);
fundamental_frequency = (max_location-1)*fs/n;
display(fundamental_frequency)
display(max_location)

% Frequency vector
w = zeros(1,length(bins));
for k = 1:1:bins
    w(k) = (k-1)*fs/n;
end

% Plot (half of) the FFT
if mod(length(w),2) == 0
    index = length(w)/2;
else
    index = (length(w)-1)/2;
end

plot(w(1:index),ft_mod(1:index)); hold on;
xlabel('Frequency Hz');
ylabel('Magnitude');
title('FTT of the recording');

% Apply a filtering rule (in this case I'm letting through only
% frequencies between 200 and 1800)
minFreq = 200;      %400;
maxFreq = 1600 ;    %1100;

for k= 1:1:length(w)
    if w(k) < minFreq || w(k) > maxFreq
        FFT(k) = 0;
        ft_mod(k) = 0;
    end
end

% Plot the edited FFT over the full one
plot(w(1:index),ft_mod(1:index)); hold off;

% Get back the recording
y = ifft(FFT);

% Play the result
sound(abs(y),fs);