a = rand(1, 512);
plot(a);
b = rand(1, 512);
A = fft(a);
B = fft(b);
C = fft(cconv(a,b, 512));
norm(A .*B - C) % check convolution theorem

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load gong.mat
y = y(1:40000); % Note y is a column vector
sound(y, Fs)
YY = fft(y'); % fft of transpose to get row vectors
plot(abs(YY).^2)

F1 = [zeros(1, 5000) ones(1, 30000) zeros(1,5000)];
plot(F1)
ylim([-.1,1.1])
F2 = ones(1,40000) - F1;
plot(F2)
ylim([-.1,1.1])

Z1 = YY.* F1; % only central portion
Z2 = YY.* F2; % only edge portion

plot(abs(Z1).^2)
plot(abs(Z2).^2)

z1 = real(ifft(Z1)); % get rid of small imag parts from roundoff
z2 = real(ifft(Z2));

sound(z1, Fs) % only high freq remain
sound(z2, Fs) % so edges are low freq

plot(abs(fftshift(YY)).^2) % move low freq to middle.