%% Signal Reconstruction Using Inverse Discrete Cosine Transform
% Generate a signal that consists of a 25 Hz sinusoid sampled at 1000 Hz for 1 second. The sinusoid is embedded in white Gaussian noise with variance 0.01.

rng('default')

Fs = 1000;
t = 0:1/Fs:1-1/Fs;
x = sin(2*pi*25*t) + randn(size(t))/10;

%
% Compute the discrete cosine transform of the sequence. Determine how many of the 1000 DCT coefficients are significant. Choose 1 as the threshold for significance.

y = dct(x);

sigcoeff = abs(y) >= 1;

howmany = sum(sigcoeff)

%
% Reconstruct the signal using only the significant components.

y(~sigcoeff) = 0;

z = idct(y);

%
% Plot the original and reconstructed signals.

subplot(2,1,1)
plot(t,x)
yl = ylim;
title('Original')

subplot(2,1,2)
plot(t,z)
ylim(yl)
title('Reconstructed')

% Copyright 2012 The MathWorks, Inc.