Inverse discrete cosine transform
discrete cosine transform reconstructs a sequence from its discrete
cosine transform (DCT) coefficients. The
is the inverse of the
the inverse discrete cosine transform of
= length(x), which is the same as
The series is indexed from n
= 1 and k
= 1 instead of the usual n
= 0 and k
= 0 because MATLAB® vectors
run from 1 to N instead of from
0 to N-1.
zeros or truncates the vector
y to length
y is a matrix,
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, that is, greater than 1.
y = dct(x); sigcoeff = abs(y)>=1; howmany = sum(sigcoeff)
howmany = 17
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')
 Jain, A. K. Fundamentals of Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
 Pennebaker, W. B., and J. L. Mitchell. JPEG Still Image Data Compression Standard. New York: Van Nostrand Reinhold, 1993.