dct

Signal Processing Toolbox

Discrete cosine transform (DCT).

y = dct(x)
y = dct(x,n)

Description

y = dct(x)

returns the discrete cosine transform of

where N is the length of x, and x and y are the same size. If x is a matrix, dct transforms its columns. The series is indexed from n + 1 and k + 1 instead of the usual n and k because MATLAB vectors run from 1 to N instead of from 0 to N- 1.

y = dct(x,n)

pads or truncates x to length n before transforming.

If x is a matrix, dct transforms its columns.

The DCT is closely related to the discrete Fourier transform. You can often reconstruct a sequence very accurately from only a few DCT coefficients, a useful property for applications requiring data reduction.

Example

Find how many DCT coefficients represent 99% of the energy in a sequence:

x = (1:100) + 50*cos((1:100)*2*pi/40);
X = dct(x);
[XX,ind] = sort(abs(X)); ind = fliplr(ind);
i = 1;
while (norm([X(ind(1:i)) zeros(1,100-i)])/norm(X)<.99)
 i = i + 1;
end

i = 
      3

See Also


`fft`	One-dimensional fast Fourier transform.
`idct`	Inverse discrete cosine transform.
`dct2`	Two-dimensional DCT (see Image Processing Toolbox User's Manual).
`idct2`	Two-dimensional inverse DCT (see Image Processing Toolbox User's Manual).

[ Previous | Help Desk | Next ]