Performs a forward or inverse discrete Cosine transform of 1D or 2D array

dst = cv.dct(src)
dst = cv.dct(src, 'OptionName',optionValue, ...)

Input

• src input floating-point single-channel array.

Output

• dst output array of the same size and type as src.

Options

• Inverse performs an inverse 1D or 2D transform instead of the default forward transform. default false
• Rows performs a forward or inverse transform of every individual row of the input matrix. This flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transforms and so forth. default false

The function cv.dct performs a forward or inverse discrete Cosine transform (dct) of a 1D or 2D floating-point array:

• Forward Cosine transform of a 1D vector of N elements:

  Y = CN * X
  

  where

  CN(j,k) = sqrt(alpha_j/N) * cos((pi*(2k+1)*j)/2N)
  

  and alpha_0=1, alpha_j=2 for j>0.

• Inverse Cosine transform of a 1D vector of N elements:

  X = inv(CN) * Y = transpose(CN) * Y
  

  (since CN is an orthogonal matrix, CN * transpose(CN) = I)

• Forward 2D Cosine transform of MxN matrix:

  Y = CN * X * transpose(CN)
  

• Inverse 2D Cosine transform of MxN matrix:

  X =  transpose(CN) * X * CN
  

The function chooses the mode of operation by looking at the transformation flags and size of the input array:

• If Inverse = true, the function does a forward 1D or 2D transform. Otherwise, it is an inverse 1D or 2D transform.
• If Rows = true, the function performs a 1D transform of each row.
• If the array is a single column or a single row, the function performs a 1D transform.
• If none of the above is true, the function performs a 2D transform.

Note: Currently cv.dct supports even-size arrays (2, 4, 6, etc.). For data analysis and approximation, you can pad the array when necessary. Also, the function performance depends very much, and not monotonically, on the array size (see cv.getOptimalDFTSize). In the current implementation, dct of a vector of size N is calculated via DFT of a vector of size N/2. Thus, the optimal dct size N1 >= N can be calculated as:

function N1 = getOptimalDCTSize(N)
    N1 = 2 * cv.getOptimalDFTSize(fix((N+1)/2));
end

Note: cv.idct is equivalent to cv.dct(..., 'Inverse',true).