Spectral response of the discrete cosine and Walsh-Hadamard transforms

Abstract
It is becoming increasingly popular, when considering transform coding schemes for images, to attempt to take the spatial frequency response of the human observer into account by performing a classical one- or two-dimensional filtering (pre-emphasis) operation upon the coefficients of the Fourier transformed image, and it would be advantageous if such a procedure could be carried out with more commonly used image transforms, notably the discrete cosine and Walsh-Hadamard transforms. It is demonstrated here that, notwithstanding the theoretical difficulties associated with the convolution/multiplication operation where the discrete cosine transform is concerned, its spectral response and the nature of the appropriate filtering characteristic are such that an operation of the above mentioned kind may be carried out, and the benefits of psychovisual coding obtained. On the other hand, the results obtained in the case of the Walsh-Hadamard transform show that it is unlikely that its performance will be found satisfactory in such an application.

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