A neural net approach to DCT-I, DST-I, and DFT

This paper presents an electronic circuit, using the Tank and Hopfield linear programming neural net to compute the discrete cosine transform-I (DCT-I), discrete sine transform-I(DST-I) and discrete Fourier transform (DFT). First, particular attention is paid to the properties of the DCT-I matrix C^I and the DST-I matrix S´. The relationship between the real (or imaginary) part of the N-point DFT and the (N/2+1)-point DCT-I (or (N/2-1)-point DST-I) is explored. Then, it is shown analytically that the neural net for computing the DCT-I or DST-I is guaranteed to settle into the correct values within RC time constants. The N-point DFT is obtained by having a (N/2+1)-point DCT-I neural net and a (N/2-1)-point DST-I neural net operate in parallel. Finally, the simulation and comparison are made. The advantage of our DCT-I, DST-I and DFT, implementations is the speed, the simplicity and the tolerance of inaccuracies in the C^I matrix or S^I matrix. Compared with the DFT implementation using the DHT neural net introduced by Culhane et al., our DFT implementation requires a half of the number of the elements of the interconnect conductance matrix