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Approximate methods have been considered as a means to the evaluation ofdiscrete transforms. In this work, we propose and analyze a class of integertransforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT,and DCT), based on simple dyadic rational approximation methods. The introducedmethod is general, applicable to several block-lengths, whereas existingapproaches are usually dedicated to specific transform sizes. The suggestedapproximate transforms enjoy low multiplicative complexity and theorthogonality property is achievable via matrix polar decomposition. We showthat the obtained transforms are competitive with archived methods inliterature. New 8-point square wave approximate transforms for the DFT, DHT,and DCT are also introduced as particular cases of the introduced methodology.

An Integer Approximation Method for Discrete Sinusoidal Transforms