Effect of weight inaccuracy in neural network for computation of discrete Hartley and Fourier transforms

Recently, a neural network for fast computation of discrete Hartley and Fourier transforms has been proposed. In this paper the sensitivity of the network to weight errors is investigated. Sensitivity formulas are derived which give the partial derivatives of the network outputs with respect to weight variations. Then, assuming that the weight errors are independent random variables, the exact probability density functions are derived for the errors in the Hartley transform (DHT) and in both magnitude and phase of the Fourier transform (DFT). It is shown that the magnitude relative error of an N-point DFT decreases as 1/ square root N when N increases.<
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