Analysis of fixed point roundoff effects in transform domain LMS adaptive filters

One of the disadvantages of the well known LMS FIR adaptive digital filter is that, for a colored noise input signals, the filter tends to converge slowly. One way to improve the convergence rate is to prefilter the input signal with an orthogonalizing transform, such as the Karhunen-Loeve transform (KLT). The transform domain LMS algorithm utilizes a discrete orthogonal transform such as the discrete Fourier transform (DFT), in an attempt to approximate the performance of the KLT. In addition to the DFT, this paper also considers the discrete cosine transform (DCT), the Walsh-Hadamard transform (WHT), and the discrete Hartley transform (DHT). Both the theoretical and experimental results seem to indicate that, when the numbers of quantization bits used by the transform domain filters are the same as those used by the time domain adaptive filter, the transform domain filters studied in this work perform as well as or even better than the time domain adaptive filter when the number of the coefficient bits is sufficiently larger than that of the data bits.