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). However, this optimal solution requires a priori knowledge of the input statistics and there is currently no fast algorithm that would allow for its real-time implementation. Thus, suboptimal solutions known as transform domain LMS algorithms have been proposed in the literature as an alternative to the KLT that can be implemented in practical applications. 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, the authors also consider the discrete cosine transform (DCT), the Walsh-Hadamard transform (WHT), and the discrete Hartley transform (DHT)