Steady-state performance limitations of subband adaptive filters

Abstract

Nonperfect filterbanks used for subband adaptive filtering (SAF) are known to impose limitations on the steady-state performance of such systems. In this paper, we quantify the minimum mean-square error (MMSE) and the accuracy with which the overall SAF system can model an unknown system that it is set to identify. First, in case of MMSE limits, the error is evaluated based on a power spectral density description of aliased signal components, which is accessible via a source model for the subband signals that we derive. Approximations of the MMSE can be embedded in a signal-to-alias ratio (SAR), which is a factor by which the error power can be reduced by adaptive filtering. With simplifications, SAR only depends on the filterbanks. Second, in case of modeling, we link the accuracy of the SAF system to the filterbank mismatch in perfect reconstruction. When using modulated filterbanks, both error limits-MMSE and inaccuracy-can be linked to the prototype. We explicitly derive this for generalized DFT modulated filterbanks and demonstrate the validity of the analytical error limits and their approximations for a number of examples, whereby the analytically predicted limits of error quantities compare favorably with simulation

Design of near perfect reconstruction oversampled filter banks for subband adaptive filters

“…Simulations using the filter banks, together with adaptive filters, which are not presented in this paper, have shown that the performance in terms of minimum mean-squared error is limited by the amount of inband aliasing and reconstruction error, which come from the used filter bank [29]. For colored-noise input signals, however, in general these subband structures have shown an improvement in terms of convergence speed.…”

Performance limitation of subband adaptive equalisers

“…Subband adaptive equaliser: An adaptive equaliser based on the subband decomposition method has been demonstrated to exhibit fast convergence speed at low computational complexity when long equalisers w[n] are employed using the LMS-type algorithm [2,3]. In related adaptive filtering application, subband techniques were previously proposed for echo cancellation applications [4] where the achievable MMSE performance has a lower limit imposed by the employed filter bank structure through aliasing in the subbands [5]. The schematic of a subband adaptive equaliser is shown in Fig.…”

“…2. Oversampled modulated filter banks are used for subband adaptive equalisation such that aliasing is restricted to the stopband of the analysis filters and can therefore be controlled by appropriate filter bank design [5]. Analysis filters h k [n] and sysnthesis filters g k [n] are derived from a real-valued lowpass prototype FIR filter p[n] by using a generalised discrete Fourier transform (GDFT).…”

An oversampled channelized UWB receiver

“…The low pass filter in the analysis filters is an eighth order Butterworth filter, and its 3dB frequency is at . is a ten tap filter and is obtained from [13] [14]. Figure 6 : SNR loss v.s.…”