Multiplier-less Filter Banks Research Articles

A Low-Complexity Multiplier-Less Filter Bank Based on Modified IFIR for the SDR Channelizer

Digital filter banks are extensively used in an SDR channelizer for channelization. The objective of this research work is to design a low computational complexity FIR filter bank for generating sharp transition width channels for SDR. The design of unified and variable bandwidth channels for SDR using the proposed structure is based on the modified IFIR filter structure and cosine modulation technique (CMT). The performance of the proposed structure is demonstrated with the help of an example. The results show that the multiplier complexity of the proposed structure is less than those of other state-of-the art methods. The optimization techniques are incorporated in this work to further reduce the complexity of the proposed structure. With the help of canonical signed digit (CSD), multi-objective artificial bee colony (MOABC) and shift inclusive differential coefficients (SIDC) – common sub-expression elimination (CSE) optimization, the filter used in this structure is made multiplier-less.

Multiplierless filter Bank design: structures that improve both hardware and image compression performance

Design techniques for high-performance, fixed-point, multiplierless filter banks are presented. Image compression using the biorthogonal 9/7 discrete wavelet transform provides a motivating example. Image compression and hardware performance of two commonly used filter structures, direct and cascade, and two known filter bank structures, nonpolyphase and polyphase, are compared. A technique is shown for designing a fixed-point polyphase filter structure, which is highly efficient from a hardware standpoint, such that image-compression quality is not significantly deteriorated by the use of fixed-point mathematics. The result is a polyphase structure with about twice the throughput rate of nonpolyphase structures, and peak signal-to-noise ratio values for lossy compression within 0.2 decibels of those achieved using floating-point filters.

Discrete Lagrangian Methods for Designing Multiplierless Two-Channel PR-LP Filter Banks

In this paper, we present a new search method based on the theory of discrete Lagrange multipliers for designing multiplierless PR (perfect reconstruction) LP (linear phase) filter banks. To satisfy the PR constraints, we choose a lattice structure that, under certain conditions, can guarantee the resulting two filters to be a PR pair. Unlike the design of multiplierless QMF filter banks that represents filter coefficients directly using PO2 (powers-of-two) form (also called Canonical Signed Digit or CSD representation), we use PO2 forms to represent the parameters associated with the lattice structure. By representing these parameters as sums or differences of powers of two, multiplications can be carried out as additions, subtractions, and shifts. Using the lattice representation, we decompose the design problem into a sequence of four subproblems. The first two subproblems find a good starting point with continuous parameters using a single-objective, multi-constraint formulation. The last two subproblems first transform the continuous solution found by the second subproblem into a PO2 form, then search for a design in a mixed-integer space. We propose a new search method based on the theory of discrete Lagrange multipliers for finding good designs, and study methods to improve its convergence speed by adjusting dynamically the relative weights between the objective and the Lagrangian part. We show that our method can find good designs using at most four terms in PO2 form in each lattice parameter. Our approach is unique because our results are the first successful designs of multiplierless PR-LP filter banks. It is general because it is applicable to the design of other types of multiplierless filter banks.

Discrete Lagrangian methods for optimizing the design of multiplierless QMF banks

In this paper, we present a new discrete Lagrangian method for designing multiplierless quadrature mirror filter banks. The filter coefficients in these filter banks are in powers-of-two, where numbers are represented as sums or differences of powers of two (also called canonical signed digit representation), and multiplications are carried out as additions, subtractions, and shifts. We formulate the design problem as a nonlinear discrete constrained optimization problem, using reconstruction error as the objective, and stopband and passband energies, stopband and passband ripples, and transition bandwidth as constraints. Using the performance of the best existing designs as constraints, we search for designs that improve over the best existing designs with respect to all the performance metrics. We propose a new discrete Lagrangian method for finding good designs and study methods to improve the convergence speed of Lagrangian methods without affecting their solution quality. This is done by adjusting dynamically the relative weights between the objective and the Lagrangian part. We show that our method can find designs that improve over Johnston's benchmark designs using a maximum of three to six ONE bits in each filter coefficient instead of using floating-point representations. Our approach is general and is applicable to the design of other types of multiplierless filter banks.