Recent work on filter banks and related expansions has revealed an interesting insight: Different filter bank trees can be regarded as different ways of constructing orthonormal bases for linear signal expansion. In particular, fast algorithms for finding best bases in an operational rate-distortion (R/D) sense have been successfully used in image coding. Independently of this work, recent rese...

Abs#ruct-Multirate filter banks produce multiple output signals by filtering and subsampling a single input signal, or conversely, generate a single output by upsampling and interpolating multiple inputs. Two of their main applications are subband coders for speech processing and transmultiplexers for telecommunications. Below, we derive a theoretical framework for the analysis, synthesis, and ...

This paper presents a new method for designing orthonormal wavelet filter banks using the Remez exchange algorithm. It is well known that orthonormal wavelet bases can be generated by paraunitary filter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary filter banks. From the orthonormality and regularity of wavelets, we derive some conditions that m...

A new combinational window family for the design of prototype FIR filter of two-channel Quadrature Mirror Filter (QMF) bank is introduced. One variable window, viz., Kaiser Window is also used to design prototype filters. The design equations of variable window function based filter banks is also given in this article. Reconstruction error, which is used as an objective function, is minimized b...

The regularity property was first introduced by wavelet theory for octave-band “dyadic” filter banks. In this paper, we provide a detailed theoretical analysis of the regularity property in the more flexible case of filters banks with rational sampling changes. Such filter banks provide a finer analysis on fractions of an octave, and regularity is equally important as in the dyadic case. Sharp ...

B. Wohlberg and C. Brislawn, " Reversible integer-to-integer transforms and symmetric extension of even-length filter banks " , c 2003 Society of Photo-Optical Instrumentation Engineers. This paper will be published in Proceedings VCIP 2003 and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multi...

In the design of two channel perfect reconstruction filter banks, most of the conventional methods optimize the frequency response of each filter to meet the perfect reconstruction condition. However, quantization of the filter coefficients results in some errors in the frequency response, so it is not guaranteed that the perfect reconstruction condition is still satisfied. In this paper, we pr...

We study the design of signal–adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi–infinite programming (SIP) ...

A new approach to implement computationally efficient reconfigurable filter banks for software defined radio receivers is presented in this paper. If the coefficients of a finite impulse response (FIR) filter are decimated by M, i.e., if every M-th coefficient of the filter is kept unchanged and remaining coefficients are replaced by zeros, a multi-band frequency response will be obtained. The ...

In this paper, we consider the design of 2D (two-dimensional) H R (finite impulse response) multirate filter banks. For a given 2D FIR analysis filter bank, we design a 2D FIR synthesis filter bank to minimize the reconstruction error of the filter banks such that the worst case energy gain between the input and the reconstruction error is below a prescribed bound. Our solution is formulated in...