A new realization of 2-D adaptive separable-denominator state-space filters based on DLMS algorithm suitable for parallel processing

https://doi.org/10.1016/j.jfranklin.2004.04.002Get rights and content

Abstract

In the application of 2-D adaptive filters, a large amount of data must be processed and real-time processing is often required. In this paper, a new parallel-form realization of 2-D adaptive separable-denominator state-space filters suitable for high-speed processing is proposed. First, the 2-D local state-space model suitable for parallel processing is introduced. Next, the adaptive algorithm for this model is developed. This algorithm is based on the delayed least mean square (DLMS) method. In addition, the computation time required for the update of the coefficients is investigated. Finally, the proposed technique is applied to the design of 2-D digital filters in the spatial domain.

Introduction

An adaptive filter has been applied to various fields of signal processing, such as echo canceller, system identification and adaptive equalizer. Nowadays, it also has been extended to process multi-dimensional signals for the purpose of the noise reduction of image data, multi-dimensional system identification and multi-dimensional digital filter design, which results that multi-dimensional adaptive filters have been proposed and their researches are getting more popular [8], [10], [11], [12]. One concern, however, is that a multi-dimensional adaptive filter not only has to process a large amount of data, like an image, but sometimes has to perform real-time processing to handle such large data. Therefore, high-speed processing should be required for high-dimensional adaptive filters. One of the ideas for that is to apply the parallel processing structure of adaptive filters.

For 2-D digital filters, several methods suitable for the parallel processing have been proposed [1], [2]. Besides, we have some studies on 2-D adaptive filters suitable for the parallel processing where 2-D digital filter for parallel processing is applied to the structure of 2-D adaptive filters [3], [4], [5] and also extended to 3-D case [6].

This paper proposes a new parallel-form realization of a 2-D adaptive filter based on the Roesser local state-space model with separable denominator. The DLMS algorithm [7] is adopted as an adaptive algorithm in this realization. The class of separable denominator is one of the most important classes, since almost frequency specification can be implemented. The effective parallel form realization can also be achieved. However, such realizations by the general local state-space model are difficult because of its complicated feedback structure.

At first, the parallel-form realization of a 2-D digital filter with separable denominator proposed by Dabbagh and Alexander [1] is brought up for consideration. Then, a new adaptive algorithm is introduced by the combination of the DLMS algorithm and the adaptive algorithm for a 2-D state-space digital filter with separable denominator [8]. The computational time required for the filtering and the coefficient update is also evaluated to prove that the use of the DLMS algorithm leads a faster algorithm than the algorithms reported in [3], [4]. Finally, the effectiveness of the proposed technique is confirmed by applying it to 2-D digital filter design in the spatial domain.

Section snippets

Parallel implementation of 2-D state-space filters with separable denominator

In this section, the parallel-form implementation of 2-D state-space filter with separable denominator reported in [5] is introduced to be prepared for deriving the corresponding adaptive algorithm [9].

Consider the following irreducible 2-D separable-denominator transfer function:H(z1,z2)=N(z1,z2)D1(z1,z2)D2(z1,z2),whereN(z1,z2)=i=0Mj=0Nbijz1iz2j,D1(z1)=i=0Mαiz1i,D2(z2)=j=0Nβjz2j,αMN=1.

The 2-D separable denominator transfer function expressed in Eq. (1) can be represented byH(z1,z2)=i=0M

Adaptive algorithm and its evaluation

In this section, an adaptive algorithm derived from the DLMS algorithm and the corresponding computational time is estimated in order to show the effect of the parallel processing.

Simulation

To demonstrate the effectiveness of the proposed algorithm, we have carried out the simulation applied to 2-D digital filter design in the spatial domain.

The unit sample response of the Gaussian filter is given by the following equation:r(n1,n2)=0.256322exp[−0.103203{(n1−4)2+(n2−4)2}](n1,n2)∈Sh,whereSh={(n1,n2)|0⩽n1⩽10;0⩽n2⩽10}.The order of the filter was chosen as M=N=3, and the input signal was assumed to beu(n1,n2)=1(n1=n2=0),0(otherwise).The step-size parameter was chosen to be μ=0.0007 and

Conclusion

The new parallel-form realization of 2-D adaptive filters, based on the Roesser local state-space model with separable denominator, has been proposed. The DLMS method has been applied to implement the adaptive algorithm and proved out to reduce the minimum computation time for each input. The proposed adaptive filter has been developed by combining the parallel-form realization with the adaptive algorithm for 2-D separable-denominator digital filters. Also, the computational time required for

References (12)

  • M. Muneyasu et al.

    A 2-D cascade-parallel adaptive IIR filter using backpropagation method

    J. Franklin Institute

    (1996)
  • M.Y. Dabbagh et al.

    Multiprocessor implementation of 2-D denominator-separable digital filters for real-time processing

    IEEE Trans. Acoust. Speech Signal Process.

    (1989)
  • T. Hinamoto et al.

    Realization of 2-D separable-denominator digital filters for real-time and parallel processing

    Trans. IEICE, J74-A

    (1991)
  • M. Muneyasu et al.

    Parallel-from realization of 2-D adaptive separable-denominator state-space filters

    Trans. IEICE J77-A

    (1994)
  • M. Muneyasu, N. Ishizaki, T. Hinamoto, A realization of 2-D adaptive separable-denominator state-space filters for...
  • M. Muneyasu, N. Ishizaki, T. Hinamoto, A realization of 3-D adaptive separable-denominator state-space filters for...
There are more references available in the full text version of this article.

Cited by (3)

  • Design of M-channel cosine modulated filter bank using modified Exponential window

    2012, Journal of the Franklin Institute
    Citation Excerpt :

    However, in some applications such as video processing and communication systems, linear-phase finite impulse response (FIR) filters are used for designing the multirate systems. Three most common methods used for designing FIR filters are windowing, frequency sampling and optimum equiripple filter design technique [7,9,10]. Window technique is most straightforward and commonly used in designing multirate filter banks as the window functions possess the closed form expressions which reduce the computational complexity [9].

  • A simple design method for the cosine-modulated filter banks using weighted constrained least square technique

    2011, Journal of the Franklin Institute
    Citation Excerpt :

    Initially, the concept of sub-band coding was used in speech coding; now, it is being used in several other fields. Among all the filter banks, the cosine-modulated filter bank (CMFB) is one of the most frequently used filter banks in audio coding [28–30], adaptive signal processing [31,32], and ECG signal processing [33–36], because of its matching properties of the analysis filter bank to the characteristics of the input signal. In ECG signal processing, CMFB filter banks are used in several applications such as beat detection, signal enhancement, beat classification, and compression.

  • QMF bank design with Cosh-Hamming window

    2015, 2015 23rd Signal Processing and Communications Applications Conference, SIU 2015 - Proceedings

The results in this paper were partially presented at the 1998 IEEE International Workshop on Intelligent Signal Processing and Communication Systems.

View full text