Digital Signal Processing

Proceedings of 1994 37th Midwest Symposium on Circuits and Systems

New systolic and semi-systolic implementations of polyphase FIR and IIR decimators and interpolators with integer/fractional compression/expansion factors are derived using an algebraic mapping technique. The control signals necessary to implement the polyphase structures are explicitly identified. The new structures have the advantages of being modular, regular, hierarchical, and pipelined.

1999

Recently, most DSP systems have used multirate signal processing techniques or transforms for reducing computational complexity without compromising the system quality. In these techniques, realizing each constant separately is a redundant process as some constants appear more than once, and increases area and power consumption of the system. This paper introduces the concept of handling all coefficients in the system at the same time. To do this, the two-term expressions of constants in a system for adder and shifter minimization is presented.

IEE Proceedings - Circuits, Devices and Systems, 1994

An algebraic technique for mapping FIR decimator and interpolator algorithms with integer compression/expansion factors on systolic and semisystolic structures is described. The technique is based on the time-domain representation of the algorithms. The advantages of this technique are that it is suitable for describing multirate algorithms and that the required arithmetic operations are explicitly stated. Applying the algebriac technique, various structures can be obtained in which the number of multipliers is reduced in proportion to the decimation or interpolation factor. Pipelining can be introduced at the input and/or the output. An example is given to illustrate the flexibility and simplicity of the proposed technique.

1989

Multidimensional Systems and Signal Processing, 2004

In this paper we present a new and numerically efficient technique for designing 2-D linear phase octagonally symmetric digital filters using Schur decomposition method (SDM) and the diagonal symmetry of the 2-D impulse response specifications. This technique is based on two steps. First, the 2-D impulse response matrix is decomposed into a parallel realization of k sections, each comprising two cascaded linear phase SISO 1-D FIR digital filters. It is shown that using the symmetry property of the 2-D impulse response matrix and the fact that the left and right eigenspaces obtained by SDM are transpose of each other, the design problem of two 1-D digital filters is reduced to the design problem of only one 1-D digital filter in each section. In the second step, the 2-D linear phase FIR filter is converted to 2-D IIR filter. This is done by converting the constituent N-order 1-D FIR filters to an n-order IIR filters, where n < N using the given model reduction algorithm. The reduced order IIR filters are obtained without computing the balancing transformation, but by finding the orthonormal eigenspaces associated with the largest eigenvalues of the cross-Gramian matrix W CO. Two design examples are given to illustrate the advantages of the proposed technique.

2005

This thesis studies the structures, design procedures and implementations of FIR perfect-reconstruction digital filter banks. The first part of the thesis deals with the structures and the design procedures of the perfect-reconstruction filter banks where the polyphase transfer matrices are lossless. These structures are parameterized by a set of rotation angles [37]. The usual procedure is to blindly optimize these angles to minimize an objective function where the objective function consists of all the stopband energies of the filters which we would like to design. This procedure is very time-consuming because of the nonlinear objective function and the large number of parameters to be optimized. The pairwise-symmetry property is imposed on these perfect reconstruction systems as a means of decreasing the number of parameters (rotation angles). The pairwise-symmetric property together with a method to initialize these rotation angles gives a very efficient design procedure. Design...

2001

A digital signal processing based on a representation over various algebraic systems is discussed. Theorems of spectral decomposition of a multiple-valued function are formulated. Examples of the function decomposition are given. i i a i t t f

Eastern-European Journal of Enterprise Technologies, 2020

IEEE Transactions on Signal Processing, 2000

A matrix theory is developed for the noncausal polyphase representation that underlies the theory of lifted filter banks and wavelet transforms. The theory presented here develops an extensive matrix algebra framework for analyzing and implementing linear phase twochannel filter banks via lifting cascade schemes. Whole-sample symmetric and half-sample symmetric linear phase filter banks are characterized completely in terms of the polyphasewith-advance representation, and new proofs are given of linear phase lifting factorization theorems for these two principal classes of linear phase filter banks. The theory benefits significantly from a number of group-theoretic structures arising in the polyphase-withadvance representation and in the lifting factorization of linear phase filter banks. These results form the foundations of the lifting methodology employed in Part 2 of the ISO/IEC JPEG 2000 still image coding standard. DRAFT 3 and the existence and specific form of the linear phase factors for whole-sample symmetric and half-sample symmetric filter banks are derived in Sections V and VI. A. Comparison to Prior Work The theory of lifted filter banks originated with Bruekers and van den Enden [14] and was subsequently rediscovered in the context of wavelet transforms and extensively developed by Sweldens and collaborators [15], [16], [17], [18]. While lifting structures have been used by some authors (e.g., [19]) as parameter spaces for numerical filter bank design, the present paper deals with the problem of factoring a given linear phase filter bank into linear phase lifting steps of prescribed form, following the definition of lifting presented by Daubechies and Sweldens [17]. This covers the situation created by the JPEG 2000 standard, which allows users to employ filter banks designed by any method (e.g., the structures introduced in [20]), provided their implementation is specified in terms of a lifting factorization. The existence of factorizations with linear phase lifting steps is also exploited by efficient hardware implementations of lifted wavelet transforms [21]. Recent work on filter bank design has focused on M-channel systems, including linear phase systems [22], [23], [24] and lifting structures for M-channel filter banks and regular Mband wavelets [25], [26]. In particular, several papers have combined lifting with other lattice structures that structurally enforce linear phase [27], [28], [29]. In [23], linear phase matrices were decomposed into first-order polyphase factors, G i (z), having the form

Research Letters in Signal …, 2007

A novel realization of IIR decimation filters is proposed which is based on merged delay transformation. The transformation is derived analytically and can be applied directly to first-and second-order IIR filters. Computational efficiency is enhanced because the current output can be directly computed from Mth old output. The output data rate is decreased by M by merging M number of delay elements in the recursive path. The proposed transformation is applied to higher-order IIR filter by decomposing it into parallel first-order and second-order sections. This transformation not only gives better stability for coefficient quantization but also reduces the requirement on processing clock, for sample, rate reduction. Filtering and down sampling are performed in the same stage. Number of multiplications is reduced by 45% as compared to the conventional IIR filters where all output samples are computed.