R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Transactions on Signal Processing, vol. 42, no. 9, pp. 2242--2256, September 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....we address the optimal approximation of the ideal filters using FIR filters and a min max reconstruction error criterion. We formulate the design problem as a semi infinite linear program. Semi infinite formulations have been successfully applied to other multirate filter design problems [32, 33] and solved using standard techniques [34] Our FIR filter design formulation is fairly general and can be used to design the interpolation filters for those generalized sampling schemes discussed above. The paper is organized as follows. Section II, contains some basic notation and definitions. ....

R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Sig. Process., vol. 42, no. 9, pp. 2242--2255, September 1994.

....approach may be viewed as a generalization of the Fourier transform in the FR operators framework of Araki, Ito Hagiwara (1993) The idea of lifting in frequency domain is not new; it was developed in the signal processing literature for linear discrete time periodic systems. See for example Shenoy, Burnside Parks (1994). Let y be a signal in the space L 2 (0; 1) Then, it is a fact that its Fourier transform Y(j ) belongs to L 2 ( 1;1) Now, from Y(j ) construct the sequence of functions fY k (j )g k = fY(j( k s ) g k ; 8) for in the Nyquist range Omega N and k integer. Arrange this sequence in an ....

Shenoy, R., Burnside, D. & Parks, T. (1994), `Linear periodic systems and multirate filter design', IEEE Trans. on Signal Processing 42(9), 2242--2256.

....for PR may not be suitable in some applications. It is the goal of synthesis filter banks to satisfy the PR condition. If PR is not possible, then the synthesis filter bank should be designed such that it minimizes certain measure for the reconstruction error that is referred to as model matching [7, 1]. We consider only two channel QMF bank as shown in Figure 1. The analysis filter bank consists of H 0 (z) and H 1 (z) and synthesis filter bank consists of F 0 (z) and F 1 (z) that are restricted to be This research is supported in part by AFOSR, ARO, and LEQSF. 1 causal and stable transfer ....

....The IIR example is compared with its counterpart in [1] Finally our paper is concluded with Section 5. 2 Design of Synthesis Filter Banks with H1 Optimizations In existing literatures, analysis and synthesis filter banks are often designed simultaneously. A new development is the work of [7, 1] where analysis and synthesis filter banks are designed separately. 2 The underlying philosophy is that the analysis filter bank be designed to satisfy the specification in frequency domain required for subband coding, while the synthesis filter bank be designed to satisfy the PR condition. If ....

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R.G. Shenoy, D. Burnside, and T.W Parks, "Linear periodic systems and multirate filter design", IEEE Trans. Signal Processing, Vol. 42, 2242-2256, 1994.

....it minimizes certain measure for the reconstruction error. Therefore an important issue that has been overlooked in the past is the design of synthesis filter bank, for the given analysis filter bank, to meet the required specification for the reconstruction error. This issue was investigated in [15, 1] as a model matching problem where solutions are derived which provide design procedures for synthesis filter banks. In [4] an alternate method is proposed for two channel QMF banks that achieves zero aliasing error, and that provides a more efficient design algorithm with lower order synthesis ....

....input signal x(n) Optimal solutions will be derived and numerical algorithms for computing the optimal synthesis filter banks will be developed. The advantage of our proposed approach is the simplicity and efficiency of the design algorithm, as well as zero aliasing error which is in contrast to [15, 1]. It should be mentioned that our design algorithm is applicable to a class of nonuniform multirate filter banks in light of the results in [3, 6, 8] Moreover our design algorithm can be modified to solve H 2 optimization based design that aims to minimize the squared integral of the transfer ....

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R.G. Shenoy, D. Burnside, and T.W Parks, "Linear periodic systems and multirate filter design", IEEE Transactions on Signal Processing, Vol. 42, pp.2242-2256, 1994.

....changer shown in Figure 1, where m is m F # n u y Figure 1. A sample rate changer. the expander by a factor m, # n the decimator by n, and F a suitable LTI filter. The output sample rate is m=n times the input sample rate. Such rate changers are not only useful in their own right [12], e.g. sample rate conversion for bandlimited signals, they are also fundamental building blocks for multirate filter banks with uniform [13] or nonuniform [10, 6] bands. The rate changer in Figure 1 is in fact a dual rate system with the input output property that shifting the input (u) by n ....

....using the structure in Figure 3 no longer exist. In this case, optimal design based on model matching theH0 : 3; 6) F0 : 6; 3) H1 : 2; 6) F1 : 6; 2) h H2 : 1; 6) F2 : 6; 1) h u y v0 v1 v2 Figure 4. A filter bank with general structures. ory, which was advocated in [12] for multirate filter design and in [2] for uniform filter bank design, can be accomplished with relative ease. 2. GENERAL DUAL RATE SYSTEMS In this section we study basic concepts of linear dual rate systems such as shift invariance, causality, and their various representations. Let be the ....

R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Processing, vol. 42, pp. 2242-2256, 1994.

....changer shown in Figure 1, where m is the ex m F # n u y Figure 1: A sample rate changer. pander by a factor m, # n the decimator by n, and F a suitable LTI filter. The output sample rate is m=n times the input sample rate. Such rate changers are not only useful in their own right [30], e.g. sample rate conversion for bandlimited signals, they are also fundamental building blocks for multirate filter banks with uniform [8, 33] or nonuniform [26, 17] bands. Multirate signal processing has been studied a great deal, see recent books [18, 1, 21, 33, 9, 35, 32] and their ....

....general structures. because four of the six dual rate filters used in Figure 4, H 0 ; H 1 ; F 0 and F 1 , have common factors in their m and n and hence are more general; they allow extra freedom in system design. In this case, optimal design based on model matching theory, which was advocated in [30] for multirate filter design and in [6] for uniform filter bank design, can be accomplished with relative ease detailed discussion to be given later. Briefly, the paper is organized as follows. Section 2 defines precisely what we mean by dual rate systems and studies their fundamental ....

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R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Processing, vol. 42, pp. 2242-2256, 1994.

.... are two ways to describe their frequency responses using matrices: The first one is based on a time domain technique called lifting in control [8] or blocking in signal processing [11] the second one is a frequency domain technique, also independently used in control [7] and signal processing [10]. Though the two techniques are essentially related [9] here we adopt the latter for better insight in the frequency domain. Briefly, the paper is organized as follows. In the next section we discuss a frequencydomain representation for LPTV systems, which is relevant to our studies later. ....

....5 we show the relevance of the work here to an example of LPTV systems in signal processing, namely, the multirate filter bank system used in, e.g. subband coding. Finally, we conclude in Section 5. 2 Frequency Response Matrices We begin with the definition of frequency response matrices from [7, 10]. A continuous time analog of this was introduced in [1] It is convenient to define the exponential signal of frequency f : e f (k) e j2 fk : If H were LTI and stable, the output of H due to this input e f (k) would be H(f)e f (k) H(f) being the frequency response. Now let H denote ....

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R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Processing, vol. 42, pp. 2242-2256, 1994.

....However, the time domain approach in [20] is quite different. Finally, we remark that a different approach for frequency domain modeling of multirate systems is based on alias component matrices; this approach was developed for certain multirate systems involving fractional sampling factors in [25, 24]; see also [23] 3.4 Implementation via Blocking We shall conclude Section 3 by looking at an alternative structure, based on the n Theta n analysis and synthesis matrices, to implement the multirate system T in Figure 1. Recall that the cascaded LTI system S A equals the blocked T , namely, L ....

R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Processing, vol. 42, pp. 2242-2256, 1994.

....the design of nonlinear phase FIR filters with constraints on the group delay. 2. 2 Approximation by Operator Norms Weisburn, Parks, and Shenoy [38] present a rigorous motivation for the use of the Chebyshev and L 2 error measures and discuss the use of zero weighted transition bands (see also [30, 31]) Using the theory of operator norms, they show that best Chebyshev filters minimize a worst case error signal energy, while best L 2 filters minimize a worst case pointwise error in the time domain. However, to show this optimality in the operator norm sense when a zero weighted transition band ....

R. G. Shenoy, D. Burnside, and T. W. Parks. Linear periodic systems and multirate filter design. IEEE Trans. on Acoust., Speech, Signal Proc., 42(9):2242--2256, September 1994.

....theory and, in particular, L 2 induced norm model matching in continuous time has been thoroughly studied (e.g. 3] The optimal model matching approach to multirate filter design was advocated by Shenoy in [17] as was the possibility of using H1 optimization. Shenoy, Burnside, and Parks [18] formulate the problem of 2 induced norm model matching for discrete time periodic systems. They showed that the problem can be converted to a frequency domain one of H1 norm optimization of the alias component matrix of the error system. They also observe that one could equivalently convert to ....

....10 12 10 9 10 6 10 3 10 0 10 3 10 6 0 10 20 30 40 50 60 Figure 18: Hankel singular values oe k versus k for F 0 (z) Example 1 (solid) Example 2 (dash) Example 3 (dot) Acknowledgement The authors are grateful to Dr. Ram Shenoy for helpful discussions and for an advance copy of [18], and to the reviewers for constructive comments. ....

R.G. Shenoy, D. Burnside, and T.W. Parks. Linear periodic systems and multirate filter design. IEEE Trans. Signal Processing, vol. 42, pp. 2242--2256, 1994.

....of v 0 (Nk 1) and v 1 (Nk 1) is permissible. Nevertheless, it is possible to show that the optimizing design can be effected using optimal compaction filters. 7 Concluding Remarks Other interesting applications of H1 optimization in communication problems are to FIR multirate filter design [31], D A conversion [21] and channel equalization [11] A worst case approach to the complete subband coding problem, including quantization, might be an interesting line of research. Multirate filter banks have interesting generalizations. One is a tree structure obtained by iterating on one output ....

R.G. Shenoy, D. Burnside, and T.W. Parks. Linear periodic systems and multirate filter design. IEEE Trans. on Signal Processing, 42:2242--2256, 1994.

....paper are to define several notions of gain of a general linear periodic system, to compare the results with the usual case of a linear time invariant (LTI) filter, and to show the relevance of gain to aliasing, magnitude, and phase distortion in multirate filter banks. This paper is a followup to [6] and [3] In [6] linear periodic systems were studied in the frequency domain by defining a generalized frequency response. Also, several multirate filter design problems were formulated as model matching problems, where the generalized frequency response of an error system is optimized. In [3] ....

....several notions of gain of a general linear periodic system, to compare the results with the usual case of a linear time invariant (LTI) filter, and to show the relevance of gain to aliasing, magnitude, and phase distortion in multirate filter banks. This paper is a followup to [6] and [3] In [6] linear periodic systems were studied in the frequency domain by defining a generalized frequency response. Also, several multirate filter design problems were formulated as model matching problems, where the generalized frequency response of an error system is optimized. In [3] basically the same ....

[Article contains additional citation context not shown here]

R.G. Shenoy, D. Burnside, and T.W. Parks. Linear periodic systems and multirate filter design. IEEE Trans. Signal Processing, vol. 42, pp. 2242-2256, 1994.

....filter banks but is under control in hybrid filter banks since analog filters are incorporated in the design. Norm based optimization is central in modern control theory; see, e.g. 8, 7, 4] Optimal design using the 2 induced norm is also advocated and studied in multirate filter design [11, 12] and digital multirate filter bank design for perfect reconstruction [5] Connections of this paper to these results will be given later at appropriate places. We mention that induced norms are also used to design robust wavelet multiresolution analysis in [6] Finally, the paper is organized as ....

R. G. Shenoy, D. Burnside and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal processing, vol. 42, pp. 2242-2256, 1994.

....to a general class of input signals, 3) usage as a method of comparing LTI designs and PBTV designs, 4) direct interpretation as a measure of system performance, and (5) incorporation of aliasing error. The error criterion we propose is the 2 norm of the PBTV operator which satisfies (1) 5) [7]. In particular, the 2 norm criterion arises from the interpretation of the Chebyshev criterion for LTI system design as the relative 2 (Z) error for the model matching problem [7, 8] Since the 2 norm applies to any linear system, 3) and (4) are directly satisfied. Additionally, the ....

....of aliasing error. The error criterion we propose is the 2 norm of the PBTV operator which satisfies (1) 5) 7] In particular, the 2 norm criterion arises from the interpretation of the Chebyshev criterion for LTI system design as the relative 2 (Z) error for the model matching problem [7, 8]. Since the 2 norm applies to any linear system, 3) and (4) are directly satisfied. Additionally, the criterion has a natural interpretation in terms of aliasing since the alias components of the commutator form filters appear in the error criterion. The starting point for the analysis of the ....

R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Processing, vol. 42, pp. 2242--2256, Sept. 1994.

....multirate systems. If little is known about the class of inputs, a general approach is preferrable. In order to address this concern, we explore the 2 operator norm as a criterion for the design of these systems. This error criterion was recently examined for general multirate systems design [6, 7] and has been used for the design of decimators and interpolators [7] we analyze its application to rate changing systems. This error measure also appears in control theory [8] where it is used for control related design; H1 optimization methods have recently been applied to the design of ....

....approach is preferrable. In order to address this concern, we explore the 2 operator norm as a criterion for the design of these systems. This error criterion was recently examined for general multirate systems design [6, 7] and has been used for the design of decimators and interpolators [7]; we analyze its application to rate changing systems. This error measure also appears in control theory [8] where it is used for control related design; H1 optimization methods have recently been applied to the design of multirate filter banks [9] Our design method is different and is based upon ....

R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Processing, vol. 42, pp. 2242--2256, Sept. 1994.

No context found.

R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Transactions on Signal Processing, vol. 42, no. 9, pp. 2242--2256, September 1994.

No context found.

R. G. Shenoy, D. Burnside and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Processing, vol. 42, pp. 22422256, 1994.

No context found.

R.G. Shenoy, D. Burnside, and T.W. Parks. Linear periodic systems and multirate filter design. IEEE Trans. Signal Processing, vol. 42, pp. 2242-2256, 1994.

No context found.

R.G. Shenoy, D. Burnside, and T.W. Parks. Linear periodic systems and multirate filter design. IEEE Trans. Signal Processing, vol. 42, pp. 2242-2256, 1994.

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