P. P. Vaidyanathan, Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property, IEEE Trans. Acoust. Speech Signal Processing 35 (1987) 476--492.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....MA 02215 USA. S. R Broadstone is with Teratech Corporation, Burlington, MA 01803 USA. Publisher Item Identifier S 1053 587X(98)02607 5. Fig. 1. M channel, maximally decimated, parallel, filter bank. theory for perfect reconstruction (PR) nonhybrid filter banks has recently been established [4] [7] Using a filter bank for analog to digital (A D) or digital toanalog (D A) conversion is an unconventional application of the filter bank architecture that improves the speed and resolution of the conversion over the standard time interleaved array conversion technique. The hybrid filter ....

P. P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M; having perfect reconstruction property," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 476--492, Apr. 1987.

....as the product of order one paraunitary matrices. From (9) with arbitrary unitary matrices , the order of cannot be higher than . Therefore, we can use these structures to design filterbanks with constrained filter length. In fact, the structure of (9) was used in the design of paraunitary system [27]. This order one form is more suitable than the degree one form when the filter length is constrained. In the rest of this subsection, we will show that any causal FIR paraunitary matrix of order can be factorized into the form of (9) Given a causal FIR paraunitary matrix , it can be expressed ....

P. P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M , having perfect reconstruction property," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 476--492, Apr. 1987.

.... (12) go(z) diag(Go(z) G(z) 6k, 2o ( 0 a ( GM (Z) 13) N I ( l)k) 5) 14) Using the above E(z) and R(z) one obtains the expression for P(z) B(z)E(z) as follows: o( P) P(z) z l)0( z 2) gl( z ) C C(z lgl( z2) 15) For a PR filter bank, P(z) must have the form [10] (0 z It ) 16) P(z) z ( i 2 0 where v is a positive integer, and the dimensions of I and 12 add to M. Our objective is to simplify (15) in order to obtain 476 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL, 44, NO. 3, MARCH t996 the necessary and sufficient conditions on 9(z) g = 0, 1 for ....

.... bank (where N = 2rM [15] can be parametrized using the lattice coefficients, a possible approach is to optimize these lattice coefficients to minimize the stopband error T of H(e ) only the stopband of H(e ) is needed in the objective function since the filter bank satisfies the PC properties [10]) The drawback of the lattice approach is that the cost function T is a highly nonlinear function with respect to the lattice coefficients [15] Consequently, PR filter banks, where the analysis filters have high stopband altenuation, are difficult to obtain. Instead of optimizing in the lattice ....

P. P. Vaidyanathan, "Theory, and design of M-channel maximally decimated quadrature rain-or filters with arbitrary M, having perfect reconstruction property," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 476-492, Apr. 1987.

....paraunitary 5 matrices. From eq. 9) with arbitrary unitary matrices U k , the order of E(z) can not be higher than K 1. Therefore we can use these structures to design lter banks with constrained lter length. In fact, the structure of (9) was used in the design of paraunitary system [26]. This orderone form is more suitable than the degree one form when the lter length is constrained. In the rest of this subsection, we will show that any causal FIR paraunitary matrix E(z) of order K 1 can be factorized into the form of (9) Given a causal FIR paraunitary matrix E(z) it can be ....

P. P. Vaidyanathan, \Theory and design of M-channel maximally decimated quadrature mirror lters with arbitrary M, having perfect reconstruction property," IEEE Trans. Acoustics, Speech, and Signal Processing, Vol.35, No.4, pp. 476-492, 1987.

....of compactly supported wavelets originated both from mathematical analysis and the signal processing community. The roots of critically sampled wavelet transforms are actually older than the word wavelet and go back to the context of subband filters, or more precisely quadrature mirror filters [36, 37, 41, 51, 52, 53, 54, 58, 56, 59]. In mathematical analysis, wavelets were defined as translates and dilates of one fixed function and were used to both analyze and represent general functions. 15, 20, 25, 35, 24] In the late eighties the introduction of multiresolution analysis and the fast wavelet transform by Mallat and ....

P. P. Vaidyanathan. Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having perfect reconstruction property. IEEE Trans. Acoust. Speech Signal Process., 35(2):476-- 492, 1987.

.... developed [46] Perfect reconstruction in two band FIR banks can be achieved using the conjugate quadrature filters (CQF) introduced in [218] CQF filters can be easily designed from Kaiser windows [151] The general formulation for M band perfect reconstruction filter banks was introduced in [261], using paraunitary polyphase matrices. A similar formulation, based on alias cancellation matrices, was presented in [277] Cosine Modulated Banks One practical problem with the filter banks in Fig. 1 is that the computational complexity grows linearly with the number of subbands, M. If the ....

P.P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect reconstruction property," IEEE Trans. Acoust., Speech, Signal Processing, vol. 35, no. 4, pp. 476-492, Apr. 1987.

....Also, they help in understanding the fundamental algebraic structure of PR filter banks. Using factorization, a higher order filter bank is achieved by adding an extra element to a lower order bank. Such a lattice type structure was considered to characterize all M channel paraunitary filter banks [1]. Partial results on factorization of general PR filter banks have been recently reported where, although the proposed factorization characterizes a large class of PR filter banks, it lacks completeness [2] Such structures have also been proposed for the bi orthogonal linear phase filters [3] ....

P. P. Vaidyanathan, "Theory and design of M channel maximally decimated QMF with arbitrary M , having perfect reconstruction property," IEEE Trans. on ASSP, No. 4, April 1987.

.... Mallat s algorithm [5] 6] 7] Both orthogonal and biorthogonal wavelet bases correspond to perfect reconstruct filter banks (PRFBs) Research on wavelets mainly concerns real valued wavelet bases and filter banks as is evident by a large number of publications on the subject [5] 6] 7] [8], 9] 10] 11] 12] 13] 14] However, complex wavelet bases and filter banks have been seldom discussed. Both the continuous wavelet transform (CWT) and Fourier transform are defined for signals that are complex as well as real. The basis functions of the Fourier transform are the complex ....

P. P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M , having perfect reconstruction properties," IEEE Trans. ASSP, vol. 35, no. 4, pp. 476--492, Apr. 1987.

....index samples) see figure 1. The reconstruction consists of upsampling ( 2) i.e. adding a zero between every two samples) followed by filtering and addition. One can show that the conditions (24) correspond to the exact reconstruction of a subband coding scheme. More details can be found in [96, 108, 109, 110]. An interesting problem is: given a function f , determine, with a certain accuracy and in a computationally favorable way, the coefficients n;l of a function in the space Vn which are needed to start the fast wavelet transform. A trivial solution could be n;l = f(l=2 n ) Other sampling ....

P. P. Vaidyanathan. Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having perfect reconstruction property. IEEE Trans. on Acoust. Signal Speech Process., 36:476--492, 1987.

....filter bank shown in Figure 7 was introduced in the early 1980 s. It has only two channels. These 2 channel PRFBs have been studied and characterized thoroughly with many different design methods based on spectral factorization [50] 74] 35] lattice structure [96] 53] 101] [97], time domain optimization [51] quadratic constrained least squares (QCLS) optimization [55] Lagrange multiplier approaches [26] ect. x[n] 0 p p 2 w F (z) 0 1 F (z) H (z) 0 1 H (z) H (z) 0 2 2 F (z) 0 2 1 F (z) 1 H (z) 2 x[n] Figure 7: A typical two channel filter bank. 21 The ....

P. P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having perfect reconstruction property," IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. 35, pp. 476-492, Apr. 1987.

....on Image Processing, 1999 INTRODUCTION Over the last decade several constructions of compactly supported wavelets have originated both from signal processing and mathematical analysis. In signal processing, critically sampled wavelet transforms are known as filter banks or subband transforms [34, 44, 55, 57]. In mathematical analysis, wavelets are defined as translates and dilates of one fixed function and are used to analyze and represent general functions [23, 33] Multiresolution analysis provided the connection between filter banks and wavelets [30, 33] This lead to the construction of smooth, ....

P. P. Vaidyanathan. Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having perfect reconstruction property. IEEE Trans. Acoust. Speech Signal Process., 35(2):476--492, 1987.

.... is given in Figure 1(b) One of the easiest ways to achieve perfect reconstruction (i.e. to obtain the output as a perfect replica of the input) is to construct a paraunitary analysis matrix (or orthogonal, lossless) In other words, the analysis polyphase matrix has to satisfy the following [11] H t p (z Gamma1 ) Delta H p (z) I: 3) Then the synthesis polyphase matrix can be chosen as z Gammak H t p (z Gamma1 ) which in turn yields filters that are the same as the analysis filters (within shift reversal) Let us also point out some facts on multirate filtering that are ....

....Indirect Method versus Partial Solution Case 1: As the first step let us construct such a filter bank indirectly (see Figure 4(a) Thus a 3 channel analysis filter bank and a 2 channel synthesis bank are needed. We use optimized lossless filter banks that already appeared in the literature in [11] and [14] Since both banks are orthogonal the resulting filter bank is going to be orthogonal as well. To prove this fact, after some manipulations, the equivalent polyphase matrix becomes G p (z) 1 H p (z) 39) where H p (z) G p (z) are the 3 Theta 3 analysis and 2 Theta 2 synthesis ....

[Article contains additional citation context not shown here]

P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect reconstruction property," IEEE Trans. Acoust., Speech, and Signal Proc., vol. 35, pp. 476--492, April 1987.

....moduated, via a transform (such as a DCT) to create the bank. These filter banks are typically very efficient computationally because fast transforms algorithms are generally employed. There have been many contributions in the literature focusing on various aspects of the design problem [1] [2], 5] 6] 7] In this paper, a new formulation is introduced that attempts to provide a broader range of design flexibility than reported previously while maintaining a simple and compact framework. The new formulation allows for the design of a variety of efficient modulated filter banks with ....

P.P. Vaidyanathan:" Theory and Design of M-channel Maximally Decimated Quadrature Mirror Filters with Arbitrary M, having the Perfect-Reconstruction Property", Trans. ASSP, April, 1987, pp.476-492.

....filter bank. The theory of two channel orthogonal filter banks and the corresponding lattice structure are reported by Smith and Barnwell [1] Ramstad [2] and Vaidyanathan [3] respectively. The generalization to M channel paraunitary filter bank is reported by Vetterli [4] and Vaidyanathan [5]. Two channel orthogonal system cannot have linearphase except in a simple structure (sum and difference of two delays) In order to obtain filter banks with linearphase, orthogonal property must be sacrified which leads to the discovery of two channel biorthogonal linear phase filter banks [6, 8, ....

Vaidyanathan, P. P., "Theory and design of M-channel maximally decimated quadrature mirror filter wth arbitrary M, having perfect reconstruction property," IEEE Trans. on ASSP, pp. 476-492, April 87.

....and subband coding were made by Crochiere, Webber, and Flanagan [12] and Croisier, Esteban, and Galand [13] and others. Later, perfect reconstruction filter banks were studied in depth by many, with major contributions by Mintzer [31] Smith and Barnwell [43] Vetterli [55] and Vaidyanathan [53]. Wavelet transforms have proven to be extremely useful for image coding as many have shown (e.g. 6] 27] 9] Consequently, many image compression schemes have adopted the use of such transforms. In 1993, Shapiro [41] first introduced the notion of embedded coding. His coding scheme, called ....

P. P. Vaidyanathan. Theory and design of m-channel maximally decimated quadrature mirror filters with arbitrary m, having the perfect-reconstruction property. IEEE Transactions on Acoustics, Speech, and Signal Proceesing, 35(4):476--492, April 1987.

....i and then T (z) S(z) A(z) The transfer matrix T (z) serves as a frequency domain model for the general multirate system in Figure 1. The analysis and synthesis matrices A(z) and S(z) can be regarded as generalization of the polyphase representation matrices for uniform filter banks [29, 26]. Since we assumed that p i and q i are coprime, there exist one to one correspondences between A and fH i g and between S and fF i g (Lemma 5) In [14] nonuniform filter banks are studied by converting them into uniform filter banks via block diagram manipulations. The frequency domain model ....

P. P. Vaidyanathan, "Theory and design of M-channel maximally decimated Quadrature mirror filters with arbitrary M , having the perfect-reconstruction property," IEEE Trans. Acoustics, Speech, Signal Processing, vol. 35, no. 4, pp. 476-492, 1987.

....filtered signal. Under certain conditions, the original signal can be reconstructed exactly from this decimated M band representation. The ideas leading to the perfect reconstruction conditions were discovered in stages by a number of investigators, including Croisier et al. 16] Vaidyanathan [17], Smith and Barnwell [18, 19] and Vetterli [20, 21] For a detailed presentation of these developments, we refer the reader to the comprehensive texts by Vaidyanathan [22] and Vetterli and Kovacevic [23] We have seen in our discussion of quantization strategies that we need to decorrelate pixels ....

P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having perfect reconstruction property," IEEE Trans. ASSP, vol. ASSP-35, pp. 476-- 492, April 1987.

....to IEEE Transactions on Image Processing Over the last decade several constructions of compactly supported wavelets have originated both from signal processing and mathematical analysis. In signal processing, critically sampled wavelet transforms are known as filter banks or subband transforms [32, 43, 54, 56]. In mathematical analysis, wavelets are defined as translates and dilates of one fixed function and are used to analyze and represent general functions [23, 31] Multiresolution analysis provided the connection between filter banks and wavelets [28, 31] This lead to the construction of smooth, ....

P. P. Vaidyanathan. Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having perfect reconstruction property. IEEE Trans. Acoust. Speech Signal Process., 35(2):476-- 492, 1987.

No context found.

P. P. Vaidyanathan, Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property, IEEE Trans. Acoust. Speech Signal Processing 35 (1987) 476--492.

No context found.

P. P. Vaidyanathan, "Theory and Design of M Channel Maximally Decimated QMF with Arbitrary M, having Perfect Reconstruction Property," IEEE Trans. on Acoustics, Speech, and Signal Processing, April 1987.

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P.P. Vaidyanathan, ;;Theory and Design of M-Channel Maximally Decimated Quadrature Mirror Filters with Arbitrary M, Having Perfect Reconstruction Property," IEEE Trans. on ASSP, vol. ASSP-35, pp. 476-492, April 1987.

No context found.

P. P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property," IEEE Trans. Acoust., Speech,and Signal Proc., Vol. 35, No. 4, pp. 476-492, 1987.

No context found.

P.P. Vaidyanathan, "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M , having perfect reconstruction property", IEEE Transactions on Acoustics, Speech and Signal Processing, Vol.ASSP-35, pp.476-492, April 1987.

No context found.

Vaidyanathan, P. P., "Theory and design of M-channel maximally decimated quadrature mirror filter with arbitrary M, having perfect-reconstruction property," IEEE Trans. on ASSP, pp. 476-492, April 87.

No context found.

Vaidyanathan, P. P., "Theory and Design of M-Channel Maximally Decimated Quadrature Mirror Filter with Arbitrary M, Having Perfect-Reconstruction Property," IEEE Trans. on ASSP, pp. 476-492, April 87.

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