K. Nayebi, T. P. Barnwell, and M. J. T. Smith, Nonuniform Filter banks: a reconstruction and design theory, IEEE Trans. Signal Proc., vol. 41, June 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....PR nonuniform FB. This is done by using ideal complex brickwall analysis and synthesis filters with bandwidths inversely proportional to the decimation factors, as shown in Fig. 3. With realizable filters, we can achieve approximate or near perfect reconstruction in several ways, as is shown in [3, 4] and in references therein. A more general situation where the decimators could be fractional has been considered in [5] However many theoretical issues involved in obtaining exact reconstruction remain unresolved even when the decimators are integers. These issues do not arise if near PR ....

K.Nayebi, T.P.Barnwell,III, and M.Smith, "Nonuniform Filter Banks: A Reconstruction and Design Theory, " IEEE Trans. SP, pp. 1114-1127, Mar. 1993.

.... decompositions with partial subband combinations [2, 3] the so called direct method where upsampling preceeds the standard multirate FB operation [3] the concept of compatible sets where the FB structure is again direct but all decimation ratios are of the form 1 n, and timedomain approaches [4]. Problems with those constructions are with the non realizability of arbitrary combinations of decimation factors. Other researchers propose structures restricted to the 2 band FB case [5] Our new approach offers realizable structures for arbitrary 1 p or p q split schemes in terms of ideal ....

....complexity is not increased by much. 5. Extension to the General Case In general the decimation factors are allowed to be of the form p q, p q N. This leads to splits (p 0 q 0 , p 1 q 1 , pL 1 q L 1 ) where we additionally require #=0 p # q # = 1. Using a trick from [4] we transform the p q construction to the above 1 n construction. More precisely, the following holds: Theorem 3 Consider a (p 0 q 0 , pL 1 q L 1 ) split, P : lcm(p 0 , pL 1 ) and Q : lcm(q 0 , q L 1 ) For 0 # L, p # q # N, q # : P p # , p # : # 1 ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Nonuniform filter banks: A reconstruction and design theory. IEEE Trans. SP, 41(3):1114--1127, March 1993.

.... 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 function of the error system. H z ( H ( z ) z ( H 0 1 M 1 ) 0 z ( z 1 ) z ( M 1 F F F e(n) x(n) x(n) M M M M M M T id ( z ) c x(n d) c ....

K. Nayebi, T.P. Barnwell, and M.J.T. Smith, "Nonuniform filter banks: a reconstruction and design theory", IEEE Transactions on Signal Processing, Vol.41, pp.1114-1127, 1993. 17

....Possible design objectives of filter banks and an illustration of the design objectives of a single low pass filter. 0; p ] is the pass band; s ; the stop band; p ; s ] the transition band. designs, and all existing PR LP designs in signal processing are based on real coefficients [1, 10, 24, 12]. In a general two band filter bank, the reconstructed signal is: X(z) X(z) 2 [H 0 (z)F 0 (z) H 1 (z)F 1 (z) 1) X( Gammaz) 2 [H 0 ( Gammaz)F 0 (z) H 1 ( Gammaz)F 1 (z) where X(z) is the original signal, and H i (z) and F i (z) are, respectively, the response of the analysis and ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Nonuniform filter banks: A reconstruction and design theory. IEEE Trans. on Signal Processing, 41(3):1114--1127, March 1993.

....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 samples results in shifting the output (y) by m samples. Such a property is defined as (m;n) shift invariance, which is a generalization of time invariance for ....

....the system achieves perfect reconstruction with time delay z Gamma6 . The synthesis matrix in (4) corresponds to some general dualrate structures in Figure 8. The above observation can be generalized to nonuniform multirate filter banks with multiple channels and arbitrary decimation ratios [10, 6]: If the synthesis subsystems are replaced by appropriate dual rate structures, incompatibility [4] and structural dependency [6, 1] disappear; and perfect reconstruction is always possible. One advantage of eliminating structural dependency is to allow optimal design of synthesis systems; we ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, "Nonuniform filter banks: a reconstruction and design theory," IEEE Trans. Signal Processing, vol. 41, no. 3, pp. 1114-1127, 1993.

....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 references. 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 samples results in shifting the output (y) ....

....in (24) and hence does not give rise to the traditional synthesis structure in Figure 3; it corresponds to some general dual rate structures in Figure 12. The above observation can be generalized to nonuniform multirate filter banks with multiple channels and arbitrary fractional decimation ratios [26, 17, 5]: If the synthesis subsystems are replaced by appropriate dual rate structures, incompatibility [13] and structural dependency [17, 5] disappear; and perfect reconstruction is always possible. One advantage of eliminating structural dependency is to allow optimal design of synthesis systems; we ....

K. Nayebi, T. P. Barnwell, III, and M. J. T. Smith, "Nonuniform filter banks: a reconstruction and design theory," IEEE Trans. Signal Processing, vol. 41, no. 3, pp. 1114-1127, 1993.

....In the past few years the design of nonuniform filter banks has gained much attention for applications in multiresolution spectral analysis and speech coding systems. The analysis of multirate nonuniform filter banks has been intensively studied and various design theories have been proposed [5, 8, 9, 10, 11]. Although the principal design issues like perfect reconstruction properties and selection of subsampling factors have been investigated in detail, the problem of finding the coefficients of the analysis and synthesis filter bank stages is still under debate. This is due to the fact that ....

K. Nayebi, T. B. Barnwell, III, M. J. T. Smith, "Nonuniform Filter Banks: A Reconstruction and Design Theory", IEEE Trans. Signal Processing, Vol. 41, March 1993, pp. 1114-1127.

.... filter banks are especially useful in digital audio [5, 27] Perfect reconstruction nonuniform filter banks were studied before: Hoang and Vaidyanathan [9] treated a nonuniform system and gave a necessary condition for cases in which alias cancellation is impossible to achieve; Nayebi et al. [20] developed a time domain design approach for FIR filters; Kovacevi c and Vetterli [14] accomplished design of nonuniform filter banks by transforming them into uniform systems; finally, Liu and Bruton [16] treated perfect reconstruction in a somewhat different setup involving certain modulators. ....

....them into uniform filter banks via block diagram manipulations. The frequency domain model derived here amounts to accomplish the same but uses only matrix manipulations. One can perhaps argue that the method in this paper is more systematical and concise. 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 ....

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K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, "Nonuniform filter banks: a reconstruction and design theory," IEEE Trans. Signal Processing, vol. 41, no. 3, pp. 1114-1127, 1993.

....play a dominant role at some point. Now some words on the literature. Vaidyanathan s book [19] gives a comprehensive treatment of multirate filter banks, with a detailed historical survey of the literature up to 1992. The subject is a very active one at present: In references [1] 6] 7] [11], 12] and [13] the constraint of perfect reconstruction is placed on the system; in [5] and [15] this is relaxed to a weaker constraint (nearly allpass system with small aliasing) The idea of optimal model matching is central in modern control theory and, in particular, L 2 induced norm ....

K. Nayebi, T.P. Barnwell III, and M.J.T. Smith. Nonuniform filter banks: a reconstruction and design theory. IEEE Trans. Signal Processing, vol. 41, pp. 1114--1127, 1993.

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K. Nayebi, T. P. Barnwell, and M. J. T. Smith, Nonuniform Filter banks: a reconstruction and design theory, IEEE Trans. Signal Proc., vol. 41, June 1993.

No context found.

K. Nayebi, T. P. Barnwell, and M. J. T. Smith, "Nonuniform filter banks: A reconstruction and design theory," IEEE Trans. Signal Processing, vol. 41, no. 3, pp. 1114--1127, Mar. 1993.

No context found.

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, "Nonuniform filter banks: A reconstruction and design theory," IEEE Trans. on Signal Processing, vol. 41, pp. 1114--1127, Mar. 1993.

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