K. Nayebi, T. P. Barnwell, and M. J. T. Smith, "Time Domain Filter Bank Analysis: A New Design Theory," IEEE Transactions on Signal Processing, pp. 1412--1429, June 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....RESULTS AND COMPARISONS This section provides some design examples. We compare our filters with those obtained by other existing methods. Quite a few design algorithms are now classical in the dyadic orthonormal case [3] 4] 13] 14] 31] as well as in the dyadic biorthonormal case [9] [32]. In contrast, much less [16] 22, orthonormal] 32, biorthonormal] has been done in the true rational case. We shall first compare our new algorithm with others in the dyadic case. Then, for , we shall see that our designed filter shows better characteristics than Kova cevi c s [16] 22] ....

K. Nayebi, T. P. Barnwell, III, and M. J. T. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Trans. Signal Processing, vol. 40, pp. 1412--1429, June 1992.

....into constraints, and define the constraints with respect to a reference design. The specific measures constrained may be application and filter dependent [198] Constraint based methods have been applied to design QMF banks in both the frequency [112, 36, 43, 120, 183, 187] and time domains [140, 185]. In the frequency domain, the most often considered objectives are E r (reconstruction error) and # s (stopband ripple) As stopband ripples cannot be formulated in closed form, stopband attenuation is used instead (represented as E s in Figure 5.1) In the time domain, Nayebi [140] gave a ....

....domains [140, 185] In the frequency domain, the most often considered objectives are E r (reconstruction error) and # s (stopband ripple) As stopband ripples cannot be formulated in closed form, stopband attenuation is used instead (represented as E s in Figure 5. 1) In the time domain, Nayebi [140] gave a time domain formulation with constraints in the frequency domain and designed filter banks using an iterative time domain design algorithm. Next we formulate the design of QMF banks in the most general form as a nonlinear constrained optimization problem using the reconstruction error as ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

.... overcome this problem by simplifying strategies like cosine modulation of a prototype low pass lter [8] 11] or factorizations of the associated polyphase matrix [12] 15] Design and optimization strategies in the time domain and directly on the impulse responses of the lters are also employed [16] [18] See also [19] for a di erent approach. It is always of interest to nd computationally ecient transforms, such as lters with integer valued impulse responses or transform implementations with small number of arithmetic operations as well as with other possible VLSI advantages. It is ....

K. Nayebi, T. Barnwell and M. J. Smith, \Time-domain Filter Bank Analysis: A New Design Theory," IEEE Trans. on Signal Proc., Vol. 40, No. 6, pp. 1412-1429, June 1992.

.... on the Type IV discrete cosine transform or DCT IV [8] 10] 12] 15] 24] and the modified discrete Fourier transform (MDFT) 5] 9] These filter banks offer the advantage of high computational efficiency (employing fast DCT or DFT algorithms) and high performance filter designs [17], 21] The first fundamental constructions of modulated filter banks were based on a linear phase prototype filter of length 2 with reconstruction delay 2 1. Later work extended the PR constructions to arbitrary length prototypes [19] and DCT II modulation [7] 11] Systems with linearphase ....

.... prototypes [19] and DCT II modulation [7] 11] Systems with linearphase prototype filters face a tradeoff between latency and filter performance shorter filters will decrease the system latency at the cost of poorer subchannelization (as measured by stopband attenuation) Several authors [17], 18] 20] 30] have introduced more general values 2 1 for the reconstruction delay, which force the modulated filter bank to be biorthogonal the synthesis filters will no longer be timereversed versions of the analysis filters. The authors of [29] and [34] describe the construction of ....

K. Nayebi, T. P. Barnwell, III, and M. J. T. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Trans. Signal Processing, vol. 40, pp. 1412--1429, 1992.

....amount of reconstruction distortion during the transition period. In order to preserve the exact reconstruction property in the transition area, time varying transition filter banks are required. Methods of design of TVFBs and TBFBs relying on a Least Square Approach are developed in [7] [8]. However, the filter banks obtained do not usually achieve the perfect reconstruction [9] Several solutions of perfect reconstruction two channel time varying filter banks, that can be implemented on a lattice structure, are described in [10] 11] Another approach, based on the redesign of the ....

K. Nayebi, T. P. Barnwell and M. J. T. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Trans. on Signal Processing, vol. 40, pp. 1412--1428, June 1992.

....delay # and reconstruction error # for an impulse processed through the filter bank system, and d) other properties of the filter bank system rather than the individual filters. The delay # and error # can be computed most readily with a simple modification of the method devised by Nayebi et al. [19]. The Holder regularity h can be estimated by the method of Rioul [20] or Taswell [15] The number v of vanishing moments can be numerically tested by straightforward calculations subject to a prescribed error tolerance. Such a definition interprets vanishing to mean that the required zero is ....

....to have v = 4 vanishing moments with an error of 8.4910 12 . All of the filters were confirmed to be orthogonal with an error of 4.22 10 13 . Values of # = 7 and # =4. 22 10 13 for the filter banks F and G were obtained with the modified Nayebi Barnwell Smith perfect reconstruction test [19], 16] B. Single Level Convolutions A circularly periodized convolution type was chosen for the single level decomposition and reconstruction steps and was tested with a quadruple M spike M channel test signal with M = 2. Figure 1 displays two di#erent phase variants of this convolution type: a ....

Kambiz Nayebi, Thomas P. Barnwell III, and Mark J. T. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Transactions on Signal Processing, vol. 40, no. 6, pp. 1412--1429, June 1992.

....coe#cients relative to their theoretical values, b) various norms, moments, or other measures of each individual filter in the filter banks, and c) the system delay # and reconstruction error # for an impulse processed through the system. A simple modification of the method devised by Nayebi et al. [7] provides the most convenient and general approach for testing the filter coe#cients and computing # and #. Finally, the filters may be tested numerically for well known properties such as orthogonality and energy conservation. B. Filter Convolutions Under the assumptions validating the noble ....

....of length N = 12 with 4 vanishing moments on both scaling and wavelet filters [13, page 261] were normalized in the # 2 norm to one with the sign of h 00 taken as negative. Values of # = 11 and # = 9. 487 10 12 were obtained with the modified Nayebi BarnwellSmith perfect reconstruction test [7]. B. Filter Convolutions A circularly periodized convolution type was chosen for the single level decomposition and reconstruction steps and was tested with a triple M spike signal. Figure 1 displays two di#erent phase variants of this convolution type: a causal analysis variant called peak ....

Kambiz Nayebi, Thomas P. Barnwell III, and Mark J. T. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Transactions on Signal Processing, vol. 40, no. 6, pp. 1412--1429, June 1992.

.... Most Selective (RROMS) 8] Heller Real Orthogonal M band K regular (HROMK) 3] Sherlock Real Orthogonal 2 band 1 regular [9] parameterized with Random Angles (SRORA) Hermite Real Nonorthogonal Symmetric Binomial (HRNSB) 2] and a wide assortment of filter banks available from Nayebi et al. [5]. The filter banks chosen as test examples were selected to represent a variety of di#erent classes with contrasting features. In addition, representative examples were selected for both kinds of specification, i.e. filter coe#cients generated by computational algorithms and filter coe#cients ....

....of an impulse processed through the filter bank system. For a correctly implemented system, all empirical estimates dm m =0, M 1 should equal the expected delay # that has been designed for the filter bank. Finally, note that the original criterion described by Nayebi et al. [5] was intended for use in a design and optimization algorithm rather than for use in independent tests of reconstruction error and system delay. Thus, the essential extension implemented here is the modification of the original criterion for use in evaluating the errors and delays of each of the ....

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Kambiz Nayebi, Thomas P. Barnwell III, and Mark J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

....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 most popular and also the most ....

....i (z) are such that all aliasing terms A (z) are annihilated and the distortion function T (z) becomes a pure delay z Gamma . Limiting the discussion to LPPRFB design, one has to rely upon other approaches such as lattice 26 structure parameterization [75] 62] time domain optimization [51], 55] 70] and cosine modulation [41] The most attractive amongst these is the lattice structure approach based on the factorization of the polyphase matrices E(z) and R(z) As aforementioned, the lattice structure offers fast implementation with a minimal number of delay elements, retains ....

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K. Nayebi, T. P. Barnwell, III, and M. J. T. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Trans. on Signal Processing, vol. 40, pp. 1412-1429, June 1992.

....objectives into constraints, and define the constraints with respect to a reference design. The specific measures constrained may be application and filter dependent [24] Constraint based methods have been applied to design QMF banks in both the frequency [10, 3, 5, 12, 21, 23] and time domains [15, 22]. In the frequency domain, the most often considered objectives are E r (reconstruction error) and ffi s (stopband ripple) As stopband ripples cannot be formulated in closed form, stopband attenuation is used instead (represented as E s in Figure 1) In the time domain, Nayebi [15] gave a ....

.... domains [15, 22] In the frequency domain, the most often considered objectives are E r (reconstruction error) and ffi s (stopband ripple) As stopband ripples cannot be formulated in closed form, stopband attenuation is used instead (represented as E s in Figure 1) In the time domain, Nayebi [15] gave a time domain formulation with constraints in the frequency domain and designed filter banks using an iterative time domain design algorithm. 1 Note that in QMF banks, Er is non zero. A multi rate filter bank that enforces perfect reconstruction (Er = 0) can be formulated as a constrained ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

....linear phase and perfect reconstruction properties. When M is even and fi is odd, tr(D) 1 z Gamma1 ) j z=1 = 2: Thus, we need two more symmetric filters in this case. The results from the remaining two odd M cases can be trivially obtained in a similar manner. p In time domain FB designs [22, 23], the filters symmetry polarity is not a narrow enough requirement. The filters lengths are also very important for perfect reconstruction. If the designer chooses wrong filters lengths, his optimization routine will not converge. Therefore, besides the necessary LP PR condition for the ....

Nayebi, K., Barnwell, T., and Smith, M., "Time-Domain Filter Bank Analysis: A new Design Theory," IEEE Trans. SP, V. 40, 1992.

....paraunitary filter bank (F0(z) z Gamma(N Gamma1) H0(z Gamma1 ) the algorithm by Mian and Nainer [26] is widely used. It computes the minimum phase spectral factor without finding the zeros of P (z) Other design methods includes the latticestructured approach [3] time domain approach [29], the quadratic constrained least squares approach [27] and the Lagrange multipler based approach [34, 35] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P F 0 H 0 (a) F 0 H 0 (b) Figure 5: Zero pattern of P (z) and the zero distributions of F0(z) and H0(z) The lattice structure approach is ....

....to the lattice coefficients. Thus, designing filter banks with small objective function is a problem because of the nonlinear relation between the lattice coefficients and the objective function. The time domain approach formulates the PR conditions in terms of matrices and the filter coefficients [29]. It uses optimization algorithm iteratively to solve (2) The quadratic constrained approach formulates both the objective function Phi and the PR conditions in the quadratic forms h t Ph and hQkh = ck , respectively. The design problem becomes Minimize h t Ph subject to hQkh = ck (5) where ....

Nayebi, K., Barnwell, T. P. III and Smith, M. J. T., "Time-domain filter bank analysis: A new design theory", IEEE Trans. on SP, vol. 40, June 92.

....formulation, the constraints are defined with respect to a reference design. The specific measures constrained may be application and filterdependent [256] Constraint based methods have been applied to design QMF filter banks in both the frequency [47,54,133,148,234,239] and the time domains [177,238]. In the frequency domain, the most often considered objectives are the reconstruction error, E r , and the stopband ripple, ffi s . As stopband ripples cannot be formulated in closed form, stopband attenuation, E s , is usually used instead. In the time domain, Nayebi [177] gave a time domain ....

....the time domains [177,238] In the frequency domain, the most often considered objectives are the reconstruction error, E r , and the stopband ripple, ffi s . As stopband ripples cannot be formulated in closed form, stopband attenuation, E s , is usually used instead. In the time domain, Nayebi [177] gave a time domain formulation with constraints in the frequency domain and designed filter banks using an iterative timedomain design algorithm. In this thesis, we formulate the design of a QMF filter bank in the most general form as a constrained nonlinear optimization problem [265,266] ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

....constrained formulation, constraints are defined with respect to a reference design. The specific measures constrained may be application and filterdependent [15] Constraint based methods have been applied to design QMF filter banks in both the frequency [7, 1, 2, 8, 12, 14] and the time domains [9, 13]. In the frequency domain, the most often considered objectives are the reconstruction error, Er , and the stopband ripple. As stopband ripples cannot be formulated in closed form, stopband attenuation is used instead (represented as Es in (2) In the time domain, Nayebi [9] gave a time domain ....

....the time domains [9, 13] In the frequency domain, the most often considered objectives are the reconstruction error, Er , and the stopband ripple. As stopband ripples cannot be formulated in closed form, stopband attenuation is used instead (represented as Es in (2) In the time domain, Nayebi [9] gave a time domain formulation with constraints in the frequency domain and designed filter banks using an iterative time domain design algorithm. In this paper, we formulate the design of a QMF filter bank in the most general form as a constrained nonlinear optimization problem, using the ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

.... filter bank that enforces perfect reconstruction (Er = 0) can be formulated as a constrained optimization problem with a goal of minimizing Es [25, 23] Constraint based methods have been applied to design QMF filter banks in both the frequency [26, 6, 9, 30, 45, 47] and the time domains [35, 46]. In the frequency domain, the most often considered objectives are E r , the reconstruction error, and ffi s , the stopband ripple. As stopband ripples cannot be formulated in closed form, stopband attenuation is used instead (represented as E s in Figure 5.1) In the time domain, Nayebi [35] ....

....[35, 46] In the frequency domain, the most often considered objectives are E r , the reconstruction error, and ffi s , the stopband ripple. As stopband ripples cannot be formulated in closed form, stopband attenuation is used instead (represented as E s in Figure 5. 1) In the time domain, Nayebi [35] gave a time domain formulation with constraints in the frequency domain and designed filter banks using an iterative time domain design algorithm. We formulate the design of QMF filter banks in the most general form as a nonlinear constrained optimization problem using the reconstruction error as ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

....constrained formulations should be used instead. 2.2: Single Objective Constrained Formulation In this formulation, constraints are defined with respect to a reference design. Constraint based methods have been applied to design QMF filter banks in both the frequency [5] and the time domains [9]. In the frequency domain, the most often considered objectives are E r , the reconstruction error, and ffi s , the stopband ripple. In the time domain, Nayebi [9] gave a time domain formulation with constraints in the frequency domain and designed filter banks using an iterative time domain ....

....reference design. Constraint based methods have been applied to design QMF filter banks in both the frequency [5] and the time domains [9] In the frequency domain, the most often considered objectives are E r , the reconstruction error, and ffi s , the stopband ripple. In the time domain, Nayebi [9] gave a time domain formulation with constraints in the frequency domain and designed filter banks using an iterative time domain design algorithm. In this paper, we formulate the design of QMF filter banks in the most general form as a nonlinear constrained optimization problem: Minimize E r (4) ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

....banks. They use perfect reconstruction blocks based on lossless polyphase matrices and optimize adequate parameters. Nayebi et al. 18] have developed a framework based on temporal analysis. A design technique leading to numerically perfect reconstruction filter banks has been developed as well [19]. This technique is very flexible and addresses the inclusion of additional constraints for specific applications such as low delay, linear phase and so on. Although the above techniques exist for designing M band and or perfect reconstruction filter banks, the QMFs designed by Johnston are still ....

....perfect reconstruction filter banks, the QMFs designed by Johnston are still the most cited and utilized in the image coding community. This is partly due to the simplicity of the design technique and the published tables of filter coefficients. On the other hand, filters proposed in [31] and in [19] are relatively long, and hence, are not suitable for image coding applications. Image coding applications require filter banks with specific features that differ from the classical perfect reconstruction problem or from the design of filter banks for other applications. Psycho visual properties ....

K. Nayebi, T.P. Barnwell, and M.J. Smith, "Time Domain Filter Bank Analysis: A New Design Theory", IEEE Transactions on Signal Processing, pp. 1412--1429, June 1992.

....designed FB is used for image coding purpose, the scaling function must be properly designed to suppress basis related artifacts. In order to obtain the best control of the designed filter s scaling function, time domain formulation is chosen. Similar formulation has been proposed by Nayebi et al. [1]. Nayebi considers the time domain aliasing cancellation (AC) matrix and expresses the PR property in terms of the AC matrix. Their design method requires iterative projection of the AC matrix under PR constraints for the synthesis filter for a given analysis low pass filter. In this paper, a ....

K.Nayebi, T.P.Barnwell, and M.J.T.Smith, "Time domain filter bank analysis : a new design theory," IEEE SP, pp.1412-1429, Jun 1992.

....not so easily applied to the time varying case, since the z transform is used for systems which are linear time invariant or, at worst, periodically time varying. For the case of general time varying systems we find it more convenient to use the time domain description of the filter bank operation [2, 10]. This explicitly indicates the decomposition by writing both analysis and synthesis as matrix operations. The signal is seen as a vector in a linear space, and the conventional filtering operations can be written as matrix operations on the signal vector. Viewing things in this way will prove ....

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, "Time domain filter bank analysis: A new design theory," IEEE Trans. on Signal Proc., vol. IV, pp. 1414--1429, June 1992.

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K. Nayebi, T. P. Barnwell, and M. J. T. Smith, "Time Domain Filter Bank Analysis: A New Design Theory," IEEE Transactions on Signal Processing, pp. 1412--1429, June 1992.

No context found.

Kambiz Nayebi, Thomas P. Barnwell III, and Mark J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

No context found.

K. Nayebi, T. Barnwell, and M. J. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Trans. Signal Processing, vol. 40, pp. 1412--1429, June 1992.

No context found.

Nayebi, K., T. P. Barnwell, III, and M. J. T. Smith, "Time domain filter bank analysis: A new design theory," IEEE Transactions on Signal Processing, Vol. 40, pp. 1414-1429, June 1992.

No context found.

K. Nayebi, T. Barnwell, and M. J. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Trans. on Signal Processing, vol. 40, pp. 1412-1429, June 1992.

No context found.

K. Nayebi, T. P. Barnwell III, and M. J. T. Smith. Time-domain filter bank analysis: A new design theory. IEEE Transactions on Signal Processing, 40(6):1412--1429, June 1992.

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