T. Q. Nguyen and P. P. Vaidyanathan, "Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters," IEEE Transactions on Signal Processing, vol. 37, no. 5, May 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Criteria for Filter Bank To achieve both perfect reconstruction (PR) and linear phase (LP) it is required that the sum of the lengths of filters H 0 (z) and H 1 (z) be a multiple of 4, N 0 N 1 = 4m, where N 0 and N 1 are, respectively, the lengths of filters H 0 (z) and H 1 (z) Type B filters [139] are used here for which both filters H 0 (z) and H 1 (z) are of odd length and are symmetric (namely, LP) Because of the symmetry of the filters, 1) 2 1) 2, the number of the filter coe#cients is reduced by almost half. The filter parameters are denoted by h 0 = N 0 1) 2 and ....

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect reconstruction FIR QMF structure which yield linear-phase analysis and synthesis filters. IEEE Trans. on Acoutics, Speech, and Signal Processing, 37(5):676--690, May 1989.

....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 ....

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters. IEEE Trans. Acoust. Speech Signal Process., 37:676--690, 1989.

....and thus we divide them into two categories accordingly. The first category consists of schemes such those proposed by Smith and Barnwell [SI84, SI86] and Vaidyanathan et al. [VH88] that use FIR filters that are not linear phase. The second category consists of schemes such as those reported in [ABMD90, VH88, VD89, NV89, VH90, VG89, RV91, ABMD90] that use FIR linear phase filters that give rise to a non orthogonal wavelet expansion, because they do not satisfy power complementarity. Note that approximate power complementarity implies approximate orthonormality of the underlying wavelet basis. It is not clear that the filters described ....

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters. IEEE Transactions ASSP, ASSP37 -5:pp. 676--690, May 1989.

....two subband signals, x 1 (n) and x 2 (n) are combined to form the reconstructed signal x(n) Hence the QMF bank in Figure 1 is actually a multirate system. This system is important in subband coding of speech and digital audio application, and has been studied extensively; see, for example, [1, 4, 5, 6, 8, 11] and their corresponding references. H 0 (z) H 1 (z) # 2 2 # 2 2 F 0 (z) F 1 (z) x(n) x(n) Figure 1: Two channel QMF bank. Ideally x(n) is a delayed version of x(n) that is defined as PR. However in practice PR may not be possible that would be the case when analysis ....

T.Q. Nguyen and P.P. Vaidyanathan, "Two-channel perfect reconstruction FIR QMF structures which yield linear phase analysis and synthesis filters", IEEE Transactions on Acoustics, Speech and Signal Processing, Vol.37, No.5, pp.676-690, May 1989.

....in the restricted space. The second approach [15] formulates a PR LP filter bank in a lattice structure in order to enforce some constraints in its design. Figure 2 shows an example lattice structure, where k 1 ; kN Gamma1 , B 1 and B 2 are unknown parameters. We state without proof [14] that when the filter length N is even and k i = 0 for all even i, the resulting filters H 0 (z) and H 1 (z) in Figure 2 are a PR pair that satisfy (3) Moreover, the LP constraints (4) are satisfied automatically. In short, the design a PR LP filter bank based on a lattice structure only involves ....

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect reconstruction FIR QMF structure which yield linear-phase analysis and synthesis filters. IEEETrans. on Acoutics, Speech, and Signal Processing, 37(5):676--690, May 1989.

....G 0 (z) and G 1 (z) that perform interpolation. In the end, the subband signals are added together to produce the reconstructed signal x(n) at the output. In short, output signal x(n) is a function of input signal x(n) and the filters in the filter bank, H 0 (z) H 1 (z) G 0 (z) and G 1 (z) [4, 181]. Following the top branch in Figure 5.1, we have the following equations for the analysis and synthesis filters: 0 (z) H 0 (z)X(z) 5.1) Y 0 (z) G 0 (z)F 0 (z) 5.2) We have the following equations for the down sampling and up sampling: V 0 (z) 1 2 [ 0 (z 1=2 ) 0 ( Gammaz 1=2 ) ....

.... be removed by enforcing appropriate relationships between the synthesis filters and the analysis filters; magnitude distortions can be removed by using infinite impulse response (IIR) filters; and the linear phase property can be achieved by using linear phase finite impulse response (FIR) filters [4, 181]. When all the distortions are removed, the original signal is said to be reconstructed perfectly. Based on (5.7) the perfect reconstruction of the original signal requires S(z) 0, for all z, and T (z) z Gamman 0 , where n 0 is a constant. In this case, the transfer function of the filter ....

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters. IEEE Trans. on Acoustics, Speech and Signal Processing, 37(5):676--690, May 1989.

....of wideband audio [4] In these filter banks aliasing is canceled and phase distortion is eliminated, while magnitude distortion and stopband leakage in the analysis filters are minimized. Compared to FIR PR systems with a linear phase analysis bank and with the same length analysis filters [7], Johnston filters have much greater stopband attenuation. Furthermore, in many practical applications such as audio and image coding, one does not require PR as long as the reconstruction errors are imperceptible. Once the analysis filters have been chosen, it makes sense to design the synthesis ....

T.Q. Nguyen and P.P. Vaidyanathan. Two-channel perfect reconstruction FIR QMF structures which yield linear-phase FIR analysis and synthesis filters. IEEE Trans. on Acoustics, Speech, and Signal Processing, 37:676--690, May 1989.

....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 [35, 36, 42, 50, 51, 52, 53, 57, 55, 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 [13, 18, 22, 34, 21] In the mid eighties the introduction of multiresolution analysis and the fast wavelet transform by Mallat and Meyer ....

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters. IEEE Trans. Acoust. Speech Signal Process., 37:676--690, 1989.

....is to optimize the nonlinear constrained formulation using Lagrange multiplier methods [17, 15] Nayebi [27] gave a time domain formulation with constraints in the frequency domain. The drawback of FIR filter banks is that it is impossible to obtain perfect reconstruction in a non trivial case [34]. It becomes clearer when we use a polyphase representation. In polyphase form, filter H(z) is expressed as A 0 (z 2 ) z Gamma1 A 1 (z 2 ) where A 0 (z) and A 1 (z) are polyphase filters. If H 1 (z) is the quadrature mirror image of low pass filter H 0 (z) then H 1 (z) A 0 (z) Gamma ....

....If the composing filter is N tap, then the delay of the filter bank becomes N Gamma 1. Non QMF filter banks Methods for designing non QMF FIR filter banks include unconstrained optimization methods, similar to those for designing QMF FIR filter banks except that the former has more dimensions [34], and constrained optimization methods [31, 1] including Lagrange multiplier [1, 45] and time domain methods [29] IIR filter banks Since IIR filters can be decomposed into two all pass subfilters, amplitude distortion can be zero in an IIR filter bank [55] Usually IIR filter banks have shorter ....

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters. IEEE Trans. on Acoustics, Speech and Signal Processing, 37(5):676--690, May 1989.

....sum of the filter lengths is a multiple of 4, i.e, N 0 N 1 = 4k, where N 0 and N 1 are lengths of filters H 0 (z) and H 1 (z) respectively, and then the system delay of the filter bank is (N 0 N 1 ) 2 Gamma 1. Only two types of nontrivial filter bank systems have both PR and LP features [4]. As illustration in this paper, we only discuss the case where both filters H 0 (z) and H 1 (z) have even length, H 0 (z) is symmetric, and H 1 (z) is antisymmetric. Hence, two filters need to be estimated. One is low pass filter H 0 (z) with parameters h 0 = fh 0 (n) n = 0; 1; Delta Delta ....

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect reconstruction fir qmf structure which yield linearphase analysis and synthesis filters. IEEE Trans. on Acoutics, Speech, and Signal Processing, 37(5):676-- 690, May 1989.

....accurately handle finite length signals boundaries. In this paper, we only consider linear phase maximally decimated M channel perfectreconstruction filter banks (LPPRFB) A lot of work has been done on the theory and the designs of such filter banks. However, most deals with two channel system [7, 8, 9, 10]. For M channel case, the amount of previous work is rather limited, and there are still many open problems. Saghizadeh and Willson presented in [3] a generic approached design that keys on optimizing the impulse responses of the analysis filters directly. Another interesting approach was ....

....presented in the full paper [11] We summarize the results from Theorem 1, Theorem 2 and Corollary 1 in Table 1. S stands for symmetric filters; A stands for antisymmetric filters. This is consistent with a similar result developed independently in [4] Furthermore, all published LPPRFB so far [1, 2, 3, 5, 8, 9] are also consistent with the result presented in Table 1. III. M Channel Linear Phase Paraunitary Filter Banks with Filters Length L 6= KM Interestingly, as pointed out in [1] the linear phase contraint in conjunction with the paraunitary property does not allow the length L of the filters to ....

Nguyen, T. Q. and Vaidyanathan, P. P., "Two Channel Perfect-Reconstruction FIR QMF Structures which Yield Linear-Phase Analysis and Synthesis Filters", IEEE Trans. on ASSP, pp. 676-690, May 1989.

....systems are guaranteed to satisfy the perfect reconstruction condition with R(z) chosen to be e E(z) I.1 Review of Previous Works Many works have explored the theory, structures, and design methods of linear phase FIR perfect reconstruction filter banks. Most deals with two channel systems [6, 17, 19, 21], and all solutions have been found. Type A system (fi = 0) has even length filters with different symmetry polarity (one symmetric, the other antisymmetric) Type B system (fi = 1) has odd length filters with the same symmetry polarity (both symmetric) Complete and minimal lattice structures for ....

....found. Type A system (fi = 0) has even length filters with different symmetry polarity (one symmetric, the other antisymmetric) Type B system (fi = 1) has odd length filters with the same symmetry polarity (both symmetric) Complete and minimal lattice structures for both systems were reported in [17]. However, for M channel cases, there are still many open problems. First of all, it is not clear what are the permissible choices of filters symmetry polarity and lengths. This issue has been studied by a number of authors [1, 3, 24] but their results are either not tight enough or not general ....

[Article contains additional citation context not shown here]

Nguyen, T. Q. and Vaidyanathan, P. P., "Two Channel Perfect-Reconstruction FIR QMF Structures which Yield Linear-Phase Analysis and Synthesis Filters", IEEE Trans. on ASSP, pp. 676-690, May 1989.

.... [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, 9, 10]. Linear phase filter banks are used extensively in wavelet based image coder and appeared in standard for fingerprint image compression [11] 1 Will be presented at the International Conference on Digital Signal Processing, Cypress, June 95. Efficient M channel cosine modulated filter banks ....

.... Gamma1 z Gamma2 1 z Gamma1 ff k 0 0 1 ; D ff 0 ;ff 1 = ff 0 0 0 ff 1 : In a practical system, it is sufficient to set al..l fi k equals to 0, except for fi 2 . This would help speeding up the implementation of Type B system. Procedure to find ff k and fi 2 can be found in [6, 7]. Given a linear phase halfband maxflat filter P (z) there are many ways of distributing its zeros such that both F0(z) and H0(z) are linear phase filters. Consider the case where P (z) has length 15, it can be factorized into several Type A systems, when (N0 ; N1) f(8; 8) 10; 6) 12; 4) ....

Nguyen, T. Q. and Vaidyanathan, P. P., "Two Channel Perfect Reconstruction FIR QMF Structures which Yield Linear Phase Analysis and Synthesis Filters", IEEE Trans. on ASSP, pp. 676-690, May 1989.

No context found.

T. Q. Nguyen and P. P. Vaidyanathan, "Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters," IEEE Transactions on Signal Processing, vol. 37, no. 5, May 1989.

No context found.

T. Q. Nguyen and P. P. Vaidyanathan, "Twochannel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters," IEEE Transactions on Signal Processing, vol. 37, no. 5, May 1989.

No context found.

T. Q. Nguyen and P. P. Vaidyanathan, "Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters," IEEE Trans. Acoust., Speech, Signal Process. 37, pp. 676--690, May 1989.

No context found.

T. Q. Nguyen and P. P. Vaidyanathan, "Two-Channel Perfect-Reconstruction FIR QMF Structures Which Yield Linear-Phase Analysis and Synthesis Filters," IEEE Trans. on ASSP, 37 (1989), pp. 676-690.

No context found.

T. Q. Nguyen and P. P. Vaidyanathan. Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters. IEEE Trans. on Acoustics, Speech and Signal Processing, 37(5):676-- 690, May 1989.

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