P. P. Vaidyanathan and Z. Doganata. The Role of Lossless Systems in Modern Digital Signal Processing. IEEE Trans. on Education, 32:181--197, August 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....McMillan degree N. Then, there exists a factorization of the form (68) where Uo is a constant unitary matrix where the Pi are of the form given in Eqn. 65. In particular, if UN(z) is a polynomial matrix in z 1, the factors Pi can can be shown to be of the form (69) 17 Proof: See Vaidyanathan. [45] [ Another result that we find useful when we discuss wavelet theory is the following represen tation theorem for unitary vectors on the unit circle. An M x 1 vector V(z) is said to be unitary on the unit circle if (z)V(z) 1. By McMillan degree of a unitary vector V(z) we mean the degree of ....

P. P. Vaidyanathan and Z. Doganata. The Role Of Lossless Systems in Modern Digital Signal Processing. IEEE T'as. o Educations, 32:181 197, August 1989.

....in the second sum, it follows that b k = 0 for 0 k [ 1 2 (N 1) 2 Remarks 4.3 : 1. The lemma shows why the condition (4.3) is consistent with the theory of polynomial QMF. For a QMF of degree L 1 it is well known that there are only L 2 degrees of freedom for the lter coef cients (see [17] for example) By asking N L 3 we already have M L 6 : The L 6 extra conditions in (4.3) bring the total number of conditions to L 3 L 6 = L 2 : Viewed this way, coi ets are meant to maximize both numbers of vanishing moments, while their values remain close to each other. ....

P. P. Vaidyanathan and Z. Doganata. The role of lossless systems in modern digital signal processing: A tutorial. IEEE Trans. on Education, 32(3):161, Aug. 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 ....

P. P. Vaidyanathan and Z. Doganata. The role of lossless systems in modern digital signal processing. IEEE Transactions Education, Special issue on Circuits on Systems, 32-3:pp. 181--197, August 1989.

.... so is GammaS (M ) The polyphase representation of x(n) with respect to GammaS (M) is called the dual polyphase representation of x(n) with respect to S(M) x k (n) x(Mn k) # M ] fx(n k)g for k 2 S(M) If S(M) R(M) it is called the first orthant (synthesis [20] or Type 1 [19]) polyphase representaion. The dual first orthant polyphase representation is sometimes referred to as analysis or Type 2 polyphase representation. There are infinitely many choices of generalized polyphase representation (since there are infinitely many generalized representatives of L(M ) Eqn. ....

P. P. Vaidyanathan and Z. Doganata. The Role of Lossless Systems in Modern Digital Signal Processing. IEEE Trans. on Education, 32:181--197, August 1989.

....and, moreover, the individual filters of the filter bank must meet desired frequency and phase response criteria. One of the popular methods of constructing 1 D PRFB s has been the use of filter structures that guarantee perfect reconstruction (PR) by construction. The well known lattice structure [13] [10] is an example of this. Since PR is guaranteed by these structures, the only remaining problems are those of meeting the required frequency and phase response criteria of the individual filters. It is thus important to know the design space which can by implemented by a certain structure. ....

....way) with the help of this new notation. It is shown that M D ladder structures build in a natural way M D BO systems. This brings us to the second theme, viz. ladder structures. We introduce the ladder as a structure for building perfect reconstructing filter banks, similar to lattice structures [13] [10] The basic definitions and properties of ladders are discussed. For a discussion of their implementational advantages we refer to [1] Thirdly the completeness question of ladders with respect to BO systems is raised. In the 1 D case it is shown that the ladder structure is complete: i.e. ....

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P.P. Vaidyanathan, Z. Dognognata, The role of lossless systems in modern digital signal processing. A tutorial, Special issue on Circuits and Systems, IEEE Transactions on Education 32, Np. 3, Augustus 1989, pp. 181-197.

....result in different choices for the best sequence. 3. PARAMETRIZATION OF ORTHONORMAL WAVELETS A parametrization of all orthonormal (ON) wavelets has yet to be realized. However, all 2 channel perfect reconstruction quadrature mirror filterbanks (QMF s) have been parametrized by Vaidyanathan [2]. Zou and Tewfik [3] have imposed the additional condition that the wavelet has at least one vanishing moment ( P n gn = 0) which results in the generation of tight frame, not necessarily orthonormal, wavelets. However, the set of wavelets generated with this parametrization which are not ....

Vaidyanathan, P.P., "The Role of Lossless Systems in Modern Digital Signal Processing: A Tutorial," IEEE Trans. on Education, Vol. 32, no. 3, August 1989.

....problem is given in Fig. 1. The filter bank problem involves the design of the real coefficient realizable (i.e. FIR or causal stable IIR) filters h i (n) and g i (n) with the following goals: Perfect Reconstruction (i.e. y(n) x(n) and approximation of ideal frequency responses (see Fig. 2) [37, 41, 42, 45, 49, 46, 31, 44]. Closely x(n) hM Gamma1 (n) h 1 (n) h 0 (n) # M # M # M dM Gamma1 (n) d 0 (n) d 1 (n) M : M M g M Gamma1 (n) g 1 (n) g 0 (n) j i ....

P. P. Vaidyanathan and Z. Doganata. The Role of Lossless Systems in Modern Digital Signal Processing. IEEE Trans. on Education, 32:181--197, August 1989.

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P. P. Vaidyanathan and Z. Doganata. The Role of Lossless Systems in Modern Digital Signal Processing. IEEE Trans. on Education, 32:181--197, August 1989.

No context found.

P.P. Vaidyanathan and Z. Dognognata. The Role of Lossless Systems in Modern Digital Signal Processing. A tutorial. Special issue on Circuits and Systems. IEEE Transactions on Education, 32(3):181--197, August 1989.

No context found.

P.P. Vaidyanathan and Z. Doganata, "The Role of Lossless Systems in Modern Digital Signal Processing: A Tutorial", IEEE Transactions on Education, Vol. 32 No. 3, Aug. 1989, pp.181-197.

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