G. Schuller, "A New Factorization and Structure for Cosine Modulated Filter Banks with Variable System Delay", Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 3-6, 1996  Home/Search   Document Details and Download   Summary   Related Articles   Check

....filter bank can be designed such as to be paraunitary or to result in a low system delay. In the latter case, also called biorthogonal case, the overall system delay can be chosen independently (within some fundamental limits) of the filter length and the number of subbands. As has been shown in [1, 2] one can still use a common prototype for the analysis and synthesis. Design methods for the prototype mainly base on two different philosophies: It is either possible to use a constrained optimization (with the PR conditions as constraints) of the prototype s frequency response. This has led to ....

....consists of deriving a structure that automatically guarantees PR of the filter bank. In the paraunitary case, such a structure is given by the well known lattice structure [5] containing rotations for the lattice coefficients. For biorthogonal filter banks such structures have been derived in [6, 2, 7] and non linear, non constrained optimization methods are used for the prototype design. Compared to the QCLS algorithm, the latter algorithms offer the advantage to be robust against coefficient quantization, thus allowing an efficient filter implementation with integer valued coefficients [2, 8, ....

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G. Schuller. A new factorization and structure for cosine modulated filter banks with variable system delay. In Proc. 30th Asilomar Conf., Nov. 1996.

....Note that in this example the predict filter uses extrapolation and there is no associated continuous scaling function. This is a very simple example. To get practically useful causal filters, we would need many more filter taps. Upon finishing this paper, we learned of the work of Gerald Schuller [41, 42] concerning low delay filter banks and applications in audio coding. This work, done independently from lifting, fits into the lifting framework and illustrates another feature of lifting, namely minimal delay filter banks. It is known that a filter bank with causal filters only typically achieves ....

G. Schuller. A new factorization and structure for cosine modulated filter banks with variable system delay. In Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, 1996.

....filter bank can be designed such as to be paraunitary or to result in a low system delay. In the latter case, also called biorthogonal case, the overall system delay can be chosen independently (within some fundamental limits) of the filter length and the number of subbands. As has been shown in [1, 2] one can still use a common prototype for the analysis and synthesis. Design methods for the prototype mainly base on two different philosophies: It is either possible to use a constrained optimization (with the PR conditions as constraints) of the prototype s frequency response. This has led to ....

....consists of deriving a structure that automatically guarantees PR of the filter bank. In the paraunitary case, such a structure is given by the well known lattice structure [5] containing rotations for the lattice coefficients. For biorthogonal filter banks such structures have been derived in [6, 2, 7] and non linear, non constrained optimization methods are used for the prototype design. Compared to the QCLS algorithm, the latter algorithms offer the advantage to be robust against coefficient quantization, thus allowing an efficient filter implementation with integer valued coefficients [2, 8, ....

[Article contains additional citation context not shown here]

G. Schuller. A new factorization and structure for cosine modulated filter banks with variable system delay. In Proc. 30th Asilomar Conf., Nov. 1996.

....analysis bank Biorthogonal modulated filter banks (when compared to paraunitary ones) provide the advantage that the overall system delay can be chosen independently of the filter length, thus resulting in low delay filter banks. They have recently been studied in literature by several authors [1, 2, 3, 4, 5]. While Schuller and Smith describe the filter bank by a cascade of selfinverse sparse matrices and a modulation matrix, the approach derived by Nguyen et al. is based on constraints on the polyphase filters of a common prototype filter for analysis and synthesis. Based on this formulation for the ....

....(z) in (7) and G d Gamma (z) and G d GammaM Gamma (z) respectively. Furthermore, one can increase the polyphase filter length by more than one tap per lifting or dual lifting when using filters A(z) and B(z) of higher order. Comparing the described lifting with the factorization approach in [3] it turns out that the introduced matrices A and B are submatrices of the so called Zero Delay Matrices in [3] 2.2. Increasing the Filter Bank Delay and the Filter Length In the previous section, lifting steps were introduced that did not affect the system delay. We now consider the case that ....

[Article contains additional citation context not shown here]

G. Schuller. A new factorization and structure for cosine modulated filter banks with variable system delay. In Proc. 30th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA, November 1996.

....to build both causal and anticausal Neville filters. By letting the predict be a causal Neville, and the update be the adjoint of an anticausal Neville filter, it is possible to build a filter bank with only causal lifting steps. Upon finishing this paper, we learned of the work of Gerald Schuller [39, 40] concerning low delay filter banks and applications in audio coding. This work, done independently from lifting, fits into the lifting framework and illustrates another feature of lifting, namely minimal delay filter banks. It is known that a filter bank with only causal filters typically has ....

G. Schuller. A new factorization and structure for cosine modulated filter banks with variable system delay. In Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, 1996.

....banks the overall system delay can be chosen independently of the filter length, thus being interesting for applications where a low delay of the filter bank and a higher stopband attenuation as in the paraunitary case are desirable. They have recently been studied in literature by several authors [3, 4, 5, 6, 7, 8]. Although many design methods for PR cosine modulated filter banks have been developed within the last few years, see e.g. 1, 9, 6, 4] none of these methods takes into consideration the implementation cost due to the wordlengths of the filter coefficients. For paraunitary cosine modulated ....

G. Schuller. A new factorization and structure for cosine modulated filter banks with variable system delay. In Proc. 30th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA, November 1996.

....following notation. n a and n s are limited to 0 n a ; n s N . This particular type of modulating function was chosen because it leads to filters with narrow passbands and high stopband attenuation. The polyphase matrices are now to be constructed as a product or a cascade of simpler matrices [15, 16]. First a Transform. The analysis transform is defined as [T a ] n;k : cos( N (k 0:5) n 0:5) 0 n; k N and the synthesis transform is the inverse, T s = T a Gamma1 = T a Delta 2=N . This is a DCT type 4, for which fast algorithms are available. Next this type of matrix, a filter ....

G. Schuller, "A New Factorization and Structure for Cosine Modulated Filter Banks with Variable System Delay", Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 3-6, 1996

....low system delay independent of the filter length. This enables a higher stopband attenuation and or a narrower transition bandwidth than an orthogonal filter bank with the same overall system delay. Two different approaches for cosine modulated filter banks with arbitrary delay were presented in [18] and [19] Both approaches use different phases for the modulation function. The method presented in [19] explicitly derives the constraints on the prototypes polyphase components for perfect reconstruction, and a quadratic constrained optimization is proposed for the filter design. On the other ....

....[19] Both approaches use different phases for the modulation function. The method presented in [19] explicitly derives the constraints on the prototypes polyphase components for perfect reconstruction, and a quadratic constrained optimization is proposed for the filter design. On the other hand, [18] proposes an efficient implementation that automatically guarantees perfect reconstruction and a chosen system delay of the filter bank such that the prototype filters can be designed using unconstrained optimization. This latter approach will be used in this paper. Most of the real world signals ....

G. Schuller, "A new factorization and structure for cosine modulated filter banks with variable system delay," in Proc. Asilomar Conf. Signals, Syst., Comput., vol. 2, Pacific Grove, CA, Nov. 6, 1996, pp. 1310--1314.

....next segment discusses results of the combination filter bank detection method. Finally, a summary is given. 2 The Filter Bank The filter bank used for the chirp detection is a complex filter bank, as described in [3, 4] Since we want use very non symmetric filters, we use the design method of [5, 6] as a basis to construct a complex filter bank. The complex filter bank used is a uniform modulated filter bank, which is implemented as two real valued filter banks, one for the real part and one for the imaginary part. Modulated filter banks obtain their filters by modulation, or multiplying a ....

....interestingly also for the imaginary part, although it uses a different modulation function. The design method and the structure to obtain the window functions for perfect reconstruction and an efficient implementation for the real part, that is, the cosine modulated filter bank, is described in [5, 6]. The imaginary part is obtained by replacing the Discrete Cosine Transform in [5, 6] by a Discrete Sine Transform. The coefficients of the filter bank structure stay essentially the same, except for some suitable sign changes. The window function for perfect reconstruction was then obtained by ....

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G. Schuller: "A New Factorization and Structure for Cosine Modulated Filter Banks with Variable System Delay", Proceedings: Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, Nov. 3-6, 1996

....which is important for applications like speech and audio coding. However, the problem of time varying bi orthogonal filter banks with changing numbers of subbands has not been addressed in the literature before and will be addressed in the following using the factorization or cascade described in [12], which is computationally efficient and PR even if low precision arithmetic is used. Its system delay does not need to be an integer multiple of N , it can be specified in terms of the input sampling rate, so that it can be matched more closely to some requirements. The analysis and synthesis ....

....N before processing them, the system delay is nd = N Gamma 1 d Delta N Gamma n t , where n t can be used for the fine tuning of the system delay. 3. THE NEW FILTER STRUCTURE The time varying filter banks that will be introduced are based on a new formulation for modulated FIR filter banks [12], which is briefly described next. The key for the new filter bank design is the factorization of the polyphase matrices in a product of sparse filter matrices with polynomial elements on their diagonal and antidiagonal, transform matrices Ta , Ts , and the shift matrix S(z) They all can be ....

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G. Schuller: "A New Factorization and Structure for Cosine Modulated Filter Banks with Variable System Delay", Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 3-6, 1996

....filters may be derived from different prototypes. TICSP Workshop on Transforms and Filter Banks Biorthogonal Modulated Filter Banks Two principal approaches can be observed for the design of biorthogonal cosine modulated filter banks with perfect reconstruction. The approach by Schuller et al. [SS96, Sch96, SK97] uses filter bank realizations that structurally guarantee perfect reconstruction for arbitrary system delays. It is mainly based on a factorization of the analysis polyphase matrix into a transform and special sparse matrices which are easy to invert. The inverse matrices are then used on the ....

....the analysis and synthesis prototype filters are also stated [HKN96] Furthermore, it can be shown that for certain combinations of filter lengths and overall system delay, some polyphase filters can only have one non zero coefficient. This case is not treated in the factorization proposed in [Sch96, SK97]. However, the factorization approach from Schuller et al. offers many advantages concerning the implementation of the filter bank. First of all, the structure automatically guarantees PR. This also holds true when using integer valued coefficients, because the same factorization coefficients are ....

[Article contains additional citation context not shown here]

G. Schuller. A new factorization and structure for cosine modulated filter banks with variable system delay. In Proc. 30th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA, November 1996.

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