Multirate Systems and Filterbanks

Design of practically perfect-reconstruction cosine-modulated filter banks: a second-order cone programming approach

“…The rationale of these assumptions have been addressed in the literature [23], [25], [26]. In short, these assumptions are made for the sake of system performance rather than convenience.…”

“…and the filter bank in this case is said to be orthogonal [26]. The design variables in this case are the components in the first half of the…”

“…are the alias transfer functions that determine how the aliased components X(ze −j2πl/M ) are attenuated [8], [26]. It follows that the BCM filter bank holds the PR property if and only if…”

“…Of particular interest within this filter bank class are biorthogonal cosine-modulated (BCM) filter banks as they offer reduced system delay while maintaining the perfect reconstruction (PR) or near PR (NPR) property. Recent progress in the analysis and design of BCM filter banks have been reported by several authors, see, for example, [18]- [21], [23]- [26], and [28]. Available design techniques for BCM filter banks now include the quadratic-constrained least-squares (QCLS) method [23], [20], [6] that minimizes the stopband energy of the PF subject to the PR constraints expressed as quadratic equalities in terms of the coefficients of the PF; the factorization-based method [19], [24], [25] that yields a parameterized realization in which the PR property is always ensured while minimizing the stopband energy of the PF in an unconstrained optimization setting; and the sequential design method [28] that is carried out by first designing a filter bank with a small number of channels and a relatively short filter length and then gradually increasing the number of channels as well as the filter length using a technique initiated in [5].…”

Efficient design of perfect-reconstruction biorthogonal cosine-modulated filter banks using convex Lagrangian relaxation and alternating null-space projections

“…In this paper, however, we shall concentrate on the DCT-IV BCM filter banks as specified by (1) along with the following assumptions: (i) the channel number M is even, (ii) the filter length N assumes the form N = 2mM for some positive integer m, and (iii) the system delay assumes the form D = 2sM + d where s is an integer and d = 2M -1. The rationale of these assumptions have been addressed in the literature [10] - [12]. The input-output relation of the system in the z-domain is given by In the time-domain, the PR condition can be described by the following set of quadratic equations [10]:…”