Optimized Prototype Filter Based on the FRM Approach for Cosine-Modulated Filter Banks

Abstract

A design procedure for frequency-response masking (FRM) prototype filters of cosine-modulated filter banks (CMFBs) is proposed. In the given method, we perform minimization of the maximum attenuation level in the filter's stopband, subject to intersymbol interference (ISI) and intercarrier interference (ICI) constraints. For optimization, a quasi-Newton algorithm with line search is used, and we provide simplified analytical expressions to impose the interference constraints, which greatly reduce the computational complexity of the optimization procedure. The result is lower levels of ISI and ICI for a predetermined filter order, or a reduced filter complexity for given levels of interferences. It is then illustrated how the FRM-CMFB structure is suitable for implementing filter banks with a large number of bands, yielding sharp transition bands and small roll-off factors, which is an attractive feature for a wide range of practical applications.

Two Classes of Frequency-Response Masking Linear-Phase FIR Filters for Interpolation and Decimation

“…In this way, via the use of subfilters with wide transition bands, one can generate a sharp-transition overall filter (see Figure 1). Since the order, and thereby the arithmetic complexity, of direct-form FIR filters, is inversely proportional to the transition bandwidth [10], [11], [19], the use of the FRM approach can reduce the arithmetic complexity substantially for FIR filters with sharp (narrow) transition bands [2], [5], [7], [13], [16], [22], [23], [25]- [27], [31], [34], [35], [38], [42], [43]. The same holds true for approximately linear-phase IIR filters [12], [17], [18], [28].…”

“…The frequency-response masking (FRM) approach is a technique for realizing sharp-transition filters with low complexity [2], [5], [7], [12], [13], [16], [22], [23], [25]- [28], [31], [34], [35], [38], [42], [43]. 2 The overall sharp-transition FRM filter is obtained by making use of periodic 3 model filters and nonperiodic masking filters with transition bands wider than that of the overall filter.…”

“…The FIR filters include low-delay filters [2], [42], approximately power-complementary filter pairs [13], half-band filters [38], Hilbert transformers [27], interpolation and decimation filters [26], two-channel filter banks (FBs) [16], [34], modulated multichannel FBs [7], [31], [35], [43], modulated transmultiplexers [5], and two-dimensional filters [23], [25]. The FRM approach has also been extended to infinite impulse response (IIR) filters as a means to obtain efficient high-speed recursive filters [18], approximately linearphase filters [18], [28], interpolators and decimators for sampling rate conversion by factors of two [17], and Hilbert transformers [12].…”

On Low-Delay Frequency-Response Masking FIR Filters

“…Also, wide-band (WB) filters can be designed with this method, by subtracting an NB filter from a pure delay [27], and for middle-band 2 (MB) filters, the method was generalized in [12]. The filter theory in [22] and [12] has successfully been extended to many other filter categories, such as approximately power-complementary filter pairs [8], half-band filters [30], Hilbert transformers [16], interpolation and decimation filters [15], two-channel filter banks (FBs) [9], [25], modulated multichannel FBs [4], [21], [26], [35], modulated transmultiplexers [3], two-dimensional filters [13], [14], and IIR filters [2], [10], [18].…”

Hybrid Genetic Algorithm for the Design of Modified Frequency-Response Masking Filters in a Discrete Space

“…It was reported in [1], [8], [12], [15], [20], [22]- [27], [31], and [40] that the frequency-response masking (FRM) technique is one of the most computationally efficient ways to synthesize arbitrary bandwidth sharp linear phase finite impulse response (FIR) digital filters. A great benefit of the FRM approach is a significant reduction in the number of multiplications, which can be as high as 98%, as reported in [26].…”