Frequency Response Masking Research Articles

A Weighted Least-Square-Based Approach to FIR Filter Design Using the Frequency-Response Masking Technique

This paper presents a new method for the design of sharp linear phase FIR filters using the frequency-response masking (FRM) technique. The method is based on a weighted least square (WLS) approach, and the design problem is solved iteratively. The original least square (LS) problem is decomposed into two LS problems, each of which can be solved analytically. The effectiveness of the method is demonstrated through the design of a lowpass linear phase sharp FIR digital filter.

Design of High-Resolution Cosine-Modulated Transmultiplexers with Sharp Transition Band

Due to the growing importance of multichannel modulation, there has been great interest in the design of high-performance transmultiplex systems. In this paper, a new cosine-modulated transmultiplex structure is proposed based on a prototype filter designed with the frequency-response masking (FRM) approach. This new structure leads to substantial reduction in the computational complexity (number of multiplications per output sample) of the prototype filters having sharp transition band and equivalently small roll-off values. The relation between the interpolation factor used in the FRM prototype filter and the decimation factor in the subbands leads to distinct structures. Examples included indicate that the reduction in computational complexity can be higher than 50% of the current state-of-art designs, whereas the reduction on the number of distinct coefficients of the prototype filter can be reduced even further (over 75%). As a result, the proposed approach allows the design of very selective subfilters for transmultiplexes with a very large number of subchannels.

Optimal design of IIR frequency-response-masking filters using second-order cone programming

The frequency-response-masking (FRM) technique proposed by Lim (1986) has proven effectiveness for the design of very sharp digital filters with reduced implementation complexity compared to other options. In this paper, we propose a constrained optimization method for the design of basic and multistage FRM filters where the prototype filters are of infinite-impulse response (IIR) with prescribed pole radius. The design is accomplished through a sequence of linear updates for the design variables with each update carried out using second-order cone programming. Computer simulations have demonstrated that the class of IIR FRM filters investigated in the paper offers an attractive alternative to its finite-impulse response counterpart in terms of filter performance, system delay, and realization complexity.

OPTIMIZATION OF FREQUENCY-RESPONSE MASKING BASED FIR FILTERS

A very efficient technique to drastically reduce the number of multipliers and adders in implementing linear-phase finite-impulse response (FIR) digital filters in applications demanding a narrow transition band is to use the frequency-response masking (FRM) approach originally introduced by Lim. The arithmetic complexity can be even further reduced using a common filter part for constructing the masking filters originally proposed by Lim and Lian. A drawback in the above-mentioned original FRM synthesis techniques is that the subfilters in the overall implementations are separately designed. In order to further reduce the arithmetic complexity in these two FRM approaches, the following two-step optimization technique is proposed for simultaneously optimizing the subfilters. At the first step, a good suboptimal solution is found by using a simple iterative algorithm. At the second step, this solution is then used as a start-up solution for further optimization being carried out by using an efficient unconstrained nonlinear optimization algorithm. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized filter are less than 80% compared with those of the FRM filter obtained using the original FRM design schemes in the case where the masking filters are separately implemented. If a common filter part is used for realizing the masking filters, then an additional reduction of more than 10% is achieved compared with the optimized design with separately implemented masking filters.

A MODIFIED FREQUENCY-RESPONSE MASKING STRUCTURE FOR HIGH-SPEED FPGA IMPLEMENTATION OF SHARP FIR FILTERS

This paper presents the design and implementation of high-speed, multiplierless, arbitrary bandwidth sharp FIR filters based on frequency-response masking (FRM) technique. The FRM filter structure has been modified to improve the throughput rate by replacing long band-edge shaping filter in the original FRM approach with two to three cascaded short filters. The proposed structure is suitable for FPGA as well as VLSI implementation for sharp digital FIR filters. It is shown by an example that a near 200-tap equivalent Remez FIR filter can be implemented in a single Xilinx XC4044XLA device that operates at sampling frequency of 5.5 MHz.

EFFICIENT DESIGN OF NARROWBAND COSINE-MODULATED FILTER BANKS USING A TWO-STAGE FREQUENCY-RESPONSE MASKING APPROACH

A new cosine-modulated filter bank (CMFB) structure is proposed based on the frequency-response masking (FRM) approach using masking filter decomposition. The resulting structure, the so-called FRM2-CMFB, presents reasonable computational complexity (number of arithmetic operations per output sample) and allows one to design filter banks with extremely large number of bands. The examples include the use of M=1024 bands, where the standard minimax method cannot be employed. These examples indicate that the reduction in computational complexity can be as high as 60% of the original FRM-CMFB structure, which does not use masking filter decomposition.

SINGLE FILTER FREQUENCY-RESPONSE MASKING FIR FILTERS

In this work filter structures that decrease the required number of multipliers and adders for implementation of linear-phase FIR filters using frequency-response masking techniques are introduced. The basic idea of the proposed structures is that identical subfilters are used. This leads to the same arithmetic structure can be multiplexed in the implementation, reducing the number of required multipliers and adders. The subfilters are mapped using the folding transformation to obtain an area-efficient time-multiplexed (or pipeline/interleaved) implementation. Both narrow-band and wide-band frequency-response masking as well as arbitrary bandwidth frequency-response masking techniques are considered. The filter design is discussed and for each filter structure the limits on the specifications are derived. Designed examples show the usefulness of the proposed structures.

FREQUENCY-RESPONSE MASKING BASED FIR FILTER DESIGN WITH POWER-OF-TWO COEFFICIENTS AND SUBOPTIMUM PWR

This paper presents a new method for designing sharp linear phase FIR filters with power-of-two coefficients. The method is based on a frequency-response masking technique. In this method, the power-of-two coefficients and continuous scaling parameters of the subfilters are taken to be decision variables, and minimizing peak weighted ripple (PWR) is taken to be the design objective. The resulting nonlinear mixed integer optimization problem for each subfilter is first reduced to an equivalent discrete optimization problem whose search region is then cropped for efficiency of computation, similar to the approach in Ref. 1, although a different cropping strategy is used here. The effectiveness of the method is demonstrated through a lowpass linear phase sharp FIR digital filter example.

APPLICATION OF FAST FILTER BANK FOR TRANSCRIPTION OF POLYPHONIC SIGNALS

In this paper, a novel approach to the transcription of polyphonic signals is investigated. The method makes use of top–down analysis algorithm and bottom–up reconstruction of frequency contents of musical signals using a reference database that contains the spectral profiles of all single notes. Recognition accuracy is enhanced by analyzing the time-frequency contents using a bank of narrow band filters with very sharp transition band. The filters are designed using the Frequency-Response Masking technique. The high selectivity of the filters has enhanced the frequency analysis and increased the accuracy of identification. The method was tested with musical notes generated from an acoustic piano. The results show that for single notes and chords up to four notes, perfect identification can be achieved.

Optimal design of frequency-response-masking filters using semidefinite programming

Since Lim's paper (see IEEE Trans. Circuits Syst., vol.33, p. 357-364, Apr. 1986) on the frequency-response-masking (FRM) technique for the design of finite-impulse response digital filters with very small transition widths, the analysis and design of FRM filters has been a subject of study. In this paper, a new optimization technique for the design of various FRM filters is proposed. Central to the new design method is a sequence of linear updates for the design variables, with each update carried out by semidefinite programming. Algorithmic details for the design of basic and multistage FRM filters are presented to show that the proposed method offers a unified design framework for a variety of FRM filters. Design simulations are included to illustrate the proposed algorithms and to evaluate the design performance in comparison with that of several existing methods.

Complexity Reduction For FRM-based FIR Filters Using The Prefilter-Equalizer Technique

A new method to reduce the number of arithmetic operations in a sharp FIR filter synthesized by the frequency-response masking (FRM) technique is presented. The success of the proposed method is based on a modified FRM approach where the subfilters in the FRM approach are implemented by using recently introduced prefilter-equalizer based filters. It is shown, by means of examples, that the proposed method yields considerable savings in the numbers of multipliers and adders compared to the original single-stage FRM approach.

Optimization Of FRM Filters Using The WLS–Chebyshev Approach

This paper presents efficient methods for designing linear-phase finite impulse response filters by combining the frequency-response masking (FRM) approach and the weighted least-squares (WLS)-Chebyshev method. We first use the WLS-Chebyshev method to design quasi-equiripple FRM filters, achieving better performances with respect to the passband ripple or the stopband attenuation, when compared with the standard FRM design. Then, by exploiting the concept of critical bands, introduced in this paper, we present a method for designing modified FRM filters with a further reduction in the computational complexity. This is achieved by properly relaxing the specifications for the FRM base and masking filters and using the ability of the WLS-Chebyshev method to trade off the minimum attenuation and the total energy in the filter’s stopband. Computational savings are in the order of 10%–15% of the original number of coefficients of the standard FRM design (using the concept of “don’t care” bands for the masking filters).

Two-Channel FIR Filter Banks Utilizing the FRM Approach

The frequency-response masking (FRM) approach has been introduced as a means of generating narrow transition band linear-phase finite impulse response (FIR) filters with a low arithmetic complexity. This paper proposes an approach for synthesizing two-channel maximally decimated FIR filter banks utilizing the FRM technique. For this purpose, a new class of FRM filters is introduced. Filters belonging to this class are used for synthesizing nonlinear-phase analysis and synthesis filters for two types of two-channel filter banks. For the first type, there exist no phase distortion and aliasing errors, but this type suffers from a small amplitude distortion as for the well-known quadrature mirror filter (QMF) banks. Compared to conventional QMF filter banks, the proposed banks lower significantly the overall arithmetic complexity at the expense of a somewhat increased overall filter bank delay in applications demanding narrow transition bands. For the second type, there are also small aliasing errors, allowing one to reduce the arithmetic complexity even further. Efficient structures are introduced for implementing the proposed filter banks, and algorithms are described for maximizing the stopband attenuations of the analysis and synthesis filters in the minimax sense subject to the given allowable amplitude and/or aliasing errors. Examples are included illustrating the benefits provided by the proposed filter banks.

Complexity Reduction By Decoupling The Masking Filters From The Bandedge Shaping Filter In The FRM Technique

In the frequency-response masking (FRM) approach, the complexity of two masking filters is heavily dependent on the interpolation factor and the cutoff frequencies of the bandedge shaping filter. In this paper, we propose a novel structure that decouples the masking filters from the bandedge shaping filter. The design equations together with the design procedures are presented. With the introduction of an additional decoupling stage, the complexity of the overall filter can be greatly reduced. Our example shows that more than 40% savings in the numbers of multipliers and adders can be achieved compared with the original FRM approach.

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

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 inter- symbol 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. Ke yw ords: filter banks, cosine-modulated filter banks, frequency-response masking, high resolution spectrum analysis.

FPGA Implementation of Digital Filters Synthesized Using the FRM Technique

The effective length of a filter designed using the frequency-response masking (FRM) technique is very long and requires a very large number of delay elements. In this paper, we present some useful techniques for reducing the data transfer between the field programmable gate array (FPGA) and external memory when the random logic is implemented using the FPGA and the delay elements are implemented using an external memory such as dynamic random access memory.

Use Of The Remez Algorithm For Designing FRM Based FIRr Filters

A very efficient technique for drastically reducing the number of multipliers and adders in narrow transition-band linear-phase finite impulse response (FIR) filters is to use the one-stage or multistage frequency-response masking (FRM) approach as originally introduced by Lim. In the original synthesis techniques developed by Lim and Lian, the subfilters in the overall approach were designed using time-consuming linear programming. In order to perform the overall synthesis faster, this paper shows how these subfilters can be designed with the aid of the the Remez multiple exchange algorithm, the most powerful technique for designing arbitrary-magnitude linear-phase FIR filters in the minimax sense. In addition to speeding up the overall procedure, the use of the Remez algorithm enables one to generate a very fast MATLAB program for the overall synthesis so that after being given the filter specifications as well as the number of stages, the program automatically provides the solution with the minimum number of multipliers and adders required in the overall implementation. This is possible because the MATLAB Remez routine is directly available and thus can be used for this purpose after appropriate modifications.

Special issue on the Frequency-response masking technique and its applications

Special issue on the Frequency-response masking technique and its applications

An improved frequency response masking approach for designing sharp FIR filters

A new method to reduce the number of multipliers in the design of sharp FIR filters by frequency-response masking technique is presented. The success of the proposed method is based on a modified frequency-response masking approach where one of the subfilters in the approach is implemented by interpolated finite-impulse response (IFIR) technique. We have shown by example that the proposed method yields additional savings of 21% in the number of multipliers compared to the original frequency-response masking approach.

Special issue on the frequency-response masking technique and is applications

Special issue on the frequency-response masking technique and is applications