Frequency-response Masking Approach Research Articles

A Low Complexity and High Modularity Design for Continuously Variable Bandwidth Digital Filters

ABSTRACT Digital filters with variable bandwidth can be used for a variety of applications. Arbitrary change in the bandwidth of a digital Finite Impulse Response (FIR) filter can be acquired using sampling rate converters. In this paper, a sampling rate converter is proposed which is generated from Pascal structure, a fractional delay filter having low hardware complexity and high modularity. The proposed sampling rate converter requires lesser number of multipliers for implementation when compared with the sampling rate converters in the literature. A low pass filter having a single bandwidth sandwiched between two sampling rate converters can contribute multiple bandwidths in such a way that each bandwidth is an arbitrary variation of the original bandwidth. A two stage Frequency response masking approach (FRM) is used for the hardware efficient design of the original low pass filter. A low complexity and high modularity novel design for a continuously varying bandwidth of a digital FIR filter is proposed in this paper using the proposed sampling rate converter. The modularity of the Pascal structure can be used to control both pass band ripple as well as stop band attenuation of the continuously variable bandwidth FIR filter design. Different communication standards in a Software defined radio (SDR) channelizer is realized using the proposed design of continuously variable bandwidth filter.

Design of a novel CEM‐FRM‐based low‐complexity channelised radar transmitter

With the development of the radar technology, it is required that a radar has wider bandwidth and can transmit multiple signals simultaneously. The polyphase digital channelised transmitter structure can transmit multiple signals simultaneously and increase the bandwidth of the output signal. However, in order to reduce the frequency aliasing and improve the spectrum utilisation, the prototype filter needs to have sharp transition bandwidth. The design of the prototype filter directly affects the performance of the radar transmitter. Using the complex-exponential modulation frequency-response masking (CEM-FRM) approach to design the prototype filter can obtain both sharp transition bandwidth and low complexity. The application of a polyphase structure can further reduce the complexity of the filter bank and make the sampling rate of the output signal several times the field programmable gate array operating frequency. The proposed CEM-FRM-based low complexity polyphase channelised radar transmitter is verified by MATLAB simulation and the theoretical complexity of the proposed CEM-FRM-based channelised radar transmitter structure is compared with other methods.

Design of Low-Complexity IFRM-UMFB Architecture for Wideband Digital Receivers

Modulated filter bank with low complexity is the key to realize the engineering applications for speech signal processing, multicarrier communication, and wideband digital receivers. The frequency response masking (FRM) technology is an effective method to design finite impulse response filters with narrow transition band (NTB). In this paper, an interpolation FRM unified modulated filter bank (IFRM-UMFB) architecture with NTB is proposed to reduce the computational complexity of the modulated filter bank architecture. The IFRM approach increases the transition band of two masking filters by the interpolation of N and reduces the computational complexity of two masking filters compared with classic FRM approach. The proposed IFRM-UMFB architecture with NTB is suitable for different odd-stacked or even-stacked, maximally decimated or non-maximally decimated structures. The proposed IFRM-UMFB architecture with NTB is verified to be correct through simulation. The complexity comparison result shows that the proposed IFRM-UMFB architecture offers multipliers reduction of 77.4% over the directly design approach and 26.5% over the classic FRM approach. Moreover, the proposed IFRM-UMFB architecture with NTB also can be directly applied to wideband digital receivers with high sampling rate.

Modeling and Simulation of Frequency Response Masking FIR Filter Bank using Approximate Multiplier for Hearing Aid Application

The tremendous increase in the use of portable electronic devices is due to the development in the fields of signal processing and electronic technology. These battery operated devices needs reduction in power consumption with increased performance and long battery life. Since CMOS technology scaling fast approaches its physical limit of minimum supply voltage and smaller feature size, the hardware designer has to opt for new multiplier architectures for achieving low power and high speed performance. This paper proposes an area and power efficient approximate multiplier architecture. The error metrics are estimated to verify its performance advantage over other approximate multipliers. Using Frequency Response masking approach, a 6-band non-uniform digital FIR filter bank is developed using approximate multiplier for hearing aid application. Audiogram matching is done with audiograms of two different types of hearing losses and the matching error is computed. Simulation results show that the audiogram matching error falls within +/- 4 dB range.

Add-Equalize Structures for Linear-Phase Nyquist FIR Filter Interpolators and Decimators

This paper introduces add-equalize structures for the implementation of linear-phase Nyquist ( $M$ th-band) finite-length impulse response (FIR) filter interpolators and decimators. The paper also introduces a systematic design technique for these structures based on iteratively reweighted $\ell _{1}$ -norm minimization. In the proposed structures, the polyphase components share common parts which leads to a considerably lower implementation complexity as compared to conventional single-stage converter structures. The complexity is comparable to that of multi-stage Nyquist structures. A main advantage of the proposed structures is that they work equally well for all integer conversion factors, thus including prime numbers which cannot be handled by the regular multi-stage Nyquist converters. Moreover, the paper shows how to utilize the frequency-response masking approach to further reduce the complexity for sharp-transition specifications. It also shows how the proposed structures can be used to reduce the complexity for reconfigurable sampling rate converters. Several design examples are included to demonstrate the effectiveness of the proposed structures.

Modified Metaheuristic Algorithms for the Optimal Design of Multiplier-Less Non-uniform Channel Filters

Reconfigurable non-uniform channel filters are now being widely used in software define radio (SDR). The hardware implementation of these filters requires low complexity, low chip area and low power consumption. The frequency response masking (FRM) approach is proved to be a good candidate for the realization of a sharp digital finite impulse response (FIR) filter with low complexity. To reduce the complexity further, this paper gives an optimal design method which makes the channel filters totally multiplier-less. This is done in two steps. The channel filters are designed using the FRM approach with continuous filter coefficients. To obtain multiplier-less design, these filter coefficients are converted to finite-precision coefficients using signed power of two (SPT) space and the filter coefficients are synthesized in the canonic signed-digit (CSD) format. But this may lead to degradation of the filter performance. Hence the filter coefficients synthesis in the CSD format is formulated as an optimization problem. Several meta-heuristic algorithms like Differential Evolution (DE), Artificial Bee Colony (ABC), Harmony Search Algorithm (HSA) and Gravitational Search Algorithm (GSA) are modified and deployed and the best one is selected.

Design of Multiplier-less Reconfigurable Non-uniform Channel Filters using Meta-heuristic Algorithms

Low complexity and reconfigurability are reported to be the key features in a software defined radio (SDR). To obtain these features, a reconfigurable architecture based on frequency response masking (FRM) technique can be used for the implementation of the channel filters in the SDR. The frequency response masking approach is proved to be a good candidate for the realization of a sharp digital finite impulse response (FIR) filter with low complexity. To reduce the complexity and power consumption for hardware realization, a design method which makes the channel filters totally multiplierless is proposed in this paper. Continuous filter coefficients are first converted to finite precision coefficients using signed power of two (SPT) space to obtain a multiplier-less filter. The representation of the FRM filter coefficients in the SPT space can degrade the filter performance. This calls for the use of a suitable optimization technique. The classical gradient based optimization techniques cannot be deployed here, because the search space consists of integers. In this context, meta-heuristic algorithm is a good choice as it can be tailor made to suit the problem under consideration. They are especially useful in finding near optimal solutions in multimodal, multidimensional space. Several meta-heuristic algorithms are modified in this paper to be used for the discrete optimization.

Continuously Variable Bandwidth Sharp FIR Filters with Low Complexity

In software defined radio (SDR), sharp filters of different bandwidth are required to fine tune the desired channel. This requires different computational resources and large number of filter coefficients. This paper proposes a continuously variable bandwidth sharp finite impulse response (FIR) filter with low distortion and low complexity. For this, a fixed length FIR filter is used with two arbitrary sampling rate converters. This system can be used for both the continuous increase as well as decrease of the effective bandwidth of a filter. The low complexity and sharpness are achieved by using the frequency-response masking (FRM) approach for the design of the fixed length FIR filter. The sharp transition width leads to maximum rejection to channel interference in SDR.

An Efficient Algorithm for the Optimization of FIR Filters Synthesized Using the Multistage Frequency-Response Masking Approach

A very efficient technique to drastically reduce the number of multipliers and adders in narrow transition-band linear-phase finite-impulse response digital filters is to use the one-stage or multistage frequency-response masking (FRM) approach originally introduced by Y.C. Lim (see ibid.,1986). In the original synthesis techniques developed by Lim and Lian (see ibid.,1993), the subfilters in the overall implementation are separately designed. As shown earlier by the first two authors of this contribution as well as Johansson, the arithmetic complexity in the one-stage FRM filter designs can be considerably reduced by using the following two-stage technique for simultaneously optimizing all subfilters. First, a suboptimal solution is found by using a simple design scheme. Second, this solution is used as a start-up solution for further optimization being carried out by an efficient unconstrained nonlinear optimization algorithm. This paper exploits this approach for synthesizing multistage FRM filters. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized FRM filters are approximately 70 percent compared with those of the filters synthesized using the original multistage FRM filter design schemes.

A Low Complexity Reconfigurable Multi-stage Channel Filter Architecture for Resource-Constrained Software Radio Handsets

Software defined radio (SDR) is emerging as a powerful platform for future generation cellular systems, due to its capability to operate conforming to multiple mobile radio standards. Channelizer in an SDR operates at the highest sampling rate and hence a low complexity design is needed for the most computationally intensive part of the SDR receiver. The channel filters in the channelizer extracts radio channels of varying bandwidths, corresponding to various communication standards from the wideband input signal. An architecture for implementing low complexity, low power and reconfigurable channel filter for the SDR mobile handsets, based on multi-stage frequency response masking (FRM) is proposed in this paper. The proposed architecture is unique in a way that it is able to effectively exploit the redundancy in multi-stage realization by utilizing the common masking filters and also capable of extracting varying bandwidth channels. Design examples show that the proposed architecture offers 47.5% complexity reduction and 18.1% power reduction over single-stage FRM approach.

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

This paper introduces two classes of frequency-response masking (FRM) linear-phase finite (length) impulse response (FIR) filters for interpolation and decimation by arbitrary integer factors M. As they are based on the FRM approach, the proposed filters are low-complexity (efficient) sharp-transition linear-phase FIR interpolation and decimation filters. Compared to previously existing FRM linear-phase FIR filter classes for interpolation and decimation, the new ones offer lower complexity and more freedom in selecting the locations of the passband and stopband edges. Furthermore, the proposed classes of FRM filters can, as special cases, realize efficient Mth-band FRM linear-phase FIR interpolation and decimation filters for all values of M. Previously, only half-band (M = 2) FRM linear-phase FIR filters have appeared in the literature. The paper includes design techniques suitable for the new filters and design examples illustrating their efficiency.

On the design of high-complexity cosine-modulated transmultiplexers based on the frequency-response masking approach

Two efficient techniques exploiting the frequency-response masking (FRM) approach are proposed in order to make it feasible to design prototype filters for highly selective nearly perfect-reconstruction cosine-modulated transmultiplexers and filter banks (CMTs and CMFBs) having a very large number of channels. In these design schemes, the number of unknowns is drastically reduced when compared with the corresponding techniques for designing direct-form prototype filters. Furthermore, in the proposed techniques, the main figures of merits, that is, the intersymbol interference and the interchannel interference for CMTs and the overall and aliasing distortions for CMFBs are taken into account in a controlled manner. In order to speed up the convergence of these two optimization techniques, simplifications for computing the resulting nonlinear constraints and the corresponding gradient vectors are proposed. They differ from each other in the sense that the first and second ones utilize the frequency-domain and time-domain constraints for controlling the figures of merit, respectively. Combining these two techniques results in numerically efficient algorithms for designing optimized CMTs (or CMFBs) with a reduced computational complexity (number of arithmetic operations per output sample), particularly when both branches of the FRM structure are required. Design examples are included illustrating the efficiency of the design methods and the high performance of the resulting CMT structures.

Extrapolated impulse response filter and its application in the synthesis of digital filters using the frequency-response masking technique

Techniques based on the frequency-response masking (FRM) approach are known to be highly effective for reducing the number of multipliers and adders in linear-phase finite-impulse response (FIR) filters. The basic FRM structure comprises a band-edge shaping filter and two masking filters. It is observed that the impulse response of the band-edge shaping filter of an FRM structure exhibits a quasi-periodic property. Previous study showed that lowpass or highpass digital FIR filters, whose impulse responses are quasi-periodic, can be synthesized using extrapolated impulse response technique, which leads to structure with much reduced arithmetic complexity. In this paper, an implementation of the extrapolated impulse response filter is presented. An FRM technique incorporating extrapolated impulse response band-edge shaping filter is introduced. An iterative optimization procedure is proposed to design the FRM sub-filters. It is demonstrated using an example taken from the literature that our new technique produces a saving of over 20% in the number of multipliers used.

Extrapolated impulse response filter and its application in the synthesis of digital filters using the frequency-response masking technique

Techniques based on the frequency-response masking (FRM) approach are known to be highly effective for reducing the number of multipliers and adders in linear-phase finite-impulse response (FIR) filters. The basic FRM structure comprises a band-edge shaping filter and two masking filters. It is observed that the impulse response of the band-edge shaping filter of an FRM structure exhibits a quasi-periodic property. Previous study showed that lowpass or highpass digital FIR filters, whose impulse responses are quasi-periodic, can be synthesized using extrapolated impulse response technique, which leads to structure with much reduced arithmetic complexity. In this paper, an implementation of the extrapolated impulse response filter is presented. An FRM technique incorporating extrapolated impulse response band-edge shaping filter is introduced. An iterative optimization procedure is proposed to design the FRM sub-filters. It is demonstrated using an example taken from the literature that our new technique produces a saving of over 20% in the number of multipliers used.

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.

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.

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.

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.

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.

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.