Optimal design of linear phase FIR digital filters with very flat passbands and equiripple stopbands

A new technique is presented for the design of digital FIR filters, with a prescribed degree of flatness in the passband, and a prescribed (equiripple) attenuation in the stopband. The design is based entirely on an appropriate use of the well-known Reméz-exchange algorithm for the design of weighted Chebyshev FIR filters. The extreme versatility of this algorithm is combined with certain "maximally flat" FIR filter building blocks, in order to generate a wide family of filters. The design technique directly leads to structures that have low passband sensitivity properties

On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

On prefilters for digital FIR filter design

A new family of digital prefilter structures is introduced, based on the Dolph-Chebyshev function. These prefilters can be combined with appropriately designed "equalizer" filters based on equiripple methods, leading to efficient FIR digital filter designs. Design examples are included, demonstrating the simplicity of the resulting designs, as compared to conventional equiripple designs

One- and two-level filter-bank convolvers

In a recent paper, it was shown in detail that in the case of orthonormal and biorthogonal filter banks we can convolve two signals by directly convolving the subband signals and combining the results. In this paper, we further generalize the result. We also derive the statistical coding gain for the generalized subband convolver. As an application, we derive a novel low sensitivity structure for FIR filters from the convolution theorem. We define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation. This gain serves as a figure of merit for the low sensitivity structure. Several numerical examples are included to demonstrate the usefulness of these ideas. By using the generalized polyphase representation, we show that the subband convolvers, linear periodically time varying systems, and digital block filtering can be viewed in a unified manner. Furthermore, the scheme called IFIR filtering is shown to be a special case of the convolver

Active beamforming with interpolated FIR filtering

The interpolated FIR (IFIR) radar was recently introduced in the context of MIMO radar theory. It was shown that this system has a signal to clutter ratio intermediate between those of the SIMO and MIMO radars. This paper considers the optimal design of the active IFIR beamformer in presence of jammers. It is shown that this beamformer can achieve beamwidths as sharp as those of colocated MIMO radars with full-length virtual arrays. At the same time, the extra complexity of MIMO radars, which arises from use of multiple transmitter waveforms and several sets of receiver matched filter banks, is not present in the IFIR realization. Design examples for IFIR radars which optimize the receiver beamforming weights in presence of jammers for fixed transmitter are also presented

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Low Complexity Multiplier-less Modified FRM Filter Bank using MPGBP Algorithm

The design of a low complexity multiplier-less narrow transition band filter bank for the channelizer of multi-standard software-defined radio (SDR) is investigated in this paper. To accomplish this, the modal filter and complementary filter in the upper and lower branches of the conventional Frequency Response Masking (FRM) architecture are replaced with two power-complementary and linear phase filter banks. Secondly, a new masking strategy is proposed to fully exploit the potential of the numerous spectra replicas produced by the interpolation of the modal filter, which was previously ignored in the existing FRM design. In this scheme, the two masking filters are appropriately modulated and alternately masked over the spectra replicas from 0 to 2$\pi$, to generate even and odd channels. This Alternate Masking Scheme (AMS) increases the potency of the Modified FRM (ModFRM) architecture for the design of a computationally efficient narrow transition band uniform filter bank (termed as ModFRM-FB). Finally, by combining the adjoining ModFRM-FB channels, Non-Uniform ModFRM-FB (NUModFRM-FB) for extracting different communication standards in the SDR channelizer is created. To reduce the total power consumption of the architecture, the coefficients of the proposed system are made multiplier-less using the Matching Pursuits Generalized Bit-Planes (MPGBP) algorithm. In this method, filter coefficients are successively approximated using a dictionary of vectors to give a sum-of-power-of-two (SOPOT) representation. In comparison to all other general optimization techniques, such as genetic algorithms, the suggested design method stands out for its ease of implementation, requiring no sophisticated optimization or exhaustive search schemes. Another notable feature of the suggested approach is that, in comparison to existing methods, the design time for approximation has been greatly reduced. To further bring down the complexity, adders are reused in recurrent SOPOT terms using the Common Sub-expression Elimination (CSE) technique without compromising the filter performance

Fir filter design for area efficient implementation /

In this dissertation, a variable precision algorithm based on sensitivity analysis is proposed for reducing the wordlength of the coefficients and/or the number of nonzero bits of the coefficients to reduce the complexity required in the implementation. Further space savings is possible if the proposed algorithm is associated with our optimal structures and derived scaling algorithm. We also propose a structure to synthesize FIR filters using the improved prefilter equalizer structure with arbitrary bandwidth, and our proposed filter structure reduces the area required. Our improved design is targeted at improving the prefilters based on interpolated FIR filter and frequency masking design and aims to provide a sharp transition-band as well as increasing the stopband attenuation. We use an equalizer designed to compensate the prefilter performance. In this dissertation, we propose a systematic procedure for designing FIR filters implementations. Our method yields a good design with low coefficient sensitivity and small order while satisfying design specifications. The resulting hardware implementation is suitable for use in custom hardware such as VLSI and Field Programmable Gate Arrays (FPGAs).FIR filters are preferred for many Digital Signal Processing applications as they have several advantages over IIR filters such as the possibility of exact linear phase, shorter required wordlength and guaranteed stability. However, FIR filter applications impose several challenges on the implementations of the systems, especially in demanding considerably more arithmetic operations and hardware components. This dissertation focuses on the design and implementation of FIR filters in hardware to reduce the space required without loss of performance