A direct search procedure for designing finite duration impulse response filters

Gold, B.; Jordan, K.

doi:10.1109/tau.1969.1162027

Cited by 43 publications

(4 citation statements)

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“…FIR filters, or finite-impulse-response filters, is a digital filter that captures the strength of the incoming signal for only a finite period of time [54]. The computation of the output sequence from an FIR filter can be synthesized by discrete convolution [30]. The ubiquity of FIR filters within domains such as noise removal in EKGs [13], image processing for texture mapping [38], and mobile communications [75] have consequently led to the development of highly efficient algorithms for 1D discrete convolution, such as new nesting schemes [14,78], the Fermat number transform [2], and the Good-Thomas PFA.…”

Section: Problems and Applications Of Convolutionmentioning

confidence: 99%

Derivation and Analysis of Fast Bilinear Algorithms for Convolution

Solomonik²

2019

Preprint

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The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed on terabytes or petabytes of data, so even constant factors of improvement can significantly reduce the computation time. We leverage the formalism of bilinear algorithms to describe and analyze all of the most popular approaches. This unified lens permits us to study the relationship between different variants of convolution as well as to derive error bounds and analyze the cost of the various algorithms. We provide new derivations, which predominantly leverage matrix and tensor algebra, to describe the Winograd family of convolution algorithms as well as reductions between 1D and multidimensional convolution. We provide cost and error bounds as well as experimental numerical studies. Our experiments for two of these algorithms, the overlap-add approach and Winograd convolution algorithm with polynomials of degree greater than one, show that fast convolution algorithms can rival the accuracy of the fast Fourier transform (FFT) without using complex arithmetic. These algorithms can be used for convolution problems with multidimensional inputs or for filters larger than size of four, extending the state-of-the-art in Winograd-based convolution algorithms.

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Section: Problems and Applications Of Convolutionmentioning

confidence: 99%

Derivation and Analysis of Fast Bilinear Algorithms for Convolution

Solomonik²

2019

Preprint

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“…Various optimization techniques have been proposed by Gold & Jordan [15], Rabiner et al [16], [17], Herrmann & Schuessler [18] and Herrmann [19] which, along with the classical window design methods reported by Kaiser [20] and Helms [21] provide the user with several possibilities for approximating filters with arbitrary frequency-response characteristics. [19] reported a third technique for designing FIR filters which solves a system of nonlinear equations to generate a filter with an equiripple approximation error.…”

Section: Literature Review On Fir Filters and Their Implementationmentioning

confidence: 99%

FPGA Implementation of Higher Order FIR Filter

Singh¹,

Prakash

2017

IJECE

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The digital Finite-Impulse-Response (FIR) filters are mainly employed in digital signal processing applications. The main components of digital FIR filters designed on FPGAs are the register bank to save the samples of signals, adder to implement sum operations and multiplier for multiplication of filter coefficients to signal samples. Although, design and implementation of digital FIR filters seem simple but the design bottleneck is multiplier block for speed, power consumption and FPGA chip area occupation. The multipliers are an integral part in FIR structures and these use a large part of the chip area. This limits the number of processing elements (PE) available on the chip to realize a higher order of filter. A model is developed in the Matlab/Simulink environment to investigate the performance of the desired higher order FIR filter. An equivalent FIR filter representation is designed by the Xilinx FIR Compiler by using the exported FIR filter coefficients. The Xilinx implementation flow is completed with the help of Xilinx ISE 14.5. It is observed how the use of higher order FIR filter impacts the resource utilization of the FPGA and it's the maximum operating frequency. Keyword:Fir filter FPGA Higher order fir filter Xilinx

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“…In the Gold and Jordan paper [ 5 ] , results were obtained only for a few low-pass filters. Also, the computer optimization technique was semiautomatic, requiring an online interactive display oscilloscope.…”

Section: F(x) = 7 H(z/v)w(u)v-'dvmentioning

confidence: 99%

An approach to the approximation problem for nonrecursive digital filters

Rabiner¹,

Gold

McGonegal³

1970

IEEE Trans. Audio Electroacoust.

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152

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A direct design procedure for nonrecursive digital filters, based primarily on the frequency-response characteristic of the desired filters, is presented. An optimization technique is used to minimize the maximum deviation of the synthesized filter from the ideal filter over some frequence range. Using thisfrequency-sampling technique, a wide variety of low-pass and bandpass filters have been designed, as well as several wide-band differentiators. Some experimental results on truncation of the filter coefficients are also presented. A brief discussion of the technique of nonuniform sampling is also included.

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A direct search procedure for designing finite duration impulse response filters

Cited by 43 publications

References 0 publications

Derivation and Analysis of Fast Bilinear Algorithms for Convolution

Derivation and Analysis of Fast Bilinear Algorithms for Convolution

FPGA Implementation of Higher Order FIR Filter

An approach to the approximation problem for nonrecursive digital filters

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