Synthesis of Narrowband Linear-Phase FIR Filters with a Piecewise-Polynomial Impulse Response

Lehto, R.; Saramäki, T.; Vainio, Olli

doi:10.1109/iscas.2005.1465011

Cited by 6 publications

(14 citation statements)

References 5 publications

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“…The idea in our earlier approach [9] was to divide the impulse response into subresponses and to generate each subresponse with polynomials of a given degree. If we now consider an impulse response of an optimum wideband linear-phase FIR filter, it is seen in Fig.…”

Section: The Idea For a Piecewise-polynomial Sinusoidal Approachmentioning

confidence: 99%

“…using our earlier approach for a piecewise-polynomial impulse response [9]. Create a transfer function F (z) − (ω c /π)z −N as follows:…”

Section: Implementation Of Type 1 Filtersmentioning

confidence: 99%

“…using our earlier approach for a piecewise-polynomial impulse response [9] modified by adding separately generated center coefficients.…”

Section: Implementation Of Type 4 Filtersmentioning

confidence: 99%

“…The synthesis scheme proposed in this paper is partly based on the previous work done by the authors [9] to design linearphase FIR filters with a piecewise-polynomial impulse response and on merging it with and modifying the method proposed by Chu and Burrus [4,5] for the synthesis scheme of wideband FIR filters. Chu and Burrus first designed what is called an envelope filter with a piecewise-polynomial impulse response, for which the design scheme of the authors [9] is very efficient. Secondly, the coefficient values of this envelope filter are modified by multiplying them with a sinusoidal function depending on the linear-phase FIR filter type and by adding at least one center coefficient, which leads to a wideband FIR filter.…”

Section: Introductionmentioning

confidence: 99%

“…A 2N th-order Type 3 envelope filter with a piecewise-polynomial impulse response is created by using the scheme proposed by the authors in [9]. The resulting impulse response is multiplied by a sinusoidal function sin[(n − N)ω c ], where ω c is roughly the angular frequency at which the zero-phase response of the overall filter takes on the value of half.…”

Section: Introductionmentioning

confidence: 99%

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Synthesis of Wideband Linear-Phase FIR Filters with a Piecewise-Polynomial-Sinusoidal Impulse Response

Lehto

Saramäki

Vainio

2009

Circuits Syst Signal Process

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A method is presented to synthesize wideband linear-phase finite-impulseresponse (FIR) filters with a piecewise-polynomial-sinusoidal impulse response. The method is based on merging the earlier synthesis scheme proposed by the authors to design piecewise-polynomial filters with the method proposed by Chu and Burrus. The method uses an arbitrary number of separately generated center coefficients instead of only one or none as used in the method by Chu-Burrus. The desired impulse response is created by using a parallel connection of several filter branches and by adding an arbitrary number of center coefficients to form it. This method is especially effective for designing Hilbert transformers by using Type 4 linear-phase FIR filters, where only real-valued multipliers are needed in the implementation. The arithmetic complexity is proportional to the number of branches, the common polynomial order for each branch, and the number of separate center coefficients. For other linear-phase FIR filter types the arithmetic complexity depends additionally on the number of complex multipliers. Examples are given to illustrate the benefits of this method compared to the frequency-response masking (FRM) technique with regard to reducing the number of coefficients as well as arithmetic complexity.

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Section: The Idea For a Piecewise-polynomial Sinusoidal Approachmentioning

confidence: 99%

“…using our earlier approach for a piecewise-polynomial impulse response [9]. Create a transfer function F (z) − (ω c /π)z −N as follows:…”

Section: Implementation Of Type 1 Filtersmentioning

confidence: 99%

“…using our earlier approach for a piecewise-polynomial impulse response [9] modified by adding separately generated center coefficients.…”

Section: Implementation Of Type 4 Filtersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Synthesis of Wideband Linear-Phase FIR Filters with a Piecewise-Polynomial-Sinusoidal Impulse Response

Lehto

Saramäki

Vainio

2009

Circuits Syst Signal Process

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Synthesis of recursive linear‐phase filters for fixed‐point hardware platforms

Khorbotly

Hassan

Veillette

2017

IET Circuits, Devices & Systems

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This study presents a methodology for recursive implementation of linear-phase finite impulse response (FIR) filters in fixed-point hardware platforms. The work uses a modified version of the switching and reset method to efficiently implement recursive linear-phase exponential filters. An error analysis is presented that defines the upper error bounds resulting from the switching and reset implementation of the exponential filters in fixed-point hardware. The exponential filters are then used as basis functions to synthesise other filters of interest. Gaussian filters are used as an example. The suggested recursive implementation delivers an accurate approximation of the Gaussian function. Unlike traditional techniques for implementing FIR filters, the hardware size of this recursive technique is O(1). In other words, increasing the order of a filter does not proportionally increase its hardware size. The results show that when implementing Gaussian filters on FPGAs, doubling the size of the filter, only increased the hardware size by an average of 6.12%.

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