The design of frequency sampling filters by the method of Lagrange multipliers

Stubberud, Peter; Leondes, Cornelius T.

doi:10.1109/82.215360

Cited by 12 publications

(6 citation statements)

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“…The constraints express the maximal flatness of the frequency response at zero frequency in the case of a lowpass filter and at an arbitrary frequency in the passband (typically the center frequency) in the case of a bandpass filter. This extends the results reported in [8,9] where the mean squared error is minimized only over the stopband. The simulation results will demonstrate the importance of incorporating the passband in the minimization criterion.…”

Section: Introductionsupporting

confidence: 87%

“…As expected, as the parameter α decreases the pass band frequency response improves with a corresponding deterioration in the stop band. In the extreme case of α =1 the mean squared error is minimized only in the stop band as in the work reported in [8,9]. Instead of considering the other extreme case of α = 0 where matrix P of Eq(37) becomes singular we considered α = 0.01 where the mean squared error is minimized mainly in the pass band.…”

Section: Examplementioning

confidence: 99%

“…Schuessler and Steffen designed MFLP filters by minimizing the energy of the impulse response (which is the same as the integral of the square of the magnitude of the frequency response over all frequencies) subject to several flatness constraints at the origin [7]. Medlin, Adams and Leondes [8] and Stubberud and Leondes [9] designed MFLP filters by minimizing the energy of the error between the desired and designed frequency responses only over the stopbands subject to flatness constraints at the center of the passband (zero frequency). In this paper linear phase FIR filters with symmetric or antisymmetric impulse response are designed to have a maximally flat passband.…”

Section: Introductionmentioning

confidence: 99%

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Design of linear phase FIR filters with a maximally flat passband

Hanna

1996

IEEE Trans. Circuits Syst. II

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The design of linear phase FIR digital filters having symmetric or antisymmetric impulse response is formulated as a constrained minimization problem. The constraints express the maximal flatness of the frequency response at the origin in the case of a lowpass filter or at an arbitrary frequency in the passband in the case of a bandpass filter. The objective function , which is a quadratic form in the filter coefficients , is formed as a convex combination of two objective functions representing the energy of the error between the frequency response of the designed filter and a scaled version of the frequency response of the ideal filter in both the stop and pass bands.

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Section: Introductionsupporting

confidence: 87%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design of linear phase FIR filters with a maximally flat passband

Hanna

1996

IEEE Trans. Circuits Syst. II

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“…Developing an approximation technique, that is, finding a transfer function, when designing digital filters is a complicated scientific task. Research on the solution of the problem of filter approximation based on frequency sampling began in the 1970s [2,3], was conducted in the 1990s and is ongoing to this day [4][5][6][7][8]. These are just some of the dozens of published works.…”

Section: Introductionmentioning

confidence: 99%

Research of the Sensitivity of the Quantized Coefficients of a Digital Bandpass Filters with Frequency Sampling

Volodуmуrovуch

Pavlovуch

Andriiovуch

2020

IJEEI

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The article is devoted to the applied research of the dependence of the influence of the transfer function quantized coefficients of a digital bandpass filters with frequency sampling on its attenuation characteristic. It is shown that only the coefficients, which depend on the frequency, when quantized, significantly distort the shape of the attenuation characteristic. Such coefficients in the article are called frequency coefficients. The magnitudes of the deviations of the quantized frequency coefficients from the calculated values at different values of the bit depth are analyzed. The attenuation characteristics of the digital comb of bandpass filters based on frequency sampling with calculated and quantized coefficients are analyzed. Practical recommendations are offered to minimize the influence of frequency coefficients quantization errors at the stage of solving the task of approximation of digital bandpass filters with frequency sampling. The result will be an optimal choice of the minimum number bit of the processors or programmable logic integrated circuits (FPGA), to be used for the implementation of digital bandpass filters with frequency sampling.

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“…Tap-coe cients of the ÿlter are then calculated by inverse discrete Fourier transform of the ÿlter function. Some other MAXFLAT design techniques have also been reported and can be found in References [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

New designs of low/high‐pass and mid‐pass/stop FIR digital filters

Khan

Ohba

2001

Circuit Theory & Apps

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SUMMARYNew designs of highly e cient low=high-and mid-pass=stop (centre-symmetric band-pass=stop) FIR non-recursive digital ÿlters are presented. The designs are based on the modulation property of DFT, applied to the already presented MAXFLAT halfband low-pass ÿlters. The presented ÿlters have explicit formulas for their tap-coe cients, and therefore are very easy to design. They have highly smooth frequency response and wider transition regions like MAXFLAT ÿlters. The design formulae are modiÿed to give new classes of low=high-and mid-pass=stop ÿlters, for which, like in equiripple ÿlters, the transition bandwidth can be reduced by increasing the size of ripple on magnitude response. It is shown, with the help of design examples, that the performance of these ÿlters is comparable to that of equiripple ÿlters.

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The design of frequency sampling filters by the method of Lagrange multipliers

Cited by 12 publications

References 10 publications

Design of linear phase FIR filters with a maximally flat passband

Design of linear phase FIR filters with a maximally flat passband

Research of the Sensitivity of the Quantized Coefficients of a Digital Bandpass Filters with Frequency Sampling

New designs of low/high‐pass and mid‐pass/stop FIR digital filters

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