Simultaneous amplitude and phase approximation for FIR filters

Leeb, F.; Henk, Tamás

doi:10.1109/iscas.1988.14868

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…This requires access to the phase information for each spectrogram ) and unfortunately we could not successfully train our model with phase vectors. Although, there are some approaches for phase approximation (Leeb & Henk, 1989;Mulgrew, 2013) or reconstructing signal almost without phase information (Kumar et al, 2019) using GAN, we noticed they often introduce noise (ambient, background, hissing, etc.) to the reconstructed signal.…”

Section: Spectrogram Fidelity and Varietymentioning

confidence: 79%

Conditioning Trick for Training Stable GANs

Esmaeilpour,

Sallo,

St-Georges

et al. 2020

Preprint

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In this paper we propose a conditioning trick, called difference departure from normality, applied on the generator network in response to instability issues during GAN training. We force the generator to get closer to the departure from normality function of real samples computed in the spectral domain of Schur decomposition. This binding makes the generator amenable to truncation and does not limit exploring all the possible modes. We slightly modify the BigGAN architecture incorporating residual network for synthesizing 2D representations of audio signals which enables reconstructing high quality sounds with some preserved phase information. Additionally, the proposed conditional training scenario makes a trade-off between fidelity and variety for the generated spectrograms. The experimental results on UrbanSound8k and ESC-50 environmental sound datasets and the Mozilla common voice dataset have shown that the proposed GAN configuration with the conditioning trick remarkably outperforms baseline architectures, according to three objective metrics: inception score, Fréchet inception distance, and signal-to-noise ratio.

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Section: Spectrogram Fidelity and Varietymentioning

confidence: 79%

Conditioning Trick for Training Stable GANs

Esmaeilpour,

Sallo,

St-Georges

et al. 2020

Preprint

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show abstract

“…From Equations ( 15) and (18), it is clear that θ 1 (') and θ 2 (') are the phase functions exhibited by the two branch polynomials g 1 (jj) and g 2 (jj), respectively. By applying mathematical processing, one can prove the following:…”

Section: The Scattering Properties Of Multiband Lattice Reference Str...mentioning

confidence: 99%

“…In literature, a variety of design methods and algorithms are available for low-pass lattice and bireciprocal wave digital filters approximating amplitude or simultaneous amplitude and phase requirements [15][16][17][18][19][20][21][22][23]. The design of low-pass ladder wave digital filters has been considered by Sedlmeyer and Fettweis [24], Fettweis et al [25], and Constantinides [26].…”

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confidence: 99%

On the design of multiband transmission functions synthesized by one wave digital lattice structure

Yaseen

2011

Circuit Theory & Apps

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SUMMARYIn this contribution, the design of multiband transmission functions is considered. Independent and arbitrary number of bands can be designed. Moreover, the whole transmission function is synthesized by one wave digital lattice structure. The approximation process starts by extracting the scattering matrix properties of multiband reference lattice structures. Consequently, the approximation problem reduces to generating a polynomial Q of degree n, which is the degree of the filter. The degree n is depending on the number of the designed bands. Hence, if the number of bands is even, n will be odd, and if the number of bands is odd, n will be even. The polynomial Q will approximate the difference phase function of the two branch polynomials. It is composed of two subpolynomials, one of them is Hurwitz and the other is anti-Hurwitz. The degrees of these subpolynomials differ by odd number if the number of bands is even and differ by even number if the number of bands is odd. Q is generated according to iterative interpolation and using explicit recursive formulas. After obtaining Q, the two subpolynomials are calculated and the two branch all-pass functions are constructed. Consequently, the filter is synthesized in the digital frequency domain. The method is applied through an illustrative example.

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“…Design of nonsymmetric FIR filters: As indicated in [28,45], the exact linear phase and minimum phase solutions only provide the extreme solutions, i.e., the former unnecessarily constrains the linear phase response in the full frequency domain while the latter drops the phase approximation altogether, therefore it is sometimes desired to design FIR filters whose properties are between those of exact linear and minimum phase filters. In [45] Selesnick and Burrus investigated the design of a new class of nonsymmetric maximally flat low-pass FIR filters, which can achieve a smaller group delay than symmetric filters while maintaining relatively constant group delay around ω = 0, with no degradation of the frequency response magnitude.…”

Section: Other Applicationsmentioning

confidence: 99%

Applications of Gröbner bases to signal and image processing: a survey

Lin

2004

Linear Algebra and its Applications

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This paper is a tutorial and survey paper on the Gröbner bases method and some of its applications in signal and image processing. Although all the results presented in the paper are available in the literature, we give an elementary treatment here, in the hope that it will further bring awareness of and stimulate interest in Gröbner bases among researchers in signal and image processing. We give first a tutorial on Gröbner bases, and then a survey of the design of multidimensional wavelets and filter banks. Applications of Gröbner bases to other areas of signal and image processing are also briefly reviewed.

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Simultaneous amplitude and phase approximation for FIR filters

Cited by 3 publications

References 9 publications

Conditioning Trick for Training Stable GANs

Conditioning Trick for Training Stable GANs

On the design of multiband transmission functions synthesized by one wave digital lattice structure

Applications of Gröbner bases to signal and image processing: a survey

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