Linear periodic systems and multirate filter design

Shenoy, R.G.; Burnside, D.; Parks, T.W.

doi:10.1109/78.317847

Cited by 69 publications

(29 citation statements)

References 38 publications

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“…We note that norm analyses of more general multirate systems, where 's are not powers of an integer, were provided in the papers by Shenoy [30], Weisburn et al [35] and Shenroy et al [31], but the particular case we treat here lead to significant simplifications as indicated by the proposition.…”

Section: B Methods Ii: Decomposition Of Into Subsystemsmentioning

confidence: 99%

A Subband Adaptive Iterative Shrinkage/Thresholding Algorithm

Bayram

Selesnick

2010

IEEE Trans. Signal Process.

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Abstract-We investigate a subband adaptive version of the popular iterative shrinkage/thresholding algorithm that takes different update steps and thresholds for each subband. In particular, we provide a condition that ensures convergence and discuss why making the algorithm subband adaptive accelerates the convergence. We also give an algorithm to select appropriate update steps and thresholds for when the distortion operator is linear and time invariant. The results in this paper may be regarded as extensions of the recent work by Vonesch and Unser.Index Terms-Deconvolution, fast algorithm, shrinkage, subband adaptive, thresholding, wavelet regularized inverse problem.

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Section: B Methods Ii: Decomposition Of Into Subsystemsmentioning

confidence: 99%

A Subband Adaptive Iterative Shrinkage/Thresholding Algorithm

Bayram

Selesnick

2010

IEEE Trans. Signal Process.

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“…Substituting by its Fourier series, we get (3) Therefore, the FT of (1) is where is the FT of the input of the system. Defining and we have (4) where the elements of are given by and the rest of the elements are found using the pseudo-circulant property of . Note that the numbering starts from zero.…”

Section: Alias-component Matricesmentioning

confidence: 99%

“…These systems are a generalization of linear time-invariant (LTI) systems and are used frequently in control systems and signal processing. LPTV controllers may improve certain performance specs of control systems [2], and multirate filter banks, which are inherently LPTV, find applications in digital communications [4], [6].…”

Section: Introductionmentioning

confidence: 99%

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On alias-component matrices of discrete-time linear periodically time-varying systems

Mehr

Chen

2001

IEEE Signal Process. Lett.

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We first use the Fourier series to find the steady-state response of discrete-time linear periodically time-varying (LPTV) systems to periodic inputs. Then, in order to obtain the response of LPTV systems to general inputs, we use the Fourier transform (FT) and establish a direct link between alias-component matrices and LPTV systems modeled by periodically time varying difference equations. This is given in terms of the Fourier series of the parameters in the model.Index Terms-Alias-component matrix, frequency response, periodic systems, steady-state response.

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“…This matrix is a special case for the periodic steady state of the so-called alias component matrix described in (Shenoy et al, 1994), the frequency-response matrix for the LPTV system described in (Chen and Qiu, 1997), a discrete version of the so-called bi-frequency system function used in (Zadeh, 1950), and a harmonic transfer function or a frequency lifted transfer function in the case of the periodic steady 665 state described in (Bittanti and Colaneri, 1999;2000). The coefficients of the SCPO matrix lying outside the diagonal determine the manner in which the harmonics of the input signal are mapped into other harmonics at the system output.…”

Section: Frequency Domain Representation Of the Cpomentioning

confidence: 99%

The steady-state impedance operator of a linear periodically time-varying one-port network and its determination

Kłosiński

2009

International Journal of Applied Mathematics and Computer Science

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The main subject of the paper is the description and determination of the impedance operator of a linear periodically timevarying (LPTV) one-port network in the steady-state. If the one-port network parameters and the supply vary periodically with the same period, the network reaches a periodic steady state. However, the sinusoidal supply may induce a nonsinusoidal voltage or current. It is impossible to describe such a phenomenon by means of one complex number. A periodically time-varying one-port network working in a steady-state regime can be described with a circular parametric operator. Within the domain of discrete time, such an operator takes the form of a matrix with real-valued entries. The circular parametric operator can be transformed into the frequency domain using a two-dimensional DFT. This description makes it possible to quantitatively assess LPTV system input and output harmonics aliasing. The paper also presents the derivation and the proof of convergence of an iteration scheme for the identification of circular parametric operators. The scheme may be used to determine the impedance of an LPTV one-port network. Some results of computer simulations are shown.

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Linear periodic systems and multirate filter design

Cited by 69 publications

References 38 publications

A Subband Adaptive Iterative Shrinkage/Thresholding Algorithm

A Subband Adaptive Iterative Shrinkage/Thresholding Algorithm

On alias-component matrices of discrete-time linear periodically time-varying systems

The steady-state impedance operator of a linear periodically time-varying one-port network and its determination

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