Exact deterministic and stochastic analysis of multirate systems with application to fractional sampling rate alteration

Petersohn, U.; Unger, Horst; Fliege, N.J.

doi:10.1109/iscas.1994.408933

Cited by 8 publications

(5 citation statements)

References 3 publications

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“…which is consistent with bispectrum properties described in [5,2]. In the Fourier domain, SV 2 (T ) thus is…”

Section: Fourier Characterization Of Svsupporting

confidence: 87%

“…Multirate systems with FIR filters are LPSV, and their behavior with respect to random input signals has been analyzed in, e.g., [1,2,3]. Although the shift variance of a multirate LPSV system is generated by non-ideal filtering during decimation, while cyclic nonstationarities are caused by non-ideal anti-imaging filtering during interpolation [4], the two phenomena are closely related, and were jointly treated in, e.g., [5,4]. Shift variance and the generation of cyclostationarity are, moreover, complementary in the sense that Supported partly by the Deutsche Forschungsgemeinschaft (AA5/3-1).…”

Section: Introductionmentioning

confidence: 99%

“…shift variance is analyzed with respect to deterministic signals [5,6,7], while the analysis of cyclostationarity by definition assumes random signals.…”

Section: Introductionmentioning

confidence: 99%

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Shift variance, cyclostationarity and expected shift variance in multirate LPSV systems

Aach

Führ

2011

2011 IEEE Statistical Signal Processing Workshop (SSP)

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The shift variant properties of linear periodically shift variant (LPSV) systems are generally analysed using deterministic signals. Shift variance is, however, closely related to cyclostationarities introduced by the LPSV system into originally wide sense stationary (WSS) random signals passing through the system. We first develop a Hilbert space distance measure for shift variance of LPSV operators with deterministic input signals. For an LPSV system with WSS random input signals, we examine the covariance operator associated to its wide-sense cyclostationary (WSCS) output signal. The output signal is WSCS if its covariance operator is LPSV, and WSS if its covariance operator is shift invariant. Applying the shift variance measure to the covariance operator therefore provides a direct measure of the cyclostationarity generated by the LPSV system. To comprehensively capture the shift variant effects of the LPSV system on WSS random signals, we analyze the changes in its output signal when shift operator and system are interchanged. These changes are WSCS, and can be quantified by the expected shift variance over one cycle. We apply the framework to various two-channel filter banks.

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“…which is consistent with bispectrum properties described in [5,2]. In the Fourier domain, SV 2 (T ) thus is…”

Section: Fourier Characterization Of Svsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

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Shift variance, cyclostationarity and expected shift variance in multirate LPSV systems

Aach

Führ

2011

2011 IEEE Statistical Signal Processing Workshop (SSP)

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“…The cyclic spectrum is used in [13] to numerically optimize filterbanks to minimize the reconstruction error after some subbands are dropped. In [15] and [16], Petersohn et al have presented a matrix calculus description of multirate systems. It is used to compute the spectra of output signal and noise in systems such as cascaded multirate filters and fractional decimation circuits.…”

Section: A Previous Workmentioning

confidence: 99%

Bifrequency and bispectrum maps: a new look at multirate systems with stochastic inputs

Akkarakaran

Vaidyanathan

2000

IEEE Trans. Signal Process.

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In multirate digital signal processing, we often encounter decimators, interpolators, and complicated interconnections of these with LTI filters. We also encounter cyclo-wide-sense stationary (CWSS) processes and linear periodically time-varying (LPTV) systems. It is often necessary to understand the effects of multirate systems on the statistical properties of their input signals. Some of these issues have been addressed earlier. For example, it has been shown that a necessary and sufficient condition for the output of an-fold interpolation filter to be wide sense stationary (WSS) for all WSS inputs is that the filter have an alias-free () support. However, several questions of this nature remain unanswered. For example, what is the necessary and sufficient condition on a pair (or more generally a bank) of interpolation filters so that their outputs are jointly WSS (JWSS) for all jointly WSS inputs? What is the condition if only the sum of their outputs is required to be WSS? When is the output of an LPTV system (for example a uniform filter-bank) WSS for all WSS inputs? Some of these questions may appear to be simple generalizations of the above-mentioned result for a single interpolation filter. However, the frequency domain approaches that proved this result are quite difficult to generalize to answer these questions. The purpose of this paper is to provide these answers using analysis based on bifrequency maps and bispectra. These tools are two-dimensional (2-D) Fourier transforms that characterize all linear time-varying (LTV) systems and nonstationary random processes, respectively. We show that the questions raised above can be addressed elegantly and in a geometrically insightful way using these tools. We also derive a bifrequency characterization of lossless LTV systems. This may potentially lead to an increased understanding of these systems.

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“…In other words, when m = 1, the kernel can be chosen to be LTI. The multirate system is a rate changer and can be used as an interface between systems that have different sampling rates [6], [10]. It also has applications in equalization of channels and interpolation of signals [18].…”

Section: Introductionmentioning

confidence: 99%

Alias-Component Matrices of Multirate Systems

Mehr

2009

IEEE Trans. Circuits Syst. II

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We consider a multirate system, which is a generalization of linear time-invariant systems. Such a system is invariant to a certain shift in the input sequence. In particular, assume that p and q are coprime. A multirate system with the property that a delay of mq samples in its input sequence results in a delay of mp samples in its output sequence is called an (mp, mq)-periodic system. This multirate system can be obtained by cascading an upsampler, followed by a linear periodically time-varying (LPTV) kernel system, then followed by a downsampler. Here, we study the alias-component matrices of multirate systems. We show that they can be obtained from the alias-component matrices of their LPTV kernels by some row and column additions. An example shows the use of the method to design rate changers for a specified frequency band swap.

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Exact deterministic and stochastic analysis of multirate systems with application to fractional sampling rate alteration

Cited by 8 publications

References 3 publications

Shift variance, cyclostationarity and expected shift variance in multirate LPSV systems

Shift variance, cyclostationarity and expected shift variance in multirate LPSV systems

Bifrequency and bispectrum maps: a new look at multirate systems with stochastic inputs

Alias-Component Matrices of Multirate Systems

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