Exact analysis of aliasing effects and non-stationary quantization noise in multirate systems

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

doi:10.1109/icassp.1994.390062

Cited by 4 publications

(6 citation statements)

References 2 publications

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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%

“…5 illustrates these properties. Equation (15) says that the 2-D function is nonnegative on the diagonal , and (16) says that its integrals over the hatched areas A,B are non-negative. To help understand these properties, we can draw analogies between the bispectrum and the conventional power spectrum (psd) matrix of a WSS vector process.…”

Section: General Nonstationary Processes and Bispectramentioning

confidence: 99%

“…• Although the diagonal elements of are non-negative functions, the off-diagonal elements need not even be real. Similarly, although (15), need not even be real if In general, when is not a scalar, is Hermitian positive semidefinite for all real . The Hermitian property follows from (14).…”

Section: General Nonstationary Processes and Bispectramentioning

confidence: 99%

“…M ULTIRATE systems contain interconnections of decimators, interpolators, and LTI filters. Linear periodically time-varying (LPTV) systems and cyclo-wide-sense stationary (CWSS) random processes occur frequently in multirate processing [1], [7], [13], [15]. It is often required to analyze the effects of multirate systems on the statistics of their input.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Previous Workmentioning

confidence: 99%

Section: General Nonstationary Processes and Bispectramentioning

confidence: 99%

Section: General Nonstationary Processes and Bispectramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Akkarakaran

Vaidyanathan

2000

IEEE Trans. Signal Process.

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“…. , p − 1 [11,13,18]. As will be discussed, the periodicity in an NTX results in an interesting generalization of the frequency response of periodic systems.…”

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confidence: 99%

Alias-Component Matrices of Nonuniform Transmultiplexers

Mehr

2008

Circuits Syst Signal Process

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Nonuniform transmultiplexers can be used for interconversion of signals with different sampling rates between the time-division multiplexing format and the frequency-division multiplexing format. Here, we review the polyphase representation and discuss the H ∞ model-matching design of finite impulse response nonuniform transmultiplexers by semidefinite programming. Then, we study the alias-component matrices. It will be shown that the alias-component matrices of nonuniform transmultiplexers are generalizations of those of linear periodically timevarying systems. In particular, it is shown that the output at any given frequency is only dependent on the input at a finite set of frequencies.

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Comparative Analysis of Shift Variance and Cyclostationarity in Multirate Filter Banks

Aach

2007

IEEE Trans. Circuits Syst. I

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Exact analysis of aliasing effects and non-stationary quantization noise in multirate systems

Cited by 4 publications

References 2 publications

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

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

Alias-Component Matrices of Nonuniform Transmultiplexers

Comparative Analysis of Shift Variance and Cyclostationarity in Multirate Filter Banks

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