On stationary linear time-varying systems

A comprehensive review of representations of linear timevarying systems is given, both in the time and in frequency domains. Subsequently a definition is given of a stationary deterministic signal. Based on this definition the notion of stationary systems is introduced. These systems have the useful property that the spectral relation between input and output has a simpler form than the corresponding relation for arbitrary time-varying systems. It is shown that causality puts rather severe constraints on the frequency mappings that can be realized by stationary linear systems. An extension of the theory of linear time-varying systems to the case of discrete-time and hybrid systems (analog input, digital output, or vice versa) is discussed. Examples of stationary systems are given, such as a decimator, a periodic sampler, and a bilinear A/D converter. Also, a recently proposed generalized sampling method is analyzed by means of the concepts discussed in this paper.

[1]  L. Zadeh,et al.  Frequency Analysis of Variable Networks , 1950, Proceedings of the IRE.

[2]  J. Doob.  Stochastic processes , 1953 .

[3]  M. Kendall,et al.  A Study in the Analysis of Stationary Time-Series. , 1955 .

[4]  S. Lang,et al.  An Introduction to Fourier Analysis and Generalised Functions , 1959 .

[5]  I. W. Sandberg,et al.  An alternative approach to the realization of network transfer functions: The N-path filter , 1960 .

[6]  L. Zadeh,et al.  Time-Varying Networks, I , 1961, Proceedings of the IRE.

[7]  A. Papoulis,et al.  The Fourier Integral and Its Applications , 1963 .

[8]  Allen Gersho,et al.  Characterization of time-varying linear systems , 1963 .

[9]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[10]  P. A. Franaszek,et al.  On Linear Systems Which Preserve Wide Sense Stationarity , 1967 .

[11]  Constantin Corduneanu,et al.  Almost periodic functions , 1968 .

[12]  Henry D'Angelo,et al.  Linear time-varying systems : analysis and synthesis , 1970 .

[13]  Alan V. Oppenheim,et al.  Discrete representation of signals , 1972 .

[14]  L. Rabiner,et al.  A digital signal processing approach to interpolation , 1973 .

[15]  L. Rabiner,et al.  Optimum FIR Digital Filter Implementations for Decimation, Interpolation, and Narrow-Band Filtering , 1975 .

[16]  A. Papoulis.  Signal Analysis , 1977 .

[17]  D. Goodman,et al.  Nine digital filters for decimation and interpolation , 1977 .

[18]  R.W. Brodersen,et al.  MOS sampled data recursive filters using switched capacitor integrators , 1977, IEEE Journal of Solid-State Circuits.

[19]  T. Claasen,et al.  A generalized scheme for an all-digital time-division multiplex to frequency-division multiplex translator , 1978 .

[20]  Charles M. Rader,et al.  Number theory in digital signal processing , 1979 .

[21]  M. Portnoff.  Time-frequency representation of digital signals and systems based on short-time Fourier analysis , 1980 .

[22]  J. Marino-Acebal,et al.  On generalized sampling expansions for deterministic signals , 1981 .

[23]  Jr. J. L. Brown.  Multi-channel sampling of low-pass signals , 1981 .