# On predicting a band-limited signal based on past sample values

@article{Vaidyanathan1987OnPA, title={On predicting a band-limited signal based on past sample values}, author={P. P. Vaidyanathan}, journal={Proceedings of the IEEE}, year={1987}, volume={75}, pages={1125-1127} }

The prediction of samples of a band-limited real signal xa(t) from a finite number of past samples is considered. It is shown how a signal-independent linear predictor of finite order can be constructed based on Chebyshev polynomials, such that the prediction error tends to zero for sampling rate exceeding the Nyquist rate.

## 37 Citations

Predictors for Discrete Time Processes With Energy Decay on Higher Frequencies

- PhysicsIEEE Transactions on Signal Processing
- 2012

A family of one-step-ahead predictors is suggested for processes of which the energy decays at higher frequencies for which the prediction error can be made arbitrarily small.

On Causal Estimation From Bandlimited Stationary Sequences

- MathematicsIEEE Transactions on Information Theory
- 2011

The paper derives the transfer function of such an estimation filter, discusses its stability behavior, and applies the result to the causal reconstruction of deterministic signals from its samples.

The predictability of band-limited, high-frequency and mixed processes in the presence of ideal low-pass filters

- Mathematics
- 2008

Pathwise predictability of continuous-time processes is studied in a deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely,…

Limited memory predictors based on polynomial approximation of periodic exponents

- Mathematics
- 2020

It is shown that processes with exponentially decaying Fourier transforms are predictable with these predictors in some weak sense, meaning that convolution integrals over the future times can be approximated by causal convolutions over past times.

Predictors for high frequency processes based on rational polynomials approximation of periodic exponentials

- Mathematics, Computer ScienceArXiv
- 2022

—The paper presents linear integral predictors for continuous time high-frequency processes with a a ﬁnite spectrum gap. The predictors are based on approximation of complex valued periodic…

Some results on the linear prediction of bandlimited fading processes

- Computer Science2004 IEEE 59th Vehicular Technology Conference. VTC 2004-Spring (IEEE Cat. No.04CH37514)
- 2004

The design and performance analysis of linear prediction of a bandlimited complex Gaussian fading process and the design of robust prediction filters whose coefficients are independent of the second order statistics of the fading process are studied.

3 0 A pr 2 00 8 Predictability of band-limited , high-frequent , and mixed processes in the presence of ideal low-pass filters

- Mathematics
- 2009

We study pathwise predictability of continuous time processes in deterministic setting, when the convolution integrals over future time can be approximated by integrals over past time. Uniform…

On recoverability of discrete time signals from sparse observations.

- Mathematics, Computer Science
- 2020

It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable signals and such that signals from these classes feature robust linear recoverability of their finite traces under very mild restrictions on the location of the observed data.

3 A ug 2 00 7 Predictability of band-limited and other processes

- Mathematics
- 2009

Pathwise predictability of continuous time processes is studied. We found that all band-limited processes are predictable in certain weak sense. More precisely, an integral over future time can be…

## References

SHOWING 1-9 OF 9 REFERENCES

On the prediction of a band-limited signal from past samples

- MathematicsProceedings of the IEEE
- 1986

An alternate proof is given of a recent result due to A. Papoulis on predicting the current value of a wide-sense stationary band-limited random process in terms of its past samples. The possibility…

A note on the predictability of band-limited processes

- GeologyProceedings of the IEEE
- 1985

It is shown that a band-limited process can be expressed in terms of its past samples only, provided that the sampling rate is larger than but can be chosen arbitrarily close to the Nyquist rate.

Comments on "A note on the predictability of band-limited processes"

- Computer Science
- 1986

A much simpler proof is presented which covers random and deterministic signals with uniform or nonuniform sampling and has been proved by others using different methods.

Digital filters with equiripple or minimax responses

- Geology
- 1971

Techniques for determining the coefficients of digital filters which have equiripple or minimax errors are reviewed and occasionally extended. These techniques include: 1) mapping to provide…

A separable Hartley-like transform in two or more dimensions

- MathematicsProceedings of the IEEE
- 1987

This letter introduces a discrete, separable, real-to-real transform, called the cas-cas transform. Theorems for the two-dimensional (2-D) case are presented, and the cas-cas transform is compared to…

Digital transmission in the subscriber loop

- BusinessIEEE Circuits and Devices Magazine
- 1986

Major developments by the telephone industry have launched a worldwide effort to convert the network into an integrated services digital network (ISDN). The digital transmission issues are explored…

Difference Methods and Round-off Error Bounds for the Prediction of Bandlimited Functions from Past Samples

- Computer Science
- 1985

La valeur d'un signal a bande limitee a energie finie peut etre predite a partir d'echantillons d'ensembles discrets

PCM and data transmission codes