Signal Interpolation Research Articles

Interpolation of discrete signals

An interpolation function for discrete signals is derived from the signal-theoretic point of view. Its use allows an actual sampling frequency closer to the theoretical minimum.

Polynomial interpolation of bandlimited signals

Polynomial interpolation of bandlimited signal, having bandwidth W Hz, is shown to be exact for the sample rate fs > π W in the limit of an infinite-order polynomial.

A digital signal processing approach to interpolation

In many digital signal precessing systems, e.g., vacoders, modulation systems, and digital waveform coding systems, it is necessary to alter the sampling rate of a digital signal Thus it is of considerable interest to examine the problem of interpolation of bandlimited signals from the viewpoint of digital signal processing. A frequency dmnain interpretation of the interpolation process, through which it is clear that interpolation is fundamentally a linear filtering process, is presented, An examination of the relative merits of finite duration impulse response (FIR) and infinite duration impulse response (IIR) digital filters as interpolation filters indicates that FIR filters are generally to be preferred for interpolation. It is shown that linear interpolation and classical polynomial interpolation correspond to the use of the FIR interpolation filter. The use of classical interpolation methods in signal processing applications is illustrated by a discussion of FIR interpolation filters derived from the Lagrange interpolation formula. The limitations of these filters lead us to a consideration of optimum FIR filters for interpolation that can be designed using linear programming techniques. Examples are presented to illustrate the significant improvements that are obtained using the optimum filters.

A Method of Trigonometric Interpolation for Processing Radio Direction-Finding Signals

Radio direction-finding techniques that use amplitude-trigonometric interpolation between signals received at a circular antenna array are reexamined. The accuracy of this class of direction-finding system is limited by interpolation, gain mistracking, and additive-noise errors. The channel gain mistracking error is shown to be significantly lower than previously estimated. Typical calculations show that the trigonometric interpolation technique is an order of magnitude more accurate than previously supposed.

Integrated square error for linear interpolation of band-limited signals

The integrated square error is calculated between a band-limited signal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s(t)</tex> and a linearly interpolated signal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_{L}(t)</tex> obtained from the sampled data of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s(t)</tex> . Band-limited signals, nonperiodic or periodic, are considered. It is shown that the integrated square error together with the energy of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_{L}(t)</tex> is found from a closed-form evaluation using the power spectrum of the original band-limited signal. Two examples are included to illustrate the ease of application. The integrated-square-error criterion has been used extensively in the design of filters and control systems. Minimization and calculation of the integrated square error can be found in [1]-[6], etc.

Is the Newton exploration polynomial a trustworthy and noiseproof filter?

The Newton extrapolation polynomial (NEP) is often used in the interpolation and extrapolation of sampled-data signals. In this correspondence, it is presented under a form which allows, when white noise is present 1) the easy computation of the error variance due to measurement errors, and 2) the choice of the degree of this NEP for signals which are closely polynomials in a given interval.

Error-Free Recovery of Signals from Irregularly Spaced Samples

Error free recovery of signals from irregularly spaced samples in terms of completeness of sets of nonharmonic exponentials

Toward a unified theory of modulation—Part II: Zero manipulation

Part I of this two-part paper began with a study of band-limited signals which exhibit simultaneous phase and envelope fluctuations. The real and complex zeros of such signals were shown to be crucial parameters, and a viewpoint was established wherein zeros are regarded as fundamental informational attributes of signals. In Part II, the concept of modulation as zero manipulation is developed. This concept allows one to manipulate the zeros of a signal (i.e., to modulate the signal) in any practically convenient manner provided that the original zeros can be recovered in a demodulation process. The major portion of Part II is an illustrated survey of modulation processes. Narrow-band processes are dealt with first. Both well-known techniques, such as AM and SSB, and unconventional techniques are classified and explained in terms of zero manipulations. Conventional and single-sided forms of angle modulation are studied next. The zero-manipulation concept provides insight into the nature of the redundancy in wide-band angle modulation and suggests why angle modulation is both noise resistant and inefficient as a coding process. The final portion of the paper shows that the zero-manipulation concept can be used constructively as well as interpretively. Two topics are discussed: angle coding via zero conjugation, and interpolation of binary signals.

On the interpolation and prediction of signals plus noise for infinite and finite smoothing times

The first part of the paper is concerned with the choice of the optimum filter for the extrapolation or interpolation of a signal which is contaminated by noise. The problem has been completely solved by Wiener in his book on the subject. The method used here for solving the integral equations is different and leads to the solution for the lagging case without having to approximate ε−pτ by the ratio of polynomials in p. Laplace transformations are used and lead directly to the solution. The second part of the paper deals with the solution of the optimum filter when the error is minimized at a particular time after switching on, the averaging being taken over an ensemble. Examples of each problem are given.