Interpolation of band-limited discrete-time signals by minimizing out-of-band energy

Abstract

An interpolation method for restoring burst errors in discrete-time, band-limited signals is presented. The restoration is such that the restored signal has minimal out-of-band energy. The filter coefficients depend only on the burst length and on the size of the band to which the signal is assumed to be band-limited. The influence of additive noise and the effect of violation of the band-limitedness assumption is analysed with the aid of discrete prolate spheroidal sequences and wave functions. It is indicated for what combinations of values for noise power, burst length and bandwidth the method is still stable enough to be practicable.

Discrete Prolate Spheroidal Wave Functions and Interpolation

“…To that end we assume that W has a power series expansion around 0, (.6) W(x)=.=o2 (2 In (5.10) the derivatives of the Uk's at a/2 can be expressed in terms of/xk and Uk(a/2) by evaluating and differentiating (2.5) repeatedly at 0 a/2 (where cos 27r0-cos 7ra 0). We thus find the first order approximation (k small compared to m) for …”

Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes

“…16) with respect to the values of the unknown samples, one forces the restored signal to have little (much) spectral energy in those regions in the frequency domain where the estimated spectral energy is small (large). This brings out a relation with the interpolation method of [3], where the restoration is such that the spectral energy of the restored signal is concentrated as much as possible in the assumed baseband of the original signal. It should be noted that the integral in (11.16) can be related with the work of Itakura and Saito [9] on distortion measures for spectral densities.…”

“…Examples of methods that interpolate under certain model assumptions have been given is band-limitedness of the signals to a baseband which is a fraction of the sample frequency. In this nonadaptive method, analyzed in [3] for burst errors, the restoration is done in such a way that the restored signal has minimal energy outside the prescribed baseband. Unfortunately, the latter method is very sensitive to the presence of noise and of out-of-band components in the sig-0096-3518/86/0400-0317$01 .OO 0 1986 IEEE .…”

Unification of signal reconstruction algorithms using bandwidth metric reconstruction

“…As a special case, the output noise variance is given by Most of the existing reconstruction algorithms, e. g. The method developed in [5] uses this idea to reconstruct bandlimited signals by minimizing the out-of-band energy. The authors admit that the algorithm is not very useful when more than three or four samples must be reconstructed.…”

“…produces colored noise for b, ( n ) . Now taking the expected value of (7), the expected value of b(n) is given as In the presence of additive noise, the autocorrelation of the output noise can be determined using equation (5) as follows.…”