Acquisition of High Bandwidth Signals by Sampling an Analog Chromatic Derivatives Filterbank

Abstract

A method for acquisition of high bandwidth signals is presented as a typical example of a signal processing application of chromatic derivatives and approximations. Chromatic derivatives are numerically robust differential operators based on orthogonal polynomials. Theoretical formulations required for synthesising an analog chromatic derivative filterbank based on all-pass filters is presented. Such an analog filterbank with N +1 filters can be used for digital acquisition of high bandwidth signals by simultaneously sampling the outputs of the filterbank at a rate 2/(N + 1) of the Nyquist rate, resulting in samples of the signal and higher order chromatic derivatives up to order N , which in turn are used to reconstruct the original signal back. The value of the signal at any instant is obtained from only two nearest samples of the chromatic derivatives filterbank.

Reliable Recurrence Algorithm for High-Order Krawtchouk Polynomials

“…Figure 3 shows that the initial values (K p 0 (x 0 )) are still inaccurate where these values record either NaN or Inf values. This is due to the nature of the polynomial coefficients that are obtained by the expression in (9). Thus, the initial values (K p 0 (x 0 )) seem difficult to be computed for large polynomial sizes (N).…”

“…Image signals are subject to several processes such as transmission [1], enhancement [2], transformation [3], hiding [4], and compression [5,6]. Similarly to image processing, speech signals processing is also essential [7], and involves several stages such as transfer [8], acquisition [9], and coding [10]. Pattern recognition, which is considered an automated process, is widely used in various applications such as computer vision [11], statistical data analysis [12], information retrieval [13], shot boundary detection [14], and bio-informatics [15].…”