Advanced digital imaging laboratory using matlab® by Leonid P Yaroslavsky

Author:Leonid P Yaroslavsky
Language: eng
Format: epub
ISBN: 9780750312332
Publisher: IOP Publishing
Published: 2016-08-12T00:00:00+00:00

Realizations of these oversampled signals are first band limited according to one of eight above-mentioned fractions of the signal baseband, and their ‘ideal’ derivatives are computed using the ramp-filter (the filter with linearly increasing frequency response in DFT domain) that imitates the analogue differentiating. After that, the realizations of the ‘ideal’ derivative and of initial oversampled signals are down-sampled with the chosen oversampling rate, and obtained down-sampled signals are subjected to differentiation using the above-mentioned traditional methods chosen for testing as well as using, for comparison, DFT and DCT based differentiators. The ideal sampled derivative is used as a benchmark for computing differentiation errors as sample-by-sample differences between it and the results of the differentiators under the comparison. This procedure is repeated several times using different realizations of pseudo-random test signals, and squared differentiation errors are accumulated in order to obtain sufficiently good statistical estimates of standard deviations of sample-by-sample differentiation errors. The number of realizations is a user defined parameter as well (figure 4.29).

This procedure can be performed in two versions: without and with an ‘apodization mask’ (figure 4.29). The ‘apodization mask’ is a window function that is applied as a multiplier to realizations of test signals before differentiation. It is equal to one everywhere except a certain number of samples in the vicinity of signal boards, where it gradually decays from one to zero. The purpose of the using of the ‘apodization mask’ is reducing boundary effect errors of the differentiation algorithms.

For each realization of test signals, the program displays, in one figure, plots of realizations of test signals, their ideal and obtained by DFT-method derivatives, and, in another figure, plots of estimates of standard deviations of sample-by-sample differentiation errors for all tested methods, the estimates being accumulated over the iteration steps (figure 4.30).

Figure 4.30. Comparison of numerical differentiation methods: plots of a realization of test signal, its derivatives and differentiation errors accumulated over 25 realizations.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.