Abstract
In this paper, we investigate time-domain errors occurring in the two extreme discrete-time differentiation modes of band-unlimited signals: in the full-band processing mode and in the processing mode with ideal anti-aliasing filtering (AAF) with a cut-off at the Nyquist frequency. We disclosed that regardless sampling frequency the error from AAF is greater than the aliasing error. It is found that type IV differentiators designed by three commonly known digital filter design methods approximately equally process the high frequency portion of the signal above the Nyquist frequency with nearly equal aliasing errors having a weak dependence on differentiator length. In contrast, the differentiators very differently compute the derivatives of the low frequency portion bellow the Nyquist frequency providing rather dissimilar the common differentiation accuracy. The results show that the differentiators derived by using maximal linearity constraints are more accurate than those designed by the Parks-McClellan algorithm and the impulse response truncation method.
Highlights
Despite that the philosophy of modern signal processing [1,2,3] is based mostly on signals that typically are assumed to be band-limited, there are branches of science and technology, such as material science [4, 5], mechanics [6], dielectric spectroscopy [7], geophysics [8, 9], etc., which face with processing time- and bandunlimited signals
The basic result of this study was a finding that regardless sampling frequency the anti-aliasing error in the differentiation mode with ideal antialiasing filtering (AAF) is greater than the aliasing error in the full-band processing mode
We experimentally evaluate the time-domain errors occurring in the two extreme differentiation modes: in the full-band processing mode and in the processing mode with ideal AAF with a cut-off at the Nyquist frequency
Summary
Despite that the philosophy of modern signal processing [1,2,3] is based mostly on signals that typically are assumed to be band-limited, there are branches of science and technology, such as material science [4, 5], mechanics [6], dielectric spectroscopy [7], geophysics [8, 9], etc., which face with processing time- and bandunlimited signals. Two extreme processing modes may be identified in discrete-time processing of band-unlimited signals: (i) the full-band processing when maximum aliasing error and zero anti-aliasing error are caused by HFP generated fully back to the Nyquist frequency band, and (ii) the processing mode with ideal AAF with a cutoff frequency equal to the Nyquist frequency, when maximum anti-aliasing error and zero aliasing error appear from information loss caused by complete removing HFP. Which of these errors – aliasing or antialiasing will predominate, will depend, obviously, on how input HFP generated back after sampling to the Nyquist frequency band will be processed by the discrete-time algorithm used
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