Download Digital signal processing for measurement systems: theory by Gabriele D'Antona PDF

By Gabriele D'Antona

Electronic sign Processing for dimension structures: conception and functions covers the theoretical in addition to the sensible matters which shape the foundation of the trendy DSP-based tools and size equipment. It covers the fundamentals of DSP conception sooner than discussing the severe elements of DSP specific to dimension science.
Key Features:
* techniques sign processing via a special dimension technology perspective
* Covers either concept and cutting-edge purposes, from the sampling theorem to the layout of FIR/IIR filters
* comprises vital issues, for instance, difficulties that come up whilst sampling periodic indications and the connection among the sampling cost and the SNR

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Fig. 8 b) has been drawn in the same way as Fig. 8 a), again sampling a sinewave with 20 samples/period, but not in a synchronous way (T ≠ 20Ts). It can be immediately recognized that a distortion appears in the sinewave, at zero crossing, as evidenced on Fig. 8 b) by an ellipse. The above mathematical derivation and the intuitive example reported in Fig. 8 prove that the synchronous sampling condition must be satisfied in order to preserve the original information associated with the continuous-time signal after the sampling operation.

10. 36) It can be immediately recognized that, due to the periodicity of the Dirac impulses that constitute G’(jΩ), P’(jΩ) is the periodic replica of Sct(jΩ) with period Ω s = 2π/Ts. If Sct (jΩ) is upperbounded at angular frequency Ω0 = Ω s/2, each period of P’(jΩ) is a scaled replica of Sct (jΩ), otherwise aliasing occurs, as already shown in the previous sections. Let us now consider a periodic signal sct (t), with period T. If the distribution theory is considered, it is possible to define the Fourier transform of this signal, as a combination of Dirac impulses, equally spaced, in angular frequency, by a quantity j2π/T, and weighed by the Fourier series complex coefficients appertaining to each harmonic component.

Fourier-series approach. Let sct(t) be a continuous-time signal, represented by a generally continuous function of time t, periodic with period T in t, and absolutely integrable in t. 21) which means that sct(t) has a bounded spectrum. Let us now suppose to sample sct(t) with constant sampling period Ts taken in such a way that exactly 2N+1 samples are taken over the signal period T, from -T/2 to T/2. This means that the following relationship applies between T and Ts: T = (2N + 1)Ts showing that the signal period and the sampling period are synchronous.

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