By Gabriele D'Antona

ISBN-10: 0387249664

ISBN-13: 9780387249667

Electronic sign Processing for size platforms: conception and purposes covers the theoretical in addition to the sensible matters which shape the root of the fashionable DSP-based tools and dimension equipment. It covers the fundamentals of DSP thought earlier than discussing the severe points of DSP particular to dimension science.

Key Features:

* techniques sign processing via a distinct size technology perspective

* Covers either concept and cutting-edge purposes, from the sampling theorem to the layout of FIR/IIR filters

* contains vital themes, for instance, difficulties that come up while sampling periodic signs and the connection among the sampling fee and the SNR

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**Additional resources for Digital signal processing for measurement systems: theory and applications**

**Example text**

36) to converge to H (e jω ). If this is verified, H (e jω ) is not only a continuous function of the angular frequency ω, but it is also periodic in ω with a 2π period. 36), since: 26 Chapter 2 e j (ω+ 2π )k = e jωk The fact that H(e jω ) takes the same values for any ω = ω0 and ω = ω0 + 2π means that the discrete-time system provides the same response to complex exponential sequences with these two angular frequency values. This is totally justified by the fact that the two complex exponential sequences do not differ.

40) are shown in Fig. 17 a and b respectively, for N = 8. 36) is a continuous, periodic function of ω, it can be developed in terms of Fourier series. 36) expresses H(e jω ) in terms of its Fourier series coefficients, which are equal to the samples of the unit sample sequence response h(n). 17. 41) h(n ) e − jωn n = −∞ where the first equation represents the direct Fourier series analysis for H(e jω), and the second equation represents the inverse Fourier synthesis equation. These equations can be also interpreted in a rather different, though more interesting way.

5 = 2. 13. 14. 5. At last, it can be easily checked that, for n = 9, none of the non-zero samples of the resulting sequence y(9 - k) is in the same position as the non-zero samples of sequence x(k), so that w(9) = 0. The same applies for n > 9. The convolution w(n) = x(n) ∗ y(n) is hence the sequence shown in Fig. 15. 15. Convolution result This figure shows that the obtained sequence has a longer length than that of the two starting sequences. This example can be generalized, showing that the convolution of two sequences, with finite length of N and M samples respectively, will be again a finite length sequence, with length equal to N + M - 1 samples.

### Digital signal processing for measurement systems: theory and applications by Gabriele D'Antona

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