By Gabriele D’Antona, Alessandro Ferrero (auth.)
Digital sign Processing for dimension structures: thought and Applications covers the theoretical in addition to the sensible concerns which shape the root of the trendy DSP-based tools and dimension equipment. It covers the fundamentals of DSP concept ahead of discussing the serious points of DSP designated to size science.
Approaches sign processing via a special size technological know-how perspective
Covers either conception and cutting-edge functions, from the sampling theorem to the layout of FIR/IIR filters
Includes vital subject matters, for instance, difficulties that come up while sampling periodic signs and the connection among the sampling cost and the SNR
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Extra resources for Digital Signal Processing for Measurement Systems: Theory and Applications
9. 10. x(k) and y(-k) sequences Discrete-time signals and systems 19 The next step is the generation of sequence y(n - k), obtained, for every value of n, by shifting sequence y(-k) by n. 30) has non-zero values only for 0 ≤ n ≤ 9, since the shifted sequence y(n - k) has non-zero values where x(n) has non-zero values only in this range of n values. To better understand this point, let us consider the case of n = -1. Fig. 11 shows the resulting sequences x(k) and y(-1 - k). 11. Convolution step for n = -1 It can be immediately seen that all products x(k)y(-1 - k) are zero, for every value of k, so that sample w(-1) in the convolution will be zero too.
The periodic signals need a separate analysis. It has been already shown in Chapter 2 that a sequence obtained by sampling a periodic signal might not be periodic any longer. Therefore it may happen that the sequence of the sampled values of a periodic, continuous-time signal does not allow to retrieve the information associated with the signal itself, even if the signal has been sampled with a sampling frequency greater than the Nyquist frequency, because it loses the original periodicity. Signal transformation from the continuous time to the discrete time domain 43 The sampling theorem must be hence reconsidered, in order to find if a condition exists that allows to sample a periodic signal correctly.
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. 39) as shown in Fig.