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Additional resources for Advanced Signal Processing and Noise Reduction, 2nd Edition (Electrical Engineering & Applied Signal Processing Series)
0 = Ts t ... –Fs Fs = f |X( f )| Xsh(t) S/H-sampled signal ... t ... 19 Sample-and-Hold signal modelled as impulse-train sampling followed by convolution with a rectangular pulse. frequency content (bandwidth) of B Hz, can be recovered from its samples provided that the sampling speed Fs>2B samples per second. 20. 19. 20 A simplified sample-and-hold circuit diagram. 2 Quantisation For digital signal processing, continuous-amplitude samples from the sample-and-hold are quantised and mapped into n-bit binary digits.
In this case, the analog signal can be recovered by passing the sampled signal through an analog low-pass filter with a cut-off frequency of Fs. If the sampling frequency is less than 2Fs, then the adjacent repetitions of the spectrum overlap and the original spectrum cannot be recovered. The distortion, due to an insufficiently high sampling rate, is irrevocable and is known as aliasing. This observation is the basis of the Nyquist sampling theorem which states: a band-limited continuous-time signal, with a highest 24 Introduction Time domain Frequency domain x(t) X(f) 0 B –B t f 2B × * Impulse-train-sampling function ...
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