By Saeed V. Vaseghi

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**Extra resources for Advanced Digital Signal Processing and Noise Reduction, Third Edition**

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1 SAMPLING AND RECONSTRUCTION OF ANALOGUE SIGNALS The conversion of an analogue signal to a sequence of n-bit digits consists of two basic steps of sampling and quantisation. The sampling process, when performed with sufficiently high speed, can capture the fastest fluctuations of the signal, and can be a loss-less operation in that the analogue signal can be recovered through interpolation of the sampled sequence, as described in Chapter 10. The quantisation of each sample into an n-bit digit involves some irrevocable error and possible loss of information.

The connection weights are trained to perform a signal processing function such as prediction or classification. Neural networks are particularly useful in nonlinear partitioning of a signal space, in feature extraction and pattern recognition and in decision-making systems. In some hybrid pattern recognition systems neural networks are used to complement Bayesian inference methods. 3 APPLICATIONS OF DIGITAL SIGNAL PROCESSING In recent years, the development and commercial availability of increasingly powerful and affordable digital computers has been accompanied by the development of advanced digital signal processing algorithms for a wide variety of applications such as noise reduction, telecommunications, radar, sonar, video and audio signal processing, pattern recognition, geophysics explorations, data forecasting, and the processing of large databases for the identification, extraction and organisation of unknown underlying structures and patterns.

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 bandlimited continuous-time signal, with a highest frequency content (bandwidth) of B Hz, can be recovered from its samples provided that the sampling frequency Fs > 2B samples per second. 20. 19, the staircase shape of a sample-and-hold signal can be obtained by filtering the idealised impulse-train sampled signal through a filter with a rectangular impulse response.