By Saeed V. Vaseghi
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Extra resources for Advanced Digital Signal Processing and Noise Reduction, Third Edition
Also, a white noise passing through a channel is ‘coloured’ by the shape of the frequency response of the channel. 3. 2 (a) A pink noise signal and (b) its magnitude spectrum. 3 (a) A brown noise signal and (b) its magnitude spectrum. 4 IMPULSIVE NOISE Impulsive noise consists of random short-duration ‘on/off’ noise pulses, caused by a variety of sources, such as switching noise, electromagnetic interference, adverse channel environment in a communication system, drop-outs or surface degradation of audio recordings, clicks from computer keyboards, etc.
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. However, in practice the quantisation error can be made negligible by using an appropriately high number of bits as in a digital audio hi-fi.
7) where x m is the signal to be detected, n m is the noise and b m is a binary-valued state indicator sequence such that b m = 1 indicates the presence of the signal, x m , and b m = 0 indicates that the signal is absent. 12. 8) where N is the length of x m . 12 Configuration of a matched filter followed by a threshold comparator for detection of signals in noise. 1 Four possible outcomes in a signal detection problem. 10) where bˆ m is an estimate of the binary state indicator sequence b m , and may be erroneous, particularly if the signal-to-noise ratio is low.
Advanced Digital Signal Processing and Noise Reduction, Third Edition by Saeed V. Vaseghi