Abstract
In this chapter we present four important signal processing techniques that are based on linear time-invariant (LTI) systems: convolution, cross-correlation, coherence, and the Hilbert transform. The convolution operation allows us to relate an LTI system's input and output in the time domain. A related technique is calculation of cross-correlation between two different signals or between a signal and itself (called autocorrelation). Coherence is a related type of analysis used to correlate components in the frequency domain. The latter has the advantage that frequency-specific correlations can be determined, whereas cross-correlation in the time domain mainly reflects large-amplitude components. The Hilbert transform provides a unique approach to determine instantaneous phase and amplitude of a narrow band signal.
Published Version
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