Abstract
Digital signal processing is widely used in a variety of applications from telecommunications and medical diagnostics to entertainment and recreation. The mathematics of such digital signal processing is the same in all these areas. In this chapter we take a broad overview of some of the fundamental techniques in digital signal processing, like optimal digital filtering and discrete Fourier analysis. Limitations of the Fourier transform stem from the assumption of periodicity in the calculation of the discrete Fourier transform (popularly called the FFT), as well the unavoidable compromise between time resolution and frequency resolution. Time-frequency analysis allows us to optimize the trade-off between time and frequency resolution. Wavelet decomposition uses the fact that it is possible to resolve high-frequency components within a small time window, and only low-frequency components need large time windows. An alternative to using Fourier and time-frequency analysis is to use purely time-domain analysis, like time-series methods.
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