ABSTRACT
The word spectrum has several meanings. In signal processing, the spectrum of a signal is a particular type of mapping function. In the case of a waveform, the spectrum maps the signal from the time domain to the frequency domain, showing exactly how the signal content is distributed over frequency. This chapter discusses Fourier spectrum of a signal in terms of the discrete Fourier transform (DFT) and the continuous Fourier transform. Correlation has important uses of its own in signal processing. A correlation detector is a system that correlates an incoming signal in real time with a stored “target,” the objective being to detect the presence of the target in the incoming signal. The DFTs transform the sampled waveform or image data into spectral information about the respective waveform or image. Besides the inverse transform, the DFT has other properties worth mentioning. The focus of digital signal processing is on vectors and arrays containing elements taken from discrete sample spaces.
