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Digital Signal Processing: A Practical Guide for Engineers and Scientists by Steven Smith

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CHAPTER 10

Fourier Transform Properties

The time and frequency domains are alternative ways of representing signals. The Fourier transform is the mathematical relationship between these two representations. If a signal is modified in one domain, it will also be changed in the other domain, although usually not in the same way. For example, it was shown in the last chapter that convolving time domain signals results in their frequency spectra being multiplied. Other mathematical operations, such as addition, scaling and shifting, also have a matching operation in the opposite domain. These relationships are called properties of the Fourier transform, how a mathematical change in one domain results in a mathematical change in the other domain. ...

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