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DSP A Khoa học máy tính quan điểm P4

The concept of frequency is clearest for simple sinusoids, but we saw in the previous chapter that it can be useful for nonsinusoidal periodic signals as well. The Fourier series is a useful tool for description of arbitrary periodic signals, describing them in terms of a spectrum of sinusoids, the frequencies of which are multiples of a basic frequency. It is not immediately obvious that the concepts of spectrum and frequency can be generalized to nonperiodic signals. | Digital Signal Processing A Computer Science Perspective Jonathan Y. Stein Copyright 2000 John Wiley Sons Inc. . Print ISBN 0-471-29546-9 Online ISBN 0-471-20059-X Z . The Frequency Domain The concept of frequency is clearest for simple sinusoids but we saw in the previous chapter that it can be useful for nonsinusoidal periodic signals as well. The Fourier series is a useful tool for description of arbitrary periodic signals describing them in terms of a spectrum of sinusoids the frequencies of which are multiples of a basic frequency. It is not immediately obvious that the concepts of spectrum and frequency can be generalized to nonperiodic signals. After all frequency is only meaningful if something is periodic Surprisingly the concept of spectrum turns out to be quite robust for nonperiodic signals we simply need a continuum of frequencies rather than harmonically related ones. Thus analog signals can be viewed either as continuous functions of time or as continuous functions of frequency. This leads to a pleasingly symmetric view whereby the signal can be described in the time domain or the frequency domain. The mathematical tool for transforming an analog signal from its time domain representation to the frequency domain or vice versa is called the Fourier transform FT . The name hints at the fact that it is closely related to the Fourier series that we have already discussed. For digital signals we have close relatives namely the discrete Fourier transform DFT and the z transform zT . In this chapter we introduce all of these review their properties and compute them for a few example signals. We also introduce a non-Fourier concept of frequency the instantaneous frequency. The FS FT DFT zT and instantaneous frequency each in its own domain of applicability is in some sense the proper definition of frequency. 4.1 From Fourier Series to Fourier Transform In the previous chapter we learned that the set of harmonically related sinusoids or complex exponentials .