TAILIEUCHUNG - DSP A Khoa học máy tính quan điểm P13

It is easy enough to measure the frequency of a clean sinusoid, assuming that we have seen enough of the signal for its frequency to be determinable. For more complex signals the whole concept of frequency becomes more complex. We previously saw two distinct meanings, the spectrum and the instantaneous frequency. The concept of spectrum extends the single frequency of the sinusoid to a simultaneous combination of many frequencies for a general signal; as we saw in Section the power spectral density (PSD) defines how much each frequency contributes to the overall signal. . | 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 13 Spectral Analysis It is easy enough to measure the frequency of a clean sinusoid assuming that we have seen enough of the signal for its frequency to be determinable. For more complex signals the whole concept of frequency becomes more complex. We previously saw two distinct meanings the spectrum and the instantaneous frequency. The concept of spectrum extends the single frequency of the sinusoid to a simultaneous combination of many frequencies for a general signal as we saw in Section the power spectral density PSD defines how much each frequency contributes to the overall signal. Instantaneous frequency takes the alternative approach of assuming only one frequency at any one time but allowing this frequency to vary rapidly. The tools that enable us to numerically determine the instantaneous frequency are the Hilbert transform and the differentiation filter. There is yet a third definition about which we have not spoken until now. Model based spectral estimation methods assume a particular mathematical expression for the signal and estimate the parameters of this expression. This technique extends the idea of estimating the frequency of a signal assumed to be a perfect sinusoid. The difference here is that the assumed functional form is more complex. One popular model is to assume the signal to be one or more sinusoids in additive noise while another takes it to be the output of a filter. This approach is truly novel and the uncertainty theorem does not directly apply to its frequency measurements. This chapter deals with the practical problem of numerically estimating the frequency domain description of a signal. We begin with simple methods and cover the popular FFT-based methods. We describe various window functions and how these affect the spectral estimation. We then present Pisarenko s .

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