Spectral Analysis using the FFT

[srilakshmi]

Spectral Analysis using the FFT

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1 Computing the DFT, IDFT and using them for filtering
To begin this discussion on spectral analysis, let us begin by considering the question of trying to detect
an underlying sinusoidal signal component that is buried in noise. Such problems occur, for example, very
commonly in the area of telecommunications. Suppose that such a signal-in-noise situation gives rise to
the observed data record as shown in figure 1.
Here the samples are collected at a spacing of = 0.1 second apart, and are contained in a MATLAB
vector x so that since the samples are plotted with the command

2 Spectral Resolution andWindowing
Now suppose that we have available a new 40 second data record x as shown in figure 7(a). This looks
very similar in nature to the original data record shown in figure 1, and indeed the DFT analysis performed