Example: FIR-Filtered White Noise
Let's estimate the autocorrelation and power spectral density of the ``moving average'' (MA) process
(7.34) |
where is unit-variance white noise.
Since ,
(7.35) |
for nonnegative lags ( ). More completely, we can write
(7.36) |
Thus, the autocorrelation of is a triangular pulse centered on lag 0. The true (unbiased) autocorrelation is given by
(7.37) |
The true power spectral density (PSD) is then
(7.38) |
Figure 6.3 shows a collection of measured autocorrelations together with their associated smoothed-PSD estimates.
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Example: Synthesis of 1/F Noise (Pink Noise)
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Matlab for Welch's Method