### 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