Welch's Method with Windows

As usual, the purpose of the window function (Chapter 3) is to reduce side-lobe level in the spectral density estimate, at the expense of frequency resolution, exactly as in the case of sinusoidal spectrum analysis.

When using a non-rectangular analysis window, the window hop-size cannot exceed half the frame length without introducing a non-uniform sensitivity to the data over time. In the rectangular window case, we can set and have non-overlapping windows. For Hamming, Hanning, and any other generalized Hamming window, one normally sees for odd-length windows. For the Blackman window, is typical. In general, the hop size is chosen so that the analysis window overlaps and adds to a constant at that hop size. This consideration is explored more fully in Chapter 7. An equivalent parameter used by most matlab implementations is the overlap parameter .

Note that the number of blocks averaged in (5.8) increases as decreases. If denotes the total number of signal samples available, then the number of complete blocks available for averaging may be computed as

where the floor function denotes the largest integer less than or equal to .

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Subsections

• Matlab for Welch's Method

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.