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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 8. An equivalent parameter used by most matlab implementations is the overlap parameter . Note that the number of blocks averaged in (6.27) 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 (7.28) where the floor function denotes the largest integer less than or equal to . Subsections Matlab for Welch's Method Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search [How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1. Copyright © 2022-02-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University

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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 8. An equivalent parameter used by most matlab implementations is the overlap parameter . Note that the number of blocks averaged in (6.27) 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 (7.28) where the floor function denotes the largest integer less than or equal to . Subsections Matlab for Welch's Method Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search [How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1. Copyright © 2022-02-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University

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Subsections Matlab for Welch's Method Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search [How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1. Copyright © 2022-02-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University

Note that the number of blocks averaged in (6.27) 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 (7.28) where the floor function denotes the largest integer less than or equal to . Subsections Matlab for Welch's Method Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search [How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1. Copyright © 2022-02-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University

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