Results

Figure B.5 shows the magnitude frequency response of the resulting FIR filter . Note that the upper passband edge has been moved to 6500 Hz instead of 6000 Hz, and the stop-band begins at 7500 Hz instead of 8000 Hz as requested. While this may look like a bug at first, it's actually a perfectly fine solution. As discussed earlier in §B.4, all transition widths in filters designed by the window method must be equal to the window-transform's main-lobe width. Therefore, the only way to achieve specs when there are multiple transition regions specified is to set the main-lobe width to the minimum transition width. For the others, it makes sense to center the transition within the requested transition region.

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written by 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.