Uniform Running-Sum Filter Banks

Using a length running-sum filter, let's make bandpass filters tuned to center frequencies

Since the bandwidths, as defined, are , the filter pass-bands overlap by 50%. A superposition of the band-pass frequency responses for is shown in Fig.9.14. Also shown is the frequency-response sum, which we will show to be exactly constant and equal to . This gives our filter bank the perfect reconstruction property. We can simply add the outputs of the filters in the filter bank to recreate our input signal exactly. This is the source of the name Filter-Bank Summation (FBS).

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Subsections

• System Diagram of the Running-Sum Filter Bank
• DFT Filter Bank
• Inverse DFT and the DFT Filter Bank Sum

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Order a Hardcopy of Spectral Audio Signal Processing

Previous: Making a Bandpass Filter from a Lowpass Filter
Next: System Diagram of the Running-Sum Filter Bank

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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.