| ### Jussi Pekonen, Vesa Välimäki, Jonathan S. Abel and Julius O. Smith # Spectral Delay Filters with Feedback and Time-Varying Coefficients ## DAFx-09 Companion Page | TKK / SPA / Acoustics
## Abstract A recently introduced structure to implement a continuously smooth spectral delay, based on a cascade of first-order allpass filters and an equalizing filter, is described and the properties of this spectral delay filter are reviewed. A new amplitude envelope equalizing filter for the spectral delay filter is proposed and the properties of structures utilizing feedback and/or time-varying filter coefficients are discussed. In addition, the stability conditions for the feedback and the time-varying structures are derived. A spectral delay filter can be used for synthesizing chirp-like sounds or for modifying the timbre of arbitrary audio signals. Sound examples on the use of the spectral delay filters utilizing the structures discussed in this paper can be found at http://www.acoustics.hut.fi/publications/papers/dafx09-sdf/. ### Keywords Effects processing, allpass filters, feedback, time-varying filters ## Files Paper (617 KiB, PDF) Presentation slides (850 KiB, PDF) This page and the demo files listed below zip-archive (18.5 MiB) tar.gz-archive (18.5 MiB) ## Demos The following sound examples are generated with the following notation on the spectral delay filter structure: M The number of allpass filters in cascade K The stretching factor Other parameters are given in the corresponding section. ### Original sounds to be filtered Snare pattern Drumming pattern ### A time-invariant SDF, with K = 1, with the coefficient -0.9, and without an EQ filter
M = 256 Impulse response Snare pattern Drumming pattern Drumming pattern, filtering applied to snare | M = 512 Impulse response Snare pattern Drumming pattern Drumming pattern, filtering applied to snare | M = 1024 Impulse response Snare pattern Drumming pattern Drumming pattern, filtering applied to snare
### A time-invariant SDF, with K = 1, with the coefficient -0.9, and with an EQ filter
M = 256 Impulse response Snare pattern Drumming pattern | M = 512 Impulse response Snare pattern Drumming pattern | M = 1024 Impulse response Snare pattern Drumming pattern
### A time-invariant SDF, with K = 3, with the coefficient -0.9, and with an EQ filter
M = 256 Impulse response Snare pattern Drumming pattern | M = 512 Impulse response Snare pattern Drumming pattern | M = 1024 Impulse response Snare pattern Drumming pattern
### A time-invariant SDF, with K = 1, with the coefficient -0.9, with an EQ filter, and with a feedback path performing scaled two-point moving average filtering and delaying the result by one sample, i.e., the feedback signal is w(n) = c(y(n-1) + y(n-2))
M = 256, with c = 1⁄436 Impulse response Snare pattern Drumming pattern | M = 512, with c = 1⁄872 Impulse response Snare pattern Drumming pattern | M = 1024, with c = 1⁄1744 Impulse response Snare pattern Drumming pattern
### A time-varying SDF, with K = 1, with coefficients modulated by an 8 Hz sine having amplitude 0.9, without EQ filter, and with a feedback path performing scaling by 0.99
M = 256 Impulse response Snare pattern Drumming pattern | M = 512 Impulse response Snare pattern Drumming pattern | M = 1024 Impulse response Snare pattern Drumming pattern
### A time-varying SDF, with K = 3, with coefficients modulated by an envelope follower a(n) = 0.1|v(n)| + 0.9a(n-1) where v(n) is the sum of the input and feedback signals multiplied by 0.2, without an EQ filter, with a feedback path performing scaling by 0.99
M = 256 Impulse response Snare pattern Drumming pattern | M = 512 Impulse response Snare pattern Drumming pattern | M = 1024 Impulse response Snare pattern Drumming pattern

http://www.acoustics.hut.fi/publications/papers/dafx09-sdf/ | Modified: 2009-09-03