Allpass Filter Design and Effects
Announcement: DSP Seminar Friday October 9, 2009, 2:15 PM, CCRMA Classroom
With a lot of folks attending the AES Convention, we will have a more informal DSP Seminar, with me (Jonathan A) reviewing results in allpass filter design (from a 2006 DAFx paper by Julius and me) and effects processing (from a series of papers last year with Vesa Valimaki and his group at HUT). Abstracts of the papers I'll discuss follow.
--
ASA05, DAFx06
ROBUST DESIGN OF VERY HIGH-ORDER ALLPASS DISPERSION FILTERS
Jonathan S. Abel, Julius O. Smith III
A nonparametric allpass filter design method is presented for matching a desired group delay as a function of frequency. The technique is useful in physical modeling syn-
thesis of musical instruments and emulation of audio effects devices exhibiting dispersive wave propagation. While current group delay filter design methods suffer from numerical difficulties except at low filter orders, the technique presented here is numerically robust, producing an allpass filter in cascaded biquad form, and with the filter poles following a smooth loop within the unit circle.
The technique was inspired by the observation that a pole-zero pair arranged in allpass form contributes exactly 2\pi radians to the integral of group delay around the unit circle, regardless of the (stable) pole location. To match a given group delay characteristic, the method divides the frequency axis into sections containing 2π total area under the desired group-delay curve, and assigns a pole-zero allpass pair to each. In this way, the method incorporates an or- der selection technique, and by adding a pure delay to the desired group delay, allows the trading of increased filter order for improved fit to the frequency-dependent group delay. Design examples are given for modeling the group delay of a dispersive string (such as a piano string), and a dispersive spring, such as in a spring reverberator.
DAFx09
SPECTRAL DELAY FILTERS WITH FEEDBACK AND TIME-VARYING COEFFICIENTS
Jussi Pekonen, Vesa Välimäki, Jonathan S. Abel and Julius O. Smith III
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/ .
DAFx09
SOUND SYNTHESIS USING AN ALLPASS FILTER CHAIN WITH AUDIO-RATE COEFFICIENT MODULATION
Jari Kleimola, Jussi Pekonen, Henri Penttinen, Vesa Välimäki and Jonathan S. Abel
This paper describes a sound synthesis technique that modulates the coefficients of allpass filter chains using audio-rate frequencies. We found that modulating a single allpass filter section produces feedback AM–like spectrum, and that its bandwidth is extended and further processed by non-sinusoidal FM when the sections are cascaded. The cascade length parameter provides a dynamic bandwidth control to prevent upper range aliasing artifacts, and the amount of spectral content within that band can be
controlled using a modulation index parameter. The technique is capable of synthesizing rich and evolving timbres, including those resembling classic virtual analog waveforms. It can also be used as an audio effect with pitch-tracked input sources. Software and sound examples are available at http://www.acoustics.hut.fi/publications/papers/dafx09-cm/ .
JAES09
SPECTRAL DELAY FILTERS
Vesa Välimäki, Jonathan S. Abel and Julius O. Smith III
The implementation of spectral delay using filters comprising a cascade of many low-order all-pass filters and an equalizing filter is discussed. The spectral delay filters have chirplike impulse responses causing a large, frequency-dependent delay that is useful in audio effects processing. An equalizing filter design and a multirate technique that stretches the impulse response of all-pass filters are introduced.