Abstract
Since the introduction of feedforward–feedback comb allpass filters by Schroeder and Logan, its popularity has not diminished due to its computational efficiency and versatile applicability in artificial reverberation, decorrelation, and dispersive system design. In this work, we present an extension to the Schroeder allpass filter by introducing frequency-dependent feedforward and feedback gains while maintaining the allpass characteristic. By this, we directly improve upon the design of Dahl and Jot which exhibits a frequency-dependent absorption but does not preserve the allpass property. At the same time, we also improve upon Gerzon’s allpass filter as our design is both less restrictive and computationally more efficient. We provide a complete derivation of the filter structure and its properties. Furthermore, we illustrate the usefulness of the structure by designing an allpass decorrelation filter with frequency-dependent decay characteristics.
Highlights
Since the introduction of feedforward–feedback comb allpass filters by Schroeder and Logan [1], its popularity has not diminished due to its computational efficiency and versatile applicability in artificial reverberation [2]
Allpass filters can further be generalized to multiple input and output (MIMO) systems based on unitary networks [5] or feedback delay networks (FDNs) [6]
We present an extension to the Schroeder allpass filter [1] by introducing frequency-dependent feedforward and feedback gains while maintaining the allpass characteristic
Summary
Since the introduction of feedforward–feedback comb allpass filters by Schroeder and Logan [1], its popularity has not diminished due to its computational efficiency and versatile applicability in artificial reverberation [2]. Compared to general high-order allpass filters [3], the Schroeder allpass is a sparse filter, which is less flexible, but more computationally efficient. For reverberation enhancement systems and feedback delay networks, the allpass characteristic is mathematically important to maintain the system stability. We present an extension to the Schroeder allpass filter [1] by introducing frequency-dependent feedforward and feedback gains while maintaining the allpass characteristic. We show that it is possible to achieve the desired effect on the compact feedforward/-back structure with any FIR or IIR filter.
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