Choice of Delay Lengths

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

FDN Reverberation

Triangular Feedback Matrices

Mean Free Path

The impulse signal is the shortest pulse signal. For discrete time (digital) systems, the impulse is a 1 followed by zeros. In continuous time, the impulse is a narrow, unit-area pulse (ideally infinitely narrow). The impulse is typically denoted by the Greek delta symbol δ and is often called the 'Dirac delta function', after Paul Dirac who pioneered its use (in addition to being a lead contributor in the development of Quantum Mechanics). — Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html

Reverberation is the sound created by many echoes blending together, such as you hear when you clap your hands together in an acoustically 'live' room. — Click for https://ccrma.stanford.edu/~jos/pasp/Artificial_Reverberation.html

Amplitude Modulation (AM) is said to occur when one signal modulations the amplitude of another signal. The most typical case of AM is multiplying by an offset sinusoid 1 + g sin(ω t+φ), where g is a real number between 0 and 1. — Click for https://ccrma.stanford.edu/~jos/mdft/Sinusoidal_Amplitude_Modulation_AM.html

The impulse response of a system is its output signal in response to the impulse signal. For discrete time (digital) systems, the impulse is a 1 followed by zeros. In continuous time, the impulse is a narrow, unit-area pulse (ideally infinitely narrow). — Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html

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A delay line is used to delay a signal in time. Delay lines for digital signals are typically implemented in software using a circular buffer. — Click for https://ccrma.stanford.edu/~jos/pasp/Delay_Lines.html

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

FDN Reverberation

Triangular Feedback Matrices

Mean Free Path

Choice of Delay Lengths

Following Schroeder's original insight, the delay line lengths in an FDN ( in Fig.3.10) may be chosen to be mutually prime. That is, their prime factorizations contain no common factors. This rule maximizes the number of samples that the lossless reverberator prototype must be run before the impulse response repeats.^4.14

The delay lengths should be chosen to ensure a sufficiently high mode density in all frequency bands. An insufficient mode density can be heard as ``ringing tones'' or an uneven amplitude modulation in the late reverberation impulse response.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Choice of Delay Lengths

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University