Frequency Domain Artificial Reverberation
using Spectral Magnitude Decay
Earl Vickers1, Jian-Lung (Larry) Wu2, Praveen Gobichettipalayam Krishnan3, and Ravirala Narayana Karthik Sadanandam3
1 The Sound Guy, Inc., Seaside, CA 93955 USA
2 Stanford Center for Computer Research in Music and Acoustics, Stanford, CA 94305 USA
3 University of Missouri, Rolla, MO 65409 USA
Presentation © 2006 Earl Vickers, The Sound Guy, Inc.
sfx@sfxmachine.com

Overview
Introduction
STFT & Phase Vocoder
Time-Freeze, Time-Scaling, Looping & Reverberation
Recursive Spectral Magnitude Decay
Phase Generation
Results
Remaining Problems
Conclusions

Introduction
Frequency Domain Reverb
Not using convolution
Spectral Magnitude Decay
Late reverb only
Diffuse portion of the room response
Typically after 100 ms.
Best described statistically
Early reflections would be handled separately

Reverberation
Something about reverberation echoes, resonates & reverberates deep within the human psyche
Echo & Narcissus
ÒIn Babylonian mythology there are hints of a specially constructed room in one of the ziggurats where whispers stayed forever.Ó
– Schafer

Existing Reverb Algorithms
Time domain reverbs, such as Feedback Delay Networks:
Low computational cost
Independent control over many perceptually relevant parameters
Convolution
Excellent simulation of the acoustics of a particular physical space

Inspirations for this approach
Frequency domain time-scaling often suffers from an unwanted ÒreverberantÓ effect, Òphasiness,Ó Òloss of presenceÓ
If weÕre trying to produce reverberation, this might prove to be an advantage, or at least not a liability
Ò...the responses in the finest concert halls sounded remarkably similar to white noise with an exponential amplitude envelope.Ó — James Moorer

Preview:
Spectral Magnitude Decay
Uses STFT / Phase Vocoder
Attenuates & accumulates the spectral magnitudes
Combines them with a computed phase signal
Resulting impulse response:
Smooth, exponentially decaying envelope
Independent control over room energy &
decay time at each frequency

STFT & Phase Vocoder
Analyze signal into a time-frequency grid
Change stuff
Resynthesize in the time domain

Time-Freezing
(Infinite Time Scaling)
Ongoing Parallel
Time-Freeze
Problems with the Parallel
Time-Freeze Reverb
Grows increasingly inefficient
Data storage & computation explosion
The impulse response consists of a decaying series of impulses, N samples apart

Optimizing the Parallel
Time-Freeze Reverb

Recursive
Spectral Magnitude Decay

Frequency Domain Analogue of MoorerÕs Comb Filter

Frequency-Dependent
Exponential Decay

Exponential Decay

Spectral Magnitude Decay
Impulse Response & EDC

The Phase Problem

Desired Phase Signal

Desired Phase Signal, cont.

Desired Phase Signal, cont.

The Auditory Sensation of Roughness
Out-of-tune piano: rapid beating results from nearby strings whose vibrations go in and out of phase
Rapid sequence of brief auditory events
Roughness most pronounced when sound includes spectrally coherent fluctuations
Can be minimized by randomizing the amplitudes and phases of its Fourier components
Randomization happens automatically in reverberant environments
Roughness reduction may be one of the benefits of adding reverb

Roughness & Beating —
Why CanÕt We All Just Get Along?
Amplitude fluctuations resulting from phase incoherence
Phase Generation Methods
1 - Propagation of Instantaneous Frequency
Phase Generation Methods
2 - Phase Randomization
Phase Generation Methods
3 - Partial Phase Randomization
Final Spectral Magnitude Decay Algorithm
Initial Observations
Good impulse response
Smooth envelope
Independent control of Room Energy and Decay Time as functions of frequency
Echo density doesnÕt increase over time
Maybe OK, because late reverb is defined as the point where individual reflections are indistinguishable.
Gradual attack will help blend in late reverb

Decay Time Cross-Synthesis Effect
Advantages
Compared to time domain reverb:
Less external memory needed
Fewer external memory accesses
Excellent control of room & decay spectra

Compared to convolution:
Parametric and flexible
Computation cost independent of decay time

Problems
Deterministic phases can produce echoes at period N
Less noticeable for shorter decay times
Phase randomization produces ÒwhisperizationÓ effect for short windows
Noticeable for N <= 1024
Not bad for N = 2048
Good for N >= 4192
Can use partial phase randomization
Long windows cause long latency
Early reflections could fill in the gap, for reasonable Reflections & Reverb Delays

Conclusion
No delay lines needed
Could be used for cell phones and other systems with limited memory
Flexible, detailed control of room energy & decay time as functions of frequency
Could be especially useful if youÕre already in the frequency domain
Cheaper than convolution for longer decay times
Convolution could be used for the early reflections

Slide 34