1. Implementation of an Audio Reverberation Algorithm
Fergal Dunne
Supervisor: Dr. Edward Jones

2. Project Aim
To implement a reverberation algorithm for audio applications
Gardner’s reverb algorithm - consists of three variations of the same general approach, intended to simulate rooms of different sizes
Implementation of a real-time version
Simulation in Matlab -> C
Implementation on a DSP development system/PC-Based system

3. Reverberation
A multiplicity of echoes whose speed of repetition is too quick for them to be perceived as separate from one another
Early and late reflections
Reverberation time – time taken for the sound intensity to decay to 1/1,000,000th (60 dB) of its original value

4. Gardner’s Algorithm
Combination of early and late echoes into a “unified” system, intended to simulate rooms of different sizes
Early reflections trigger late reverberation network
Late reflections delayed until after the last early echo
Tap/gain included to produce the desired level of late reverberation

5. Late Reflections Three similar algorithms – small, medium & large room
Common global structure based mainly, on allpass filters (both simple and nested) and delays, followed by a first order low pass filter
Output signal is obtained by summing signals taken from various points along the delay line

6. Which algorithm to use?
The appropriate reverb algorithm is chosen based on the reverberation time of the room to be simulated (bathroom, auditorium…)
Reverb time is calculated using Sabines Equation
Sabines equation uses information from the room to be simulated - room dimensions, material, absorption coefficients…

7. Room Responses - Bathroom

8. Early Echoes
Only one algorithm needed to simulate rooms of different sizes
Group of delays (20) followed by a first order low pass filter
Early echo output is the low pass filtered sum of each delay block

9. Early Echo Response - Auditorium

10. Unified System Response - Bathroom
Combination of both early and late reflections
Uses medium room “tail” algorithm

11. Real-time Implementation
Involves the rewriting of Gardner’s Network to process input signals on a sample-by-sample basis rather than processing bulk input samples (entire signals)
Real-time implementation of non real-time functions: splitting up functions into two parts – real-time part & non real-time part
Real-time implementation of the in-built Matlab filter function: two architectures – direct form I & II
Trade-off – Network execution time vs. No. of memory elements needed

12. Translation from Matlab to C
Real-time implementation on a suitable platform requires a translation of all real-time functions from Matlab to C
C-code equivalent versions of all real-time Matlab functions were written and verified using the originals as references
C test program results -> binary file -> read into Matlab -> verified against a Matlab equivalent program
All results agreed perfectly!

13. C Program Execution Requires three user inputs: Sampling rate
Simulation file
Binary input file name containing the samples to be reverberated

14. Functional Verification

15. Implementation on a DSP Development System
ADSP-21065L EZ-KIT Lite evaluation kit from Analog Devices
fast 32-bit DSP floating-point processor – 21065L
a full duplex, 16-bit stereo audio codec – AD1819A (ADC & DAC)
544 Kb of internal user memory
16-megaword map of external SDRAM

16. Real-time Simulation of C-code on board
Read in samples from a mic or CD player - ADC
Process the samples in real-time using Gardner’s algorithm
Send the samples out to a set of speakers - DAC
Successful: Early Echo implementation
Failure due to: lack of internal memory (big arrays), software tools…

17. Implementation on a PC-Based System
6025E DAQ plug-in device by National Instruments
A software programmable device (NI-DAQ Functions) featuring 16 channels (eight differential) of analog input, two channels of analog output
Two simulation programs:
‘Pseudo’ real-time application – records n secs of audio (mic/cd player), processes it, and plays it back in almost real-time
Real-time application – records and plays back audio in real-time (low sampling rate < 2 kHz)

18. Conclusion
Ultimate Project Goal: Real-time implementation of a reverberation algorithm for audio applications – practically realised
A real-time audio reverberation system was implemented but only for low sampling rates
A “pseudo” real-time system was also implemented
Future work: optimization of code to operate at higher sampling rates (speech, audio)
Simulation of more room types other than a bathroom, auditorium & cathedral