Implementing Professional Audio Effects with DSPs

Abstract

Digital signal processors are highly used in a large variety of today's domestic and industrial applications. This paper emphasizes on the principles and techniques involved in professional audio processing field. Some basic digital audio effects are described along with the corresponding guidelines for DSP implementation.

Full text

Buletinul Stiintific al Universitatii “Politehnica” din Timisoara, ROMANIA
Seria AUTOMATICA si CALCULATOARE (ISSN 1224-600X)
Transactions on AUTOMATIC CONTROL and COMPUTER SCIENCE, Vol. 46(60), 2001
Implementing Professional Audio Effects with DSPs
Mihai V. Micea 1, Mircea Stratulat 2, Dan Ardelean 3
and Daniel Aioanei 4
Software and Computer Engineering Department, POLITEHNICA University of Timisoara,
2, V. Parvan Blvd, 1900 – Timisoara, Romania, Phone/Fax: +40 56 192049
1 E-Mail: micha@dsplabs.utt.ro, WWW: http://dsplabs.utt.ro/~micha
2 E-Mail: smircea@cs.utt.ro, WWW: http://www.cs.utt.ro/~smircea
3 E-Mail: dardelean@dsplabs.utt.ro, WWW: http://dsplabs.utt.ro/~dardelean
4 E-Mail: daioanei@dsplabs.utt.ro, WWW: http://dsplabs.utt.ro/~daioanei
Abstract – Digital signal processors are highly used in a
large variety of today's domestic and industrial
applications. This paper emphasizes on the principles and
techniques involved in professional audio processing
field. Some basic digital audio effects are described along
with the corresponding guidelines for DSP
implementation.
Keywords: DSP, digital audio effect, chain of effects,
real-time, audio buffer, communication
protocol
1. INTRODUCTION
Professional audio processing has developed rapidly in the
last years, from predominant analog techniques to digital
processing algorithms and systems.
As result, a digital system to implement a
professional audio processor needs to meet high-
performance requirements: high-quality processing of
multiple audio channels, real-time operation capability,
stability, reliability and scalability [4].
On the other hand, as new audio effects are
continuously developed, the audio processor must be able
to implement them with little effort from the
user/developer.
A convenient solution to this problem is to design
the audio processor to provide plug-in capabilities, with the
audio effects implemented as run-time loadable modules.
In signal-based applications involving digital
processing, the most efficient implementation solution is
using specialized family of microprocessors: the digital
signal processors (DSPs).
DSPs feature high performance, autonomy and
flexibility at effective costs. Their internal architecture is
particularly designed to execute signal-processing
instructions in parallel, using specific hardware structures
(like Harvard bus structure, register file, circular memory
buffers and special internal memory and ports).
In addition, many digital signal processors, like the
Motorola DSP56037, feature a highly specialized internal
coprocessor (EFCOP – Enhanced Filter COProcessor), able
to execute autonomously various filtering and time-
consuming data manipulation algorithms.
In this paper we focus on the basic issues involved
in the design and implementation of a professional audio
processor with digital signal processors.
The next section describes some basic audio effects,
their general behavior and characteristics as algorithms
designed for digital system implementation, considering as
target a generic DSP.
Further on, the paper discusses the problem of
managing and interfacing the audio effects to the
user/developer.
As conclusions, we describe our practical approach
of this subject – a digital audio effects processor
implemented with the Motorola DSP56307, along with its
general characteristics and some performance
considerations.
2. AUDIO EFFECTS IMPLEMENTATION
Most of the audio effects used in professional sound editing
and processing application can be designed in terms of
signal processing algorithms, suitable for implementation
on digital systems, particularly on digital signal processors.
Some basic digital audio effects are described in the
following paragraphs, along with the corresponding
guidelines for DSP implementation.
2.1. Volume Effect
In its simplest form, the volume effect controls the
amplitude of the signal by varying the attenuation of the
input signal [3].
However, an active volume control will have the
ability to increase the volume (i.e. amplify the input signal)
as well as attenuating the signal:
[
][]
nxny ⋅=
υ
(1)
where:
y[n] is the current sample of the output signal,

x[n] is the current sample of the input signal,
υ
is the volume scaling factor:
υ
= 1, results in no effect on the output signal;
υ
< 1, the signal amplitude is decreased;
υ
> 1, the signal amplitude is increased.
For DSP implementation, the current audio sample can be
stored in an internal register and the volume factor as a
memory variable:
sample[i]= sample[i]·vol;
Volume controls are useful for placing between
effects, so that the relative volumes of the different effects
can be kept at a constant level.
2.2. Panning
Panning is used in stereo recordings. The volume of each
channel can be adjusted. This effectively adjusts the
position of the perceived sound within the stereo field.
The two extremes are: all sound completely on the
left or all sound completely on the right. This is commonly
referred to as balance on commercial sound systems [3, 4].
The effect implies two parameters as two decays –
one for the left channel and one for the right channel
(vol_left and vol_right).
Varying synchronously the two parameters, the
panning effect is achieved. The two parameters can appear
as one synchronized parameter to the user.
On the DSP, the signal transforming would appear
as follows:
output_left = input_left·vol_left;
output_right = input_right·vol_right;
2.3. Chorus
The chorus effect is achieved by adding an echo to the
original signal and then varying the delay of the echo
between a maximum and a minimum delay value at a
certain rate [3].
The algorithm describing the chorus effect is as
follows:
[] [] []
[
]
nnxnxny
∆
−+= (2)
where:
∆
[n] : Z → Z, is a discrete and periodic delay
function. It can be, for example, a triangular function (see
Fig. 1 and Fig. 2).
x[n]
∆
[n]
+
y[n]
Fig. 1. Chorus and Flanger effect diagram
Fig. 2. Two common waveforms for delay variation (source: [3])
The delay increases until it reaches a certain value and then
decreases to a minimum value.
The maximum value and the rate of raising and
falling of
∆
[n] function can be treated as parameters for this
effect. Typically, the delay of the echo for this effect varies
between 40 msec and 60 msec at a rate of about 0.25 Hz.
On the DSP, chorus can be implemented using a
circular buffer for audio sample processing. The output
sample results as the sum of the current input sample and a
delayed sample:
buffer[i] = input[i];
output[i] = buffer[i]+ buffer[i–offset[i]];
The delayed sample will be retrieved from the
buffer at a variable offset, calculated with the
∆
[n]
function, between a minimum value (e.g., 1) and the
maximum value set currently by the user.
2.4. Flanger
Flanging is a special case of the chorus effect: it is created
in the same way that chorus is created, that is mixing a
signal with a delayed copy of itself [4].
Typically, the delay of the echo for a flanger is
varied between 0 msec and 10 msec at a rate of 0.5 Hz (see
Fig. 1).
The delay of the signal cannot be heard by a human
ear, but it creates a series of notches in the signal. The
delay can be varied following either a sine wave or a
triangle, as shown in Fig. 2. The most common in flangers
is the triangle.
The ecuation for this effect is similar to (2).
2.5. Phaser Effect
Phasing is very similar to flanging. If two signals that are
identical, but out of phase, are added together, then the
result is that they will cancel each other out.
If, however, they are partially out of phase, then
partial cancellations and partial enhancements occur. This
leads to the phasing effect [3, 4].
In the algorithmic form, the phaser effect is given by
the equation below:
[
]
[
][]
dnxnxny −⋅−=
γ
(3)
where:
γ is a proper scaling factor (decay),
d is a discrete delay.

The implementation of the phaser effect on the DSP
involves a circular audio buffer, similar to the one
described at the chorus effect.
In algorithmic form, the phaser effect performs the
following steps:
buffer[i] = input[i];
output[i] = buffer[i] –
- decay ⋅ buffer[i - delay];
A diagram of this effect is shown in the figure bellow (APF
meaning "All-Pass Filter"):
x[n]
APF
- y[n]
Fig. 3. Block diagram of the phaser effect
2.6. Reverb Effect
Reverb is used to simulate the acoustical effect of rooms
and enclosed buildings. In a room, for instance, sound is
reflected off the walls, the ceiling and the floor. The sound
heard at any given time is the sum of the sound from the
source, as well as the reflected sound.
An impulse (such as a hand clap) will decay
exponentially. Concert halls and rooms have to be designed
such that the reverberation effect is adequate for the type of
sound that will be produced.
The digital reverberator is implemented by using a
number of comb filters ("CF") in parallel with varying
delay times. The outputs of the comb filters are summed
together through an all-pass filter ("APF") to produce the
reverb effect [3, 4]. The following diagram shows those
explained:
x[n]
+
y[n]
. . .
CF
CF
CF
APF
Fig. 4. Digital reverberator diagram
The implementation of the reverb effect on the DSP
includes several comb filters. The reverb effect can share
the same buffers that the echo effect is using.
But, unlike the echo algorithm, the reverb does not
store the modified sample (the resulted sample) in the
buffer. Instead, it stores the original sample.
The general description of the reverb effect as a
digital system is presented following algorithm:
[
]
[
]
[
][]
[][]
[][]
65
43
21
dnxdnx
dnxdnx
dnxdnxnxny
−⋅+−⋅+
+−⋅+−⋅+
+
−⋅+−
⋅
+
=
γγ
γγ
γ
γ
(4)
The delays of the comb filters (di in the previous equation)
and the general scaling factor (decay,
γ
) can be viewed as
the reverb effect main parameters.
2.7. Echo
A basic echo effect can be obtained by simply adding a
sound sample from the past to the current sound sample.
Therefore the simple echo effect involves two basic
operations: time-delay and addition, to generate the output
sample from the current one and the delayed sample (see
Fig. 5). The delay time can vary from a few miliseconds to
a few seconds.
x[n]
Time
delay
+
y[n]
Fig. 5. Diagram of an echo device
This device however, produces a very simple kind of echo
[3, 4]. A better echo device uses multiple echoes, adding a
feedback control which takes the output of the delay block
and takes it back to the input through an attenuator ("FA"),
as shown in Fig. 6.
x[n]
Time
delay
+
y[n]
+
FA
Fig. 6. Diagram of an echo device with feedback
The attenuator determines the decay of the echoes
(feedback gain should be less than 1), which is how quickly
each echo dies out.
The echo effect is described by a first order
difference equation since it involves a simple feedback
loop:
[
]
[
][]
dnynxny −⋅+=
γ
(5)
where:
y[n – d] is the sound sample from the past with its
corresponding gain, which actually creates the echo,
d is the user-adjustable delay (i.e., the actual delay
after which the echo will be heard),
γ
< 1 is the feedback gain. It controls in exponential
manner how long each echoed sample can be heard.

On the DSP, echo can be implemented using a circular
buffer for each audio channel to be processed. The buffer
contains the echo history at any time (i.e., the y[n –1] term
from (5)).
At each moment, the current audio sample is added
to a value from the buffer and the result is both sent to the
output and stored back into the buffer.
Considering the echo buffer length of N locations,
the basic algorithm for the echo effect involves the
following steps:
output = input + gain⋅buffer[k - delay];
buffer[k] = output;
k = (k+1) mod N;
k – delay = (k – delay) mod N;
where:
k is a pointer to the current location in the buffer,
gain is the feedback attenuation factor that can be
controlled by the user (gain < 1).
2.8. Ring Modulation
This effect takes two signals and multiplies them, thus
producing a signal that contains the sums and differences
of the frequencies of the two original signals. These
frequencies will typically be non-harmonic, so the ring
modulator can yield some very dissonant sounds. For that
reason ring modulator is not widely used [4].
By multipying the two input signals, the amplitude
modulation is implemented (more specifically, suppressed-
carrier modulation):
x [n]
x y[n]
x [n]
1
2
Fig. 7. A ring modulator multiplies two input signals
y[n] = x1[n] ⋅ x2[n] (6)
The ring modulator can have only one input connected to
an instrument and the other input to an internal oscillator
(which is generally considered to be the carrier signal).
Since the carrier signal doesn't appear in the output, it is
called "suppressed carrier".
Fig. 8 exemplifies the effects of a ring modulator.
Fig. 8. (a) 200 Hz sine wave, (b) 300 Hz sine wave,
and (c) the product of the two. The product is zero
when either wave is zero (source: [3]).
2.9. Equalizer
Equalization is an effect that allows the user to control the
frequency response of the output signal. The user can boost
or cut certain frequency bands to change the output sound
as needed.
It is usually performed with a number of bandpass
filters, all centered at different frequencies (outside each
other's frequency band), and the bandpass filters have
controllable gain [5].
As the human ear perceives sounds in a
logarithmic manner, the center frequencies, as well as the
pass-bands of the filters must be calculated on a
logarithmic scale (see Fig. 9).
Fig. 9. 10-band bandpass IIR filter response (source: [6])
The 10-band stereo equalizer is implemented using 10
digital IIR bandpass filters in parallel for each stereo audio
channel.
Assuming the audio codec samples the incoming
audio stream at a rate of fS Hz, the center frequencies for
these filters lie between 0 Hz to fS /2.
At each sample period, a left and right sound sample
is fed into the 10 digital filters. After each individual
bandpass filter eliminates the frequencies not in its range,
the output is scaled by a corresponding gain. Finally, the
results of the ten filters are summed together.
This process allows one to selectively remove or
limit, the gain of a particular frequency range from the
sound source (see Fig. 10).
Fig. 10. IIR equalizer data-flow diagram (source: [6])
Each bandpass filter is designed in a similar manner,
following the analog passive "RCL Bandpass Network",
with identical quality factors and with the central
frequencies based on equal intervals of the log of frequency
[5].

Hence, the IIR difference equations of the bandpass
filters follow an identical pattern:
[] [] [ ]
()
[] [ ]
()
2122 −−−+−−⋅= nynynxnxny
βγα
(7)
where:
α
,
β
and
γ
are the filter coefficients (see Fig.11).
Fig. 11. Bandpass IIR Filter Network Diagram (source: [6])
The bandpass filter coefficients in (7) can be calculated for
each filter knowing its particular center frequency,
θ
C and
the filter quality factor, Q (same for all filters):
C
θβγ
β
α
cos
2
1
;
2
2
1





+=
−
= (8)
and
C
C
Q
Q
θ
θ
β
+
−
=2
2 (9)
3. INTERFACING AND MANAGING THE AUDIO
EFFECTS PROCESSOR
Interfacing the audio effects and controlling their
parameters can be made using different approaches.
This paper emphasizes on a simple and efficient
solution: a special-purpose communication protocol and a
proper framework for managing and controlling the audio
effects.
The communication protocol is designed to provide
a real-time data link between the DSP – running the audio
processor, and a host computer – running the user interface.
To provide easy control of the system parameters
and to facilitate integration of new audio effects, we
propose a modular approach. All the audio effects are
implemented as stand-alone modules that can be activated
by the user into a "chain of effects" to be run on the DSP.
3.1. Communication protocol
The communication protocol establishes a link between the
DSP and a generic control and monitoring application, API
(this could be a keyboard, a PC application or any other
device capable of low-level serial protocol).
The protocol is based on control words, each word
having a length of 3 bytes.
The first byte specifies the parameter number to be
read/changed by the monitoring and control application and
the last two bytes specify a 16 bit value.
Protocol tasks:
(a) Read/change parameter value
(b) Synchronization
(c) Real-time communication
(a) Read/change parameter value
After each parameter ID (first command byte) received
from the API, the DSP module sends an echo value,
signaling that it has correctly received the parameter ID.
Read is performed by specifying the parameter ID in
the first command byte and the hex value of $FFFF as the
parameter value. This prevents the DSP module from
altering the parameter value. It also sends back the current
value of the parameter specified by its ID.
Change is performed by specifying the parameter
value which must be different from the hex value of $FFFF.
The DSP module answers with the old value of the
parameter, acknowledging that data was correctly received.
(b) Synchronization
A special parameter ID ($FF) is reserved for
synchronization. The value stored by the DSP module for
this parameter is $55AA.
To synchronize with the DSP module, the API has
to send a sequence of bytes with the hex value of $FF until
it receives a special sequence from the DSP module: "$FF
$55 $AA". This way the API will not to change any value of
the parameters held by the DSP module.
After receiving the "$FF $55 $AA" sequence, the
API is synchronized with the DSP module and is able to
query or change parameters (the communication protocol
treats the active chain of effects as a set of parameter IDs).
(c) Real-time communication
The DSP module performs a real time loop: receive the
audio signal sample, process it and send the processed
sample to the output.
To ensure the real time characteristics of the audio
process, the DSP module must not wait for the whole
communication word to be received.
After each sample is processed, the communication
channel is checked for a new constructed byte. Then the
byte is stored into a special buffer and when the full three-
byte word is ready, the corresponding parameter is
eventually changed.
3.2. Managing Audio Effects
The following diagram shows the actions taken by the DSP
module to apply the audio effects to the input digital signal:

Fig. 12. Audio effects management diagram
This loop should be optimized in order to consume
as little time as possible, thus leaving time for the audio
effects to process the input digital signal.
Therefore, considering the audio signals processed
at a sampling rate of fS , the overall time available to
process one audio sample through the entire chain of
effects is:
[]
sec
1
µτ
S
sample f
= (10)
With
τ
sample and the DSP clock rate, the maximum
number of instructions allowed for the chain processing can
be calculated.
In order to do this the loop has to take advantage of
the DSP parallel architecture. For easier development, the
architecture should be modular, and the audio effects
should be of plug-in type.
4. CONCLUSIONS
This paper discusses the basic issues involved in designing
a professional audio effects processor as a digital system,
presenting the corresponding algorithms of some audio
effects.
It also provides the main guidelines to implement
the algorithms with a generic digital signal processor.
As an application, we developed an audio effects
processor with the Motorola DSP56307 digital signal
processor.
Motorola DSP56307 is a 24-bit processor, working
at a maximum rate of 100 MHz, thus providing 100 MIPS
of processing power.
It features on-chip RAM memory of 64 Kwords, a
highly parallel instruction set, EFCOP (Enhanced Filter
COProcessor) running concurrently with the core, internal
timers and peripheral expansion ports, and effective off-
chip memory expansion capabilities [2].
A 16-bit CD-quality audio codec is used for
interfacing the sound channels with the audio processor.
The codec operates at 48 KHz sampling rate and is directly
connected to the DSP [1, 2].
The audio effects processor consists of two main
modules: the DSP and the PC modules, communicating
through a special-purpose serial link.
The DSP module implements both the active chain
of audio effects and the serial communication protocol with
the host computer. It is designed as a modular, open
architecture, with the audio effects developed as distinct,
plug-in modules.
Currently, the DSP module can process in real-time
a total of nine audio effects. The DSP clock rate is set to
88.47 MHz and the total time available for processing one
sample of sound through the entire chain of audio effects is
τ
sample = 20.8 µsec.
Therefore, to maintain the real-time behavior of the
audio processor, there are up to 1840 clock cycles available
to process the sound sample.
The PC module implements the graphical user
interface of the audio processor, as well as the serial
communication link with the DSP module.
It is able to synchronize with the DSP module while
the user can read or modify both the chain of active audio
effects, as well as their parameters.
Our approach demonstrates the effectiveness of
using highly-specialized processors – alias DSPs – to
implement professional applications in today's increasing
audio demands.
ACKNOWLEDGMENT
This paper is part of the research and development program
carried out by DSPLabs in close cooperation with the
Motorola Corporation, USA.
The authors are members of the DALT (Motorola
DSP Application Lab in Timisoara) project team, involved
in developing the application grant DALT.2.6/2000 –
"Audio Effects Processor with the Motorola DSP56300
Family".
REFERENCES
[1] Motorola, Incorporated, "DSP56300 Family User's Manual", 1999.
[2] Motorola, Incorporated, "DSP56307 24-Bit Digital Signal
Processor User’s Manual", 1999.
[3] Scott Lehman, "Effects Explained", Harmony Central,
(http://www.harmonycentral.com), 1996.
[4] Toby Kurien, "Audio Effects",
(http://users.iafrica.com/k/ku/kurient/dsp/effects.html), 1997.
[5] James M. Montgomery, "Implementing a 10-Band Stereo Equalizer
on the DSP56311EVM Board", Motorola Application Note,
AN2110/D, 2001.
[6] Motorola, Incorporated, "Digital Stereo 10-Band Graphic Equalizer
Using the DSP56001", Motorola Application Note, APR2, 1988.