ELEN E4896 MUSIC SIGNAL PROCESSING
Lecture 4:
Analog Synthesizers
1.
2.
3.
4.
The Problem Of Electronic Synthesis
Oscillators
Envelopes
Filters
Dan Ellis
Dept. Electrical Engineering, Columbia University
dpwe@ee.columbia.edu
E4896 Music Signal Processing (Dan Ellis)
http://www.ee.columbia.edu/~dpwe/e4896/
2013-02-11 - 1 /17
1. The Problem of Electronic Synthesis
• How can we synthesize notes and music
... and have it sound as good as real instruments?
• Real instrument tones are complex
Piano
Trumpet
Plucked Violin
Bowed Violin
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 2 /17
The Analog Synthesizer
• Minimum “useful” configuration
t
+
+
Vibrato
Oscillator
t
Cutoff
freq
Sound
Filter
f
Gain
Minimoog, 1972
(1970s technology)
Trigger
Pitch
+
Pitch + harmonics
Amplitude variation
(dynamics)
Spectral variation
Envelope
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 3 /17
Digital Simulation of Analog
Loomer Aspect
• E.g.
http://www.loomer.co.uk/aspect.htm
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 4 /17
PureData (Pd)
• Visual metaphor based on analog synths
“wires” connect modules
• Tutorial: http://en.flossmanuals.net/PureData/
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 5 /17
2. Oscillators
• Pitch = sinusoid?
only a single color
• Real instruments have more harmonics
static spectrum determines instrument sound?
• Additive: Combine individual harmonics
calculating sinusoids in real time is expensive...
• Subtractive: Shape harmonics with filters
start with a spectrally rich signal
“shape” harmonics efficiently with LTI filters
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 6 /17
Basic waveforms
• Sinusoid
• Square wave
• Pulse waveform
• Sawtooth
• Triangle
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 7 /17
Aside: Bandlimiting
• It’s easy to sample “ideal” simple waveforms
but the ideal ones are not bandlimited
➝ lots of aliased energy
• Solution: Bandlimited waveforms
e.g. fill a table with precalculated sum of sinusoids
up to a fixed frequency
• Variable waveforms can be derived
PWM by integrating bandlimited impulses
https://ccrma.stanford.edu/~stilti/papers/blit.pdf
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 8 /17
Modulation
• Stationary spectra sound unnatural
real sources have random “jitter”
• Variations in pitch
“Low Frequency
Oscillator”
frequency
modulation
random noise
• Variations in timbre
can be imposed by filters...
Pulse-width modulation
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 9 /17
Aside: PWM Spectrum
• What are harmonics of Pulse-Width Modulated
(PWM) waveforms?
consider as impulses convolved with a pulse W
➝ Fourier transforms multiply
=
time
1.5
1.5
1.5
1
1
1
0.5
0.5
0.5
0
0
0
-0.5
40
frequency
0
500
1000
-0.5
40
0
500
1000
-0.5
40
20
20
20
0
0
0
-20
-20
-20
-40
0
200
400
-40
0
200
400
-40
0
0
500
200
1000
400
or integral of sum of two opposite impulse trains
with relative delay W
pw (t) = p(t) p(t W )dt
(good for bandlimiting)
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 10/17
3. Envelopes
• Notes need to be limited in time
simple gating not enough
amplitude envelope
• Different (real) instruments have clear
variations in envelope
struck/plucked vs. bowed/blown
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 11/17
ADSR
Attack - initial rise time
Decay - fall time immediately following initial attack
Key depressed
Sustain - amplitude of
asymptote of decay
while key is held down
Release - decay from
sustain to zero after
key released
E4896 Music Signal Processing (Dan Ellis)
Tobias R. - Metoc
• 4-parameter classic envelope model
2013-02-11 - 12/17
Pd ADSR Abstraction
• Any patch can become a “unit”
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 13/17
4. Filtering
• Amplitude modulation alone is not enough
real instruments have time-varying spectra
e.g. plucked string
• Generally just LPF (+ resonance)
high frequencies die away after initial transient
resonance can give some BPF effect
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 14/17
The Biquad filter
• Flexible circuit design to achieve
variable cutoff frequency
but just single pole-pair LPF (or repeats)
constant Q (bandwidth/center freq) resonance
s plane
0.5
gain / dB
Imag
1
50
0
-0.5
-1
-1
gain / dB
0
-0.5
-1
0
Real
0
1
1
10
freq / rad/s
50
0.5
-1
-50
-1
10
1
z plane
1
Imag
0
Real
0
10
0
-50
0
0.2
0.4
0.6
norm freq / π
0.8
1
• Analog synths provided 12-24 dB/oct rolloff
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 15/17
5. Examples
• Juno-106 preset patches
from http://www.synthmania.com/juno-106.htm
Brass
Piano
E4896 Music Signal Processing (Dan Ellis)
Trumpet
Strings
2013-02-11 - 16/17
Summary
• Analog synthesizers provided
musical flexibility with simple units
20 years of evolution
• Need instrument-like dynamics
to make an interesting sound
but only up to a point...
• Analog synths provide intuitive controls
each “knob” has a distinct effect
E4896 Music Signal Processing (Dan Ellis)
2013-02-11 - 17/17