ELEN E4896 MUSIC SIGNAL PROCESSING Lecture 4: Analog Synthesizers
Transcript of ELEN E4896 MUSIC SIGNAL PROCESSING Lecture 4: Analog Synthesizers
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Lecture 4:Analog Synthesizers
Dan EllisDept. Electrical Engineering, Columbia University
[email protected] http://www.ee.columbia.edu/~dpwe/e4896/1
1. The Problem Of Electronic Synthesis2. Oscillators3. Envelopes4. Filters
ELEN E4896 MUSIC SIGNAL PROCESSING
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /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
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Piano
Plucked Violin
Trumpet
Bowed Violin
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
The Analog Synthesizer• Minimum “useful” configuration
Pitch + harmonicsAmplitude variation (dynamics)Spectral variation
(1970s technology)
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Min
imoo
g, 19
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Oscillator Filter
Envelope
PitchTrigger
Vibrato
t
t
f
+
Cutofffreq
Gain
Sound
++
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Digital Simulation of Analog• E.g. Loomer Aspect
http://www.loomer.co.uk/aspect.htm
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
PureData (Pd)• Visual metaphor based on analog synths
“wires” connect modules
• Tutorial: http://en.flossmanuals.net/PureData/
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
2. Oscillators• Pitch = sinusoid?
only a single color
• Real instruments have more harmonicsstatic spectrum determines instrument sound?
• Additive: Combine individual harmonicscalculating sinusoids in real time is expensive...
• Subtractive: Shape harmonics with filtersstart with a spectrally rich signal“shape” harmonics efficiently with LTI filters
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Basic waveforms• Sinusoid
• Square wave
• Pulse waveform
• Sawtooth
• Triangle
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Aside: Bandlimiting• It’s easy to sample “ideal” simple waveforms
but the ideal ones are not bandlimited➝ lots of aliased energy
• Solution: Bandlimited waveformse.g. fill a table with precalculated sum of sinusoids up to a fixed frequency
• Variable waveforms can be derivedPWM by integrating bandlimited impulseshttps://ccrma.stanford.edu/~stilti/papers/blit.pdf
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Modulation• Stationary spectra sound unnatural
real sources have random “jitter”
• Variations in pitch“Low Frequency Oscillator” frequency modulation
random noise
• Variations in timbrecan be imposed by filters...Pulse-width modulation
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Aside: PWM Spectrum• What are harmonics of Pulse-Width Modulated
(PWM) waveforms?consider as impulses convolved with a pulse W➝ Fourier transforms multiply
or integral of sum of two opposite impulse trains with relative delay W(good for bandlimiting)
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0 500 1000-0.50
0.51
1.5
0 500 1000-0.50
0.51
1.5
0 500 1000-0.50
0.51
1.5
0 200 400-40
-20
0
20
40
0 200 400-40
-20
0
20
40
0 200 400-40
-20
0
20
40
time
frequency
=
pw(t) =�
p(t)� p(t�W )dt
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
3. Envelopes• Notes need to be limited in time
simple gating not enoughamplitude envelope
• Different (real) instruments have clear variations in envelopestruck/plucked vs. bowed/blown
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
ADSR• 4-parameter classic envelope model
Attack - initial rise timeDecay - fall time immediately following initial attackSustain - amplitude of asymptote of decaywhile key is held downRelease - decay from sustain to zero after key released
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Tobi
as R
. - M
etoc
Key depressed
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Pd ADSR Abstraction• Any patch can become a “unit”
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
4. Filtering• Amplitude modulation alone is not enough
real instruments have time-varying spectrae.g. plucked string
• Generally just LPF (+ resonance)high frequencies die away after initial transientresonance can give some BPF effect
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
The Biquad filter• Flexible circuit design to achieve
variable cutoff frequencybut just single pole-pair LPF (or repeats)constant Q (bandwidth/center freq) resonance
• Analog synths provided 12-24 dB/oct rolloff15
-1 0 1-1
-0.50
0.51
s plane
10-1 100 101-50
0
50
gain
/ dB
freq / rad/s
-1 0 1-1
-0.50
0.51
Real
Imag
Real
Imag
z plane
0 0.2 0.4 0.6 0.8 1-50
0
50
norm freq / π
gain
/ dB
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
5. Examples• Juno-106 preset patches
from http://www.synthmania.com/juno-106.htm
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Brass Trumpet
Piano Strings
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Summary• Analog synthesizers provided
musical flexibility with simple units20 years of evolution
• Need instrument-like dynamics to make an interesting soundbut only up to a point...
• Analog synths provide intuitive controlseach “knob” has a distinct effect
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