Complex Waves

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Complex Waves

• Just like simple waves, only more complex! ?

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Simple and Complex Waves
Types of Vibration
Simple
Complex

• Periodic (repeats)
• Single frequency
• Sounds like a pure tone (definite identifiable
  pitch)

• Periodic or Aperiodic
• Multiple frequencies
• May sound tonal or not

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Simple and Complex Waves
Types of Vibration
Simple
Complex
Periodic (harmonic)
Aperiodic (inharmonic)
Quasi- periodic
Periodic (harmonic)
A complex aperiodic sound is one whose component
frequencies occur randomly across some frequency
range
A complex periodic sound is one whose component
frequencies are integer multiples of the lowest
frequency of vibration
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Ohms Law of Acoustics

• All complex sounds can be broken down into their
  pure tone components

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Analogue vs Digital

• Advantages of Digital
• Making copies
• Flexibility
• Disadvantages of Digital
• Speed
• Economy (?)

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Analogue vs Digital

• Analogue continuous in time and amplitude

1
in msecs
0
5.0
31.25
4.6
amplitude
0
62.5
3.5
93.75
-1
time
125
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Analogue vs Digital

• Digital discrete in time and amplitude

1
in msecs
0
5.0
31.25
4.6
amplitude
0
62.5
3.5
93.75
-1
time
125
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Terms/Definitions

• Fundamental Frequency (f0) lowest frequency
  pure tone component present in a complex periodic
  sound
• Harmonic (hn) integer multiple of f0
• Partial any pure tone component of a complex
  sound
• Overtone all partials above f0
• Octave successive doubling of frequency

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Building a Complex Periodic Vibration
quasi-
/h1
f0
h2
500
h3
1000
h4
inharmonic
1500
h5
2000
3387
h6
2500
h7
3000
amplitude
h8
3500
4000
frequency
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Fourier Transforms Application of Ohms Law of
Acoustics

• Fourier Analysis a complex waveform can be
  broken down (analyzed) into its pure tone
  components
• Fourier Synthesis a complex waveform can be
  formed (synthesized) by combining pure tone
  components

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f0/h1
h5
FOURIERANALYSIS
h3
h7
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Fast Fourier Transform (FFT)
FOURIERANALYSIS
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f0/h1

h3

FOURIERSYNTHESIS

h5

h7
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Effect of relative phase
FOURIERSYNTHESIS


Perfect summation
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Effect of relative phase
FOURIERSYNTHESIS


Perfect cancellation
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Effect of relative phase
FOURIERSYNTHESIS


Imperfect summation
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Effect of relative phase




FOURIERSYNTHESIS


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at t 0
1.0
f 2 Hz

0.33

f 6 Hz
FOURIERSYNTHESIS

0.33
f 10 Hz
0.33
1 sec
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at t 100ms
1.0
2

0.33

FOURIERSYNTHESIS
amplitude
0

-2
0.33
-1.22
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Modes of Vibration