LING124 Review

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LING124 Review

• September 11, 2008

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Class outline

• Review
• Discrete Fourier Transform
• Sine and cosine functions
• e.g. yAsin(2pift?)
• Representing a signal as a linear combination of
  sine and cosine functions

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Why?

• Different speech sounds have different spectra
• ltExample spectral difference per soundgt
• Whats a spectrum?
• A sound wave consists of pure tones at different
  frequencies, we call these component frequencies
• Some component frequencies affect the shape of
  the sound wave more so than others. This is
  characterized as the amplitude of component
  frequencies. Component frequency with higher
  amplitude affects the overall shape more.
• ltExample same component frequencies, different
  amplitudesgt

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Same component frequencies,different amplitudes
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So what are we interested in?

• What are the component frequencies?
• What are their amplitudes?
• Fourier analysis answers both relative
  amplitudes of individual component frequencies.
• A graphical representation of this is called a
  spectrum frequency on the x-axis, amplitude on
  the y-axis

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Discrete Fourier Transform

• What are the component frequencies?
• Harmonics of base frequency up to Nyquist
  frequency
• Why?
• What are their amplitudes?
• Correlation between component frequency and the
  original wave
• Component frequency with higher correlation will
  have higher amplitude

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The terms in the sine function

• yAsin(2pfit?)
• A amplitude
• 2p the sine function
• f frequency
• i harmonics of frequency
• ? phase
• Play with the parameters in Praat
• Praat objects NewgtSoundgtCreate sound from
  formula

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yAsin(2pfit?)

• y1sin(2p11t0)

• y2sin(2p11t0)

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yAsin(2pfit?)

• y1sin(2p11t0)

• y2sin(2p21t0)

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yAsin(2pfit?)

• y1sin(2p11t0)

• y2sin(2p12t0)

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yAsin(2pfit?)

• y1sin(2p11t0)

• y2sin(2p11t0.5 p)