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Spectrum Analysis and PVan PowerPoint PPT Presentation

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Spectrum Analysis and PVan. analog-to-digital converter. samples. time-varying Fourier Analysis. Analyze the sound. amplitudes and phases. Resynthesize the sound. Additive Synthesis. resynthesized sound. recorded sound. Spectrum Analysis. Sound Analysis What are we going to do?

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Spectrum Analysis and PVan

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Spectrum Analysis

and PVan





Fourier Analysis

  • Analyze the sound

amplitudes and phases

  • Resynthesize the sound

Additive Synthesis

resynthesized sound

recorded sound

Spectrum Analysis

  • Sound Analysis

  • What are we going to do?

    • Record a sound

  • Prepare the sound

  • Play a musical selection demonstrating the instrument design


interactive program

for spectrum analysis

analysis file with

amplitudes and frequencies


interactive program

for spectrum display


graphs of


Spectrum Analysis




Synthetic Trumpet

  • Real musical instruments produce almost-harmonic sounds

    • The waveform of this synthetic trumpet repeats more exactly than that of a real instrument

Spectrum of a Sound

  • For any periodic waveform, we can find the spectrum of the waveform.

  • The spectrum is the relative amplitudes of the harmonics that make up the waveform.

    • The plural form of the word "spectrum" is "spectra."

Spectrum of a Sound

  • Example: amp1 = 1, amp2 = .5, and amp3 = .25, the spectrum = {1, .5, .25}.

  • The following graphs show the usual ways to represent the spectrum:


Harmonic Number

Finding the Spectrum of a Sound

  • isolate one period of the waveform

  • Discrete Fourier Transform of the period.

  • These steps together are called spectrum analysis.


Fourier Analysis

Fourier Coefficients



and phases

Time-Varying Fourier Analysis


  • User specifies the fundamental frequency for ONE tone

    • Automatically finding the fundamental frequency is called pitch tracking — a current research problem

    • For example, for middle C:


Time-Varying Fourier Analysis

  • Construct a window function that spans two periods of the waveform.

    • The most commonly used windows are called Rectangular (basically no window), Hamming, Hanning, Kaiser and Blackman.

  • Except for the Rectangular window, most look like half a period of a sine wave:

Time-Varying Fourier Analysis

  • The window function isolates the samples of two periods so we can find the spectrum of the sound.

Time-Varying Fourier Analysis

  • The window function will smooth samples at the window endpoints to correct the inaccurate user-specified fundamental frequency.

    • For example, if the user estimates f1=261.6, but it really is 259 Hz.

Time-Varying Fourier Analysis

  • Samples are only non-zero in windowed region, and windowed samples are zero at endpoints.

Time-Varying Fourier Analysis

  • Apply window and Fourier Transform to successive blocks of windowed samples.

    • Slide blocks one period each time.

Spectrum Analysis

  • We analyze the tone (using the Fourier transform) to find out the strength of the harmonic partials

  • Here is a snapshot of a [i:37] trumpet tone one second after the start of the tone

Trumpet's First Harmonic

  • The trumpet's first harmonic fades in and out as shown in this amplitude envelope:

Spectral Plot of Trumpet's First 20 Harmonics

Spectra of Other Instruments

  • [i:38] English horn:

pitch is E3, 164.8 Hertz

Spectra of Other Instruments

  • [i:39] tenor voice:

pitch is G3, 192 Hertz

Spectra of Other Instruments

  • [i:40] guitar:

pitch is A2, 110 Hertz

Spectra of Other Instruments

  • [i:41] pipa:

pitch is G2, 98 Hertz

Spectra of Other Instruments

  • [i:42] cello:

pitch is Ab3, 208 Hertz

Spectra of Other Instruments

  • [i:43] E-mu's synthesized cello:

pitch is G2, 98 Hertz

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