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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


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?

    • Record a sound

  • Prepare the sound

  • Play a musical selection demonstrating the instrument design


pvan.exe

interactive program

for spectrum analysis

analysis file with

amplitudes and frequencies

soundfile.pvn

interactive program

for spectrum display

pvan.exe

graphs of

spectra

Spectrum Analysis

soundfile.wav

PC.wav-format

soundfile


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:

Frequency

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.


time-varying

Fourier Analysis

Fourier Coefficients

Math

amplitudes

and phases

Time-Varying Fourier Analysis

sound

  • 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:

f1=261.6


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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