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## PowerPoint Slideshow about ' Spectrum Analysis and PVan' - octavio-tyson

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Presentation Transcript

and PVan

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

interactive program

for spectrum analysis

analysis file with

amplitudes and frequencies

soundfile.pvn

interactive program

for spectrum display

pvan.exe

graphs of

spectra

Spectrum Analysissoundfile.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.

Fourier Analysis

Fourier Coefficients

Math

amplitudes

and phases

Time-Varying Fourier Analysissound

- 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:

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