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Physics 145 Introduction to Experimental Physics I Instructor: Karine Chesnel Office: N319 ESC Tel: Office hours: on appointment Class website:

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Lab 12 Fourier Transform

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Resonators Spring – mass resonator Tuning fork

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Time – frequency Pure sine wave Time space Frequency space

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Fourier Transform Joseph Fourier french mathematician Decomposition of functions in linear combination of sine waves Discrete Fourier series Example: N = 3 N = 10

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Fourier Transform Discrete Fourier series Using sine functions Using complexe notation Fourier’s trick where

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Fourier Transform Continuous Fourier transforms Integration over time Integration over frequency range

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Square wave Fourier Transform Time space Frequency space

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Modulated wave Fourier Transform Time space Frequency space t

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Power spectrum

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Nyquist-Shannon criterion A periodic signal needs to be sampled at least at twice the frequency to be properly measured /reconstructed

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Lab 12: Fourier Transform A. Computer generated waveforms L12.1: open Labview Fourier-waveform.vi generate different waveform examine the time functions and the frequency spectra Sine wave Square wave Modulated wave

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Lab 12: Fourier Transform C. Fourier spectra of sound-wave L12.2: open Labview Fourier-sound.vi plug microphone + headset speakers to computer sample yourself whistling… sampling at 20kHz for 1s L12.3: Record notes produced by tuning forks look at fundamental frequency f 0 and harmonics compare fundamental frequency to nominal value L12.4: Test the Nyquist criterion - use sine wave from tuning fork (f 0 = 1kHz) - sample at different frequencies from 1kHz to 10kHz… - observe what happens to the time and frequency spectra L12.5: Generate Fourier spectra from different abrupt sounds: -clapping, yelling, popping balloons… -Print spectra

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Lab 12: Fourier Transform C. Application: vowel sound recognition L12.6: generate Fourier spectra from vowels: a, e, o, u (hold the note steady for entire acquisition) L12.7: print series of spectra from different persons play to guess which spectrum correspond to which vowel L12.8: Record vocal input (sentences, etc…) - increase the sampling interval to several seconds at 20kHz - turn the frequency filter ON (band pass) - compare unfiltered (left) and filtered (right) signals L12.9: Play with parameters of band-pass filter ( low band-pass: Hz…. High band-pass 1kHz and more) listen to the resulting filtered signal, print spectra D. Application: frequency filter to vocal input

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