Lec7 Fourier Transforms

Lec7 Fourier Transforms - Summary from last week Physics...

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Physics 257 Lecture 8: Fourier Transform Prof. Matt Dobbs Physics Department, McGill U. Prof. M. Dobbs, Physics 257 Nov 9. 2006 2 Summary from last week ± Numerical minimizations of yields the best fit parameters for the function f. z In Matlab, this can be done with the fminsearch() function. ± The χ 2 function can be plotted, and the confidence interval contours superimposed. z The 1 σ error occurs at χ 2 = χ 2 min + 1 z The n σ error occurs at χ 2 = χ 2 min + n () Δ = i i i i i y a x f y 2 2 2 ) ; ( χ Prof. M. Dobbs, Physics 257 Nov 9. 2006 3 Time Domain Waveform ± A time domain waveform or timestream is just a series of data recorded versus time. z An example is the music recorded on an audio cassette or album. z Or a heart-beat scan - ± If this data is sampled at regular time intervals, it is a discrete waveform, and has been digitized. z Like the music on CDs. ± Let’s record a waveform, by digitizing it with the computer’s microphone and Microsoft sound recorder… z The timestream will be stored in a .wav file. Prof. M. Dobbs, Physics 257 Nov 9. 2006 4 Time Domain Waveform ± In matlab, change directory (cd) to the directory where we have stored the wave file. ± Our timestream has 44,100 samples per second. These samples form a digitized waveform, with a sample rate of 44,100. ± We can see the waveform just like we see any waveform on the oscilloscope. ± We can hear it too. cd 'C:\Documents and Settings\mdobbs\Desktop' [ts, sampleRate] =wavread('test.wav'); sampleRate plot( ts(1:1000) ) wavplay(ts,sampleRate)
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Prof. M. Dobbs, Physics 257 Nov 9. 2006 5 Timestream Waveform 0 100 200 300 400 500 600 700 800 900 1000 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Sample Number Amplitude Prof. M. Dobbs, Physics 257 Nov 9. 2006 6 Timestream Waveform (zoom in) 0 10 20 30 40 50 60 70 80 90 100 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Sample Number 1/44100 seconds The timestream has been sampled at a rate of 44,100 Hz (this is the standard rate for audio recordings, such as on CDs). Prof. M. Dobbs, Physics 257 Nov 9. 2006 7 Simple waveform ± y = sin (x) z Unit amplitude sine wave, sampled at 100 Hz, with a period of 1 second.
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This note was uploaded on 04/29/2008 for the course PHYS 257 taught by Professor Dobbs during the Fall '07 term at McGill.

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Lec7 Fourier Transforms - Summary from last week Physics...

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