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Spectrograms: Music Sampling and Discrete Fourier Coefficients

Learn how spectrograms help analyze sounds by representing discrete Fourier coefficients graphically. Discover the process of filtering frequencies and computing coefficients to understand wave intensities in music.

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Spectrograms: Music Sampling and Discrete Fourier Coefficients

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  1. Tim Hurley Spectrograms: Music Sampling and Discrete Fourier Coefficients

  2. Spectrograms • Spectrograms are used to identify and analyze sounds • Typically, x-axis represents time and y-axis represents frequency • Spectrograms are used to visually represent a Discrete Fourier Transform

  3. Two Ways • First way: Filters • The filter takes frequencies and passes them through and rejects frequencies that are outside of the given range

  4. Second way: Fourier coefficients • We already did that!! • Nooooo, we found something different. • Waves are continuous sinusoidal functions. • Finding the Fourier coefficients for these produced an infinite series numbers • Computers don’t like infinite numbers

  5. What we did • Recall that we wanted to find Fourier coefficients in order to find an approximation for the square wave • We took the integral from 0 to 2π and looked at different cases and found the form for an and bn. • This produced infinite number of values

  6. What I did • I started with a similar equation and took the summation of it from 0 to N-1 • N = number of samples within a given window • Difficulties arose because I had to use multiple trig identities in order to re-write the sums/products of sinusoids so they were able to be manipulated. • After tedious trig work I was able to determine the form of the coefficients

  7. Why does that have to do with spectrograms??? • Good question! • Discrete Fourier Transform looks at a small windows of a sound signal. • Breaks this window into N small fractions of seconds (ex: 0.0005 secs) • Determines the discrete Fourier coefficients for this section • Coefficients represent intensities of different frequencies of the wave • These numbers are graphed and the process is repeated

  8. For Example Blue = higher intensity frequency Red = medium intensity frequency Yellow = low intensity frequency This will happen for every ‘window’ until entire sound is analyzed and graphed

  9. “Philip’s Research” “–e–” “–s” “–ch” “Philip–” “–sear–” “re–” www.seeingwithsound.com/javoice.htm

  10. The End Questions?? By the way, this is my last assignment as an undergrad student

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