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Sound Waves and the Fourier Transform (sort of)

oxy126

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blog-0742637001386731593.gifI'm a big fan of sound. Music for me is a nice blend of science and art, and I take strides to better my understanding of it occasionally. And occasionally, I enjoy listening to chiptune songs - 8-bit music, as you may call it. A typical sound wave is sinusoidal, meaning it looks like a sine/cosine curve. This is the natural state of a pressure fluctuation that is sound. However, sound waves are (obviously) not all sine waves. Because of the constructive/destructive interference of waves, waves with a new shape - or timbre - like with a square or saw wave, essentially keeping the dominant frequency (pitch) of the note while still changing how it sounds.

What is really happening when this is going on is that, in some ways, the frequency is changing, but just not the dominant frequency. In music, an octave occurs when one note has double the frequency of another, and by changing the amount of sound energy contained in a certain frequency that is an integer multiple of the base frequency (be it an octave or a different multiple), you can change the timbre without distorting pitch. This is the fundemental basis lying behind the Fourier transform, a method for breaking down a period function into an (often infinite) sum of sine waves with different frequencies. With bar-based music visualizers, the same things is happening, with wave shapes being analyzed for the frequencies they contain. But this phenomenom is what makes music sound the way it does, and it demonstrates that wave interference can have some interesting and melodic effects.



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You'll also find tons of Fourier Analysis in advanced optics and imaging -- very useful for tons of image manipulations, lens modeling, and other cool things!

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