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Unformatted text preview: Fast Fourier Transform in MATLAB n sound, frequency (pitch) and amplitude (related to volume) are the principle elements perceived by humans both of which usually vary with time. Most sounds are composed of more than one frequency at a time. In music, this is known as a chord. If this were not the case, then we would be left with those annoying monophonic ringtones from the first cell phones. You know, the ones where there were only 10 ringtones from which to choose and the odds of more than one person having that annoying beeping rendition of Fr Elise were very high. But I digress. In MATLAB, if we plot the amplitude data vector against time we get a plot similar to the one below. Time domain plot of the intro to Sweet Child of Mine. This plot shows us how long the sound is (2 seconds) and how the amplitude (effectively related to volume) varies over time. But it also can be very useful to know how each frequency component of the sound contributes to the overall amplitude. For example, in most music the melody line has larger amplitude than the other frequency components of the sound. Think of it as if 3 different instruments played 3 different notes (frequencies) each at a different volume. We can distinguish which instrument was playing which frequency at what volume using MATLAB. This can be done by doing a Fourier Analysis of the sound data a transform from the time domain to the frequency domain. Magnitude of the Complex Amplitude In MATLAB, there is a built in function, fft( ) , which can be used to analyze the frequency components of a sound. More specifically, for each frequency we can measure two values: amplitude and phase. Phase is a more complicated topic covered in other courses. It is very common for these two values be represent together as one complex value called a complex amplitude or...
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- Spring '08