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Unformatted text preview: 525 Computing Project 2, Fall 2011 * DMTF with Compressed Sensing: The Past Meets the Future Way back in the day when we all had land lines, the phone company figured out who you were calling using a clever scheme called dual-tone multi- frequency signaling (DTMF). When pressed, each key would trigger tones corresponding to the row and a key corresponding to the column. This would give a total of 12 different sounds but only 7 different frequencies (remember, there are the “*” and “#” keys). The tones for keys 1-9 are given in Figure 1. Much more recently, the signal processing community has been enamored with compressed sensing , a technique to recover sparse signals from highly incomplete and noisy information. In this project, we’ll combine both of these ideas, trying to recover DTMF signals from very few noisy samples. Since each DTMF signal is 2-sparse in a basis of 6 sine waves, let’s explore the limits of sensing DTMF signals in noise. A sine wave is given by s ( t ) = sin (2 πft ) where f is the frequency of the sine wave. To make a discrete time approx- imation, you pick a sampling frequency...
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- Fall '11
- Signal Processing, Sin, Sine wave, sK, tk