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**Unformatted text preview: **f. That is, for a given f s and N, f= f s /N, it then follows that: 697=n 1 f. 770=n 2 f. and so forth. This, in turn means that the ratio 770/697= n 2 f/ n 1 f = n 2 f/ n 1 f = n 2 /n 1 = k. But computing the mathematical greatest common divisor shows that except for two frequencies (770 and 852), the DTMF frequencies are pairwise prime and, therefore, cannot be related by some factor k. As a consequence, a DFT can not be used as a replacement technology. >> gcd(697,770) 1 >> gcd(852,770) 2 >> gcd(852,941) 1 DFT - 1 Digital Signal Processing Dr. Fred J. Taylor, Professor >> gcd(1209,941) 1 >> gcd(1209,1336) 1 >> gcd(1477,1336) 1 >> gcd(1477,1633) 1 1 The reason that the DFT is unqualified as a replacement technology is due to the fact that the DFT is a constant bandwidth analysis tool and the POTS system is based on a constant Q (Q=BW/f ) analog technology. DFT - 2...

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