Use of the Discrete Fourier Transform in the Measurement of Frequencies and Levels of Tones

There have been numerous articles, in recent years, dealing with the use of the discrete Fourier transform (DFT) in the area of spectrum analysis. Much of this interest was motivated by the availability of a computational algorithm that facilitates the rapid computation of DFT coefficients by a digital computer. The algorithm is, of course, the fast Fourier transform (FFT). We are concerned with the problem of applying DFT techniques to the measurement of the levels and frequencies of single-frequency tones, 197 198 T H E B E L L S Y S T E M TECHNICAL J O U R N A L , FEBRUARY 1970 S(t) LOW-PASS FILTER A/D CONVERTER DIGITAL COMPUTER OUTPUT DISPLAY Fig. 1 -- A D F T measurement system.