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Dept. for Speech, Music and Hearing Quarterly Progress and Status Report Spectrum analysis using the fast Fourier transform (FFT)

By Liljencrants J

Abstract

analysis package using the FFT has been implemented, The input is present as a time series of periodic sanlples from the signal. After application of a suitable time window the corresponding discrete Fourier transform (DFT) is computed, and finally the spectral magnitude is determined. This paper will deal with some practical problems with this procedure. In particular attention is given to important limitation on the time window imposed by the sampling theorem. Thus a dual sampling theorem may be formulated, the effect of which does not seem to be generally recognized. Given a time series x k' 0 < k 5 N-1 the DFT is in general defined as The frequency series A is elegantly and economically computed using r the FFT algorith~n, ref (1,'2).~his series also contains N samples: 0 = r = N-1. These cover a frequency range from zero up to the samplin

Year: 2014
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