Tone location by cyclotomic filters

In this paper we present a tone location system that estimates the frequency of an input tone through additions and comparisons alone. The system uses “cyclotomic” filters (which operate without multiplications), requiring fewer operations than with a conventional Discrete Fourier Transform (DFT) entailing multiplications. In the system presented here, an input tone is first transformed to yield two quadrature tones, which are then digitized. Processing occurs in successive stages at successively reduced sampling rates. During each decimation stage, the system is configured to provide symmetric coverage of a subband in which the tone has been located at the previous stage. Simulations demonstrate that for the case studied, an input signal-to-noise ratio (SNR
i
) in excess of 10 dB yields an output signal-to-noise ratio (SNR
o
) that is close (within 0.3 dB) to the maximum attainable SNR
o
, where SNR
o
is measured in terms of the reduction in frequency uncertainty. Enhanced resolution is demonstrated at the expense of the number of computations, while holding the number of decimation stages constant, by using small DFTs in place of the cyclotomic filters. This method still utilizes fewer computations than a conventional DFT (with the same number of frequency cells), with approximately the same performance in the case of low noise. Thus, this alternative method is useful when circumstances prohibit using a single, large DFT.