Proposal of an accurate and low complexity method for frequency estimation using DFT interpolation

Abstract

The estimation of the frequency in a Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) is a fundamental and well-studied problem in signal processing and communications. A variety of approaches to this problem, distinguished primarily by estimation accuracy, computational complexity, and processing latency, have been developed. For a signal containing an integer number of periods there are no differences in the application of the DFT algorithm and passing the representation of the waveform in the frequency spectrum and vice versa. Transform and reverse application generates errors only due to the calculation algorithm. The direct method to get a correct estimation of a peak frequency is to increase spectrum resolution up to the value of interest. But, unfortunately, this approach requires an additional processing time, which might be considered unacceptable, especially for portable systems without a powerful computing unit. A second solution to solve this problem is to implement a method to estimate the frequency value between spectral lines to correct dispersion effect due to the signal processing by Discrete Fourier Transform (DFT). The literature describes a number of methods to determine the estimate frequency of a spectral peak and its amplitude, but most of them involve a volume of high computation and enabling the calculation only are both the real and the imaginary parts of spectrum. This paper proposes a new frequency estimator, similar with another well-known algorithm, but more accurate having also a low computational complexity.