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- Title
Improved Spectral Estimation of Signals using Quadratic Interpolation.
- Authors
Bechhoefer, Eric; Butterworth, Brent
- Abstract
Common in many fields of science and industry is the estimation of the magnitude and frequency of signals generated by periodic, sinusoidal signals. This process is ubiquitous and the foundation of many standards and procedures, and often involves use of the Fourier transform. In application, this is done with a Fast Fourier Transform (FFT). The FFT is defined only for frequencies that are exactly integers of the sample rate (fs). For other frequencies, this causes spectral leakage and error in the estimation of the FFT amplitude for frequency. On average, the magnitude error is 4%. This paper discuses an improved technique for the estimation of magnitude and frequency of a sinusoidal signal using the FFT, which reduces the magnitude error to a fraction of a percent. The improved estimation uses a transformation of the data to make the spectral peak parabolic, from which a quadratic solver is used to estimate the true magnitude peak value and frequency. This method can be proved to be optimal by reducing the FFT error in sum of square errors sense.
- Subjects
SIGNAL frequency estimation; MAGNITUDE estimation; FAST Fourier transforms; INTERPOLATION; AMPLITUDE estimation; FOURIER transforms
- Publication
International Journal of COMADEM, 2021, Vol 24, Issue 4, p13
- ISSN
1363-7681
- Publication type
Article