A Fast, Simplified Frequency-Domain Interpolation Method for the Evaluation of the Frequency and Amplitude of Spectral Components

• Published in: IEEE transactions on instrumentation and measurement Vol. 60; no. 5; pp. 1579 - 1587
• Main Authors: Ferrero, A, Salicone, S, Toscani, S
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2011; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Algorithms; Computation; Cosine windows; Errors; Exact solutions; Fast Fourier Transform (FFT); Fourier transforms; Frequency domain analysis; frequency-domain interpolation; Interpolation; Sampling; Smoothing methods; Spectra; spectral analysis; Table lookup; Uncertainty
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2010.2090051

The evaluation of the spectral components of a signal by means of discrete Fourier transform or fast Fourier transform algorithms is subject to leakage errors whenever the sampling frequency is not coherent with the signal frequency. Smoothing windows are used to mitigate these errors, and interpolation methods are applied in the frequency domain to reduce them further on. However, if cosine windows are employed, closed-form formulas for the evaluation of harmonic frequencies can be used only with the Rife-Vincent class I windows, while approximated formulas have to be used in other cases. In both cases, a high computation burden is required. This paper proposes a fast interpolation method, independent of the window type and order, based on suitable lookup tables. Experimental results are reported, and the accuracy is discussed, proving that the method provides results as good as those obtained with other methods, without requiring the same high computation burden.