Instantaneous frequency estimation by interpolating continuous wavelet transform coefficients

Abstract

Interpolated discrete Fourier transform (IpDFT) algorithms have been improved for a long time to compensate for frequency estimation bias due to quantization errors in digital signal processing. In this paper, a new interpolation algorithm, named synchro interpolation transform (SIT), is developed based on Morlet continuous wavelet transform (CWT). In Morlet CWT, approximately integer periods of sinusoid are contained within the wavelet. Therefore, the spectral leakage is much smaller than that of the DFT, so a simple interpolation algorithm using only two CWT coefficients can estimate the frequency very accurately. In addition, DFT is only suitable for the frequency analysis of stationary signals. When the frequency varies in time, time-frequency representations (TFRs) such as short time Fourier transform or CWT should be used to estimate instantaneous frequency (IF) of non-stationary signals. The accuracy of the IF measurement of a nonlinear chirp signal depends on the width of the window function used in the TFR. Instead of trying to optimize the window width to get more accurate frequencies, SIT calculates multiple spectrograms as varying the window width, and then interpolates those multiple frequencies estimated from each spectrogram to get the correct IF of the nonlinear chirp signal. In principle, SIT can measure the exact IF for any order nonlinear frequency chirp signals. The performance of SIT is investigated by analyzing simulated signals and bat sounds. A new algorithm, named iterative TFR, is developed to remove interference of multicomponent signals. Multicomponent signals are successfully analyzed by combining iterative TFR and SIT.