Comparison of the short-time Fourier transform and wavelet transform for analysis of transient signal events

Abstract

The performance characteristics of the wavelet transform and the short-time Fourier transform (STFT) for transient detection are examined by means of computer simulation. The STFT uses a power-of-two decimation-in-time FFT with various frame sizes, orders, and frame overlaps. The wavelet transform uses the Daubechies orthonormal wavelet filters. Several types of data are analyzed using both transforms, including: test files with transients embedded in noise and in a masking sinusoidal signal, speech data, and DC arcing data. Comparisons are made using spectrograms/scalograms, signal-to-noise ratio (SNR), transient-to-signal ratio (TSR), and execution speed. Simulations for the STFT show that significant gains can be made by overlapping input frames, at a significant computational penalty. Also, short frame lengths for the STFT lead to better transient detection ability. The wavelet transform is shown to detect transients better using the longer wavelet filters in most cases, at a less substantial computational penalty. Performance of the wavelet transform and the STFT for transient detection are shown to be similar in comparisons of spectrograms/scalograms and SNR, while the wavelet transform displays a substantial advantage in terms of TSR and, most importantly, computational requirements.