A Simple Wavelet Transform with Fine Time and Frequency Sampling

Wavelet transform performs frequency transform with different time window widths to enable accurate time-frequency analysis for sensing. Time and frequency sampling of scalogram are not uniform to eliminate redundancy. One method achieves fine time sampling with fewer operations, but the frequency direction sampling is not uniform or fine, and sidelobes are high. To address these problems, this study proposes a simple wavelet transform with fine time and frequency sampling. The proposed method consists of phase multiplication and signal addition. Frequency transform of any time window width is possible by changing the additive width of the signal. Furthermore, by adding the results, wavelet transform using a triangular window that lowers sidelobes is realized using a small number of complex multiplication operations. When the proposed method is applied to a chirp waveform, the frequency transition of the signal could be finely confirmed.