The detection performance of complex cosine CWT and entropy analysis for narrowband signals

The problem of detection of narrowband sinusoidal signals buried in additive noise is addressed. Detection is formulated using continuous wavelet transform (CWT) with the custom designed complex cosine wavelet and estimating the presence and frequency of useful signals in the wavelet domain. An adaptive entropy based threshold detector is proposed to detect presence and time localization of useful signal in the transform domain. A simple and pragmatic method of threshold setting as the average of minimum and maximum entropy is proposed. Application example is focused on detection of useful signal in the harmonic radar system. Simulation results show that the proposed method also allows detection of signals with negative signal-to-noise ratio (SNR). Time-frequency characteristic of the CWT is compared with the short-time Fourier transform (STFT) for the specific mother wavelet.