Detection of a sinusoid signal with unknown parameters using wavelets

The problem of detecting a signal confined to a bandwidth with unknown parameters in zero-mean Gaussian noise with unknown variance is considered. For a sinusoid of unknown amplitude, phase and frequency, the problem is converted to canonical from using wavelet Packet and a detector based on invariant tests is proposed. In addition, another view of wavelet Packet, results in a detector for an unknown bandlimited signal. In both methods, the constraints, which observed signal length implies on the filter length and number of stages in filter bank, are obtained analytically. Computer simulations compare performance with the known previous methods.