Detection of signal in noise using optimum wavelet receiver

In the paper, we proposed an optimal receiver based on discrete wavelet transform. To characterize transients in time-varying signal, a more generalized representation which can reflect both the time and the frequency behavior of signals is desirable. Wavelet was used as an orthonormal basis to represent signals in the joint time-frequency domain. We derive a sufficient statistic for the wavelet-based signal detection. An architecture of the optimum wavelet receiver was given. We discussed some issues on the detection of known signals, signals with unknown parameters and parameter estimation. We also evaluated the performance of the optimum wavelet receiver. It shows that the performance of the wavelet receiver is optimum in the sense that a specific criterion is satisfied.