Signal processing using implicit phase

A frequency-domain technique is presented for measuring the average location of the energy of, a sequence. Several properties of the measure are listed and proved. A simple time-domain approximation to the measure is derived and an upper bound on the error of approximation is found. The effects of noise on the measure are thoroughly analyzed. The measure can be used to find and remove the linear part of a Fourier transform's phase without any arctangent operations. it can be used to locate individual signal components which overlap in time but which are disjoint in frequency. The measure may be used in the estimation of time delays or time constants. The algorithms described in this paper require no inverse DFT's and, therefore, run twice as fast as algorithms which utilize FFT convolution.