EXTRACTING MULTIPLE FREQUENCIES FROM PHASE-ONLY DATA

The problem of extracting multiple frequencies from phase-only data is addressed. Multiple frequency estimation is accomplished by reconstru cting the Fourier transform of the complex-valued time signal and then finding peaks in the frequency domain. We present a set of conditions under which a discrete-time complex sequence can be completely specif ied by its phase-only information. Two candidate multiple frequency es timation schemes are introduced, one based on a closed-form least-squa res inverse, the other an iterative reconstruction algorithm. The uniq ueness of the closed-form solution and the convergence of the iterativ e scheme have been proven under certain conditions. Several examples a re given, including the case where the phase is quantized as would hap pen in an analog-to-digital (A/D) converter Extensions to the multidim ensional case, and to the case of real-part only reconstruction are st raightforward.