Multiple Tone Parameter Estimation From Discrete-Time Observations

In a previous paper,1 we reported on the estimation of the parameters of tones from a finite number of noisy, discrete-time observations and described the case of a single complex tone. In this report, we discuss the situation when the signal consists of several, say k, tones, either real or complex. By real signal we mean k s(t) = £ bi cos (ait + di). t=i The corresponding complex signal is of the form s(t) + js(t) = Z b . - e x p t j W + 0,-)], »-i where s(t) is the Hilbert transform of s(t). A computer observes, through the A-D converters, noisy versions of the signal, X(t), and possibly its Hilbert transform That is, samples are taken of X(t) = s(t) + W{t), and Y(t) = m + W(t), (1) (2)