Detection, estimation, and classification with spectrograms

A locally optimum detector correlates the data spectrogram with a reference spectrogram in order to detect (i) a known signal with unknown delay and Doppler parameters, (ii) a random signal with known covariance function, or (iii) the output of a random, time-varying channel with known scattering function. Spectrogram correlation can also be used for maximum likelihood parameter estimation, e.g., estimation of delay or center frequency of a signal. To estimate an analog input signal from its spectrogram, a modified deconvolution operation can be used together with a predictive noise canceler. If no noise is added to the spectrogram, the mean-square error of this signal estimate is independent of the window function that is used to construct the spectrogram. When estimates of specific signal parameters are obtained directly from the spectrogram, these estimates have mean-square errors that depend upon both signal and window waveforms. Spectrogram correlation can be used for classification as well as for estimation and detection. Parameter estimators and detectors are, in fact, specialized kinds of classifiers.