This paper describes the temporal response of an acoustooptic spectrum analyzer to pulse-modulated cw signals. The detected waveforms from a real-time photodetector array are analyzed as a function of pulse width, weighting function parameters, and relative photodetector to spectral centroid location. The input pulse envelope is modified in the forms of signal duration stretching, the appearance of a flattop, multiple humps, and longer rise and fall times. Various schemes are discussed on the determination of the pulse width from the detected waveform.