An analysis of the spectrum of optical pulses by dispersion-time spectrum analyzer and a diffraction grating spectral device is considered. A theory of the dispersion-time spectrum analyzer of single optical pulses is proposed, which is an optical analog of the dispersion-time method for measuring spectra of radio signals, and the optical fiber is used as the dispersive medium. A computer simulation of the evolution of a monochromatic pulse propagating in a dispersive system in optical fiber is performed, which makes it possible to determine its minimum length and the dynamics of analysis of the instantaneous spectrum of a single optical pulse when the spectrum is measured by a diffraction optical spectral device.
The outstanding role of the optical coherent Fourier processor and the instantaneous spectrum computed with is considered when performing spectral-correlation processing of the signals of the radio and optical bands. Within the framework of the performed studies, the spread functions for "real spectral devices in an ideal implementation" are established. The sampling theorem for the instantaneous spectrum is proved. These general theoretical studies are used to develop the theory of a diffraction grating spectral device of the optical range, as well as an acoustooptic (AO) radio signal analyzer, and the coordinated filter and a correlator of radio signals created on its basis.