Abstract

An acoustooptic signal processor, using two Bragg cells arranged interferometrically in space-integrating architecture, has been used to implement the multiply-convolve-multiply (M-C-M) version of the chirp transform (CT) algorithms, thereby obtaining the continuous Fourier transform (FT) of simple real signals. The Bragg cells utilize the slow shear mode in TeO₂ and have a center frequency of 150 MHz, a 3-dB bandwidth of 100 MHz, and nominal time–bandwidth of 1000. The cells, when driven with appropriately chosen chirped carriers, act in combination as a bandpass filter propagating only the appropriate conjugate chirps required to effect the CT algorithm. The resulting processor implements the first two operations of M-C-M. The third operation of postmultiplication necessary to obtain the signal transform corresponds to demodulation by a chirped carrier and requires a chirp of dispersion or slope 4× greater than the initial chirp dispersion due to a factor (2 t)² arising from the super-position of counterpropagating conjugate chirps necessary to effect the CT algorithm. The demodulating chirp must be synchronized and gated in time to obtain an undistorted transform. Analysis of the frequency characteristics of the CT processor shows that the signal spectrum can be obtained on a carrier or at base band. Mixing the detector output with the appropriate demodulating signal in one channel and with its quadrature in a parallel channel, followed by low-pass filtering, will generate the base band real I and imaginary Q spectra of the FT in the respective inphase and quadrature channels.

© 1984 Optical Society of America