In this work we implemented a hybrid joint Fourier transform correlator (JTC optical/electronic) helpful in the pattern recognition when the scene is in movement. We have been use the standard architecture JTC, but in our case, the first step of the correlation process is carried out optically, using coherent illumination to obtain the joint power spectrum (JPS) of each frame display on a spatial light modulator, we used a liquid crystal display CRL XGA4 with 1024 x 768 pixels of resolution in gray scale. It display a video sequence where is include a mobile scene and the reference, then, the JPS of each frame will be obtain in real time with the quadratic sensor (camera CCD) that is located in the back focal plane of the lens. For the second step was use the tools of the Imaging Developer Kit TMS3206711 DSP (IDK) of Texas Instruments, in order to take advantage of the high speed arithmetic offers by the Digital Signal Proccessor (DSP) and the electronics versatility offers to take decisions. The IDK is a tool of hardware and software that allows capture, process and display images in real time. The DSP microprocessor makes a Fourier transform of the image captured by the CCD, in this way, we obtain the correlation of the scene in movement in quasi real time. Using an efficient computation of the digital Fourier transform of a 2N-point real sequence, the hybrid correlator achieve 15 correlations per second, if the final result is display on the monitor the rate fall to 13 frames per second, the correlation peak was use to determine in real time the target position in the mobile scene.
Taking advantage of the high speed arithmetic offers by the parallelism of the digital signal processor DSP TMS320C6711 of TI, we implemented two algorithms to find the Fourier transform of fractional order of two dimensional signals ("The discrete fractional Fourier transform" and "Fractional Fourier Transform calculation through the fast-Fourier-transform algorithm"). As a result, we have two algorithms for calculate the fractional Fourier transform of images using a DSP, the images are captured using a camera CCD and the fractional Fourier transform is display in a monitor, both are connected to the DSP device directly. Finally, the work focuses in the evaluation of this algorithms, in order to find which is best performance related to four criteria determined from the properties of the Fourier transform of fractional order: The inverse transform, fractional Fourier transform of order one or standard Fourier transform, fractional Fourier transform of order zero or operator identity and order additivity.