C.1. Definition and history p.1-3-- C.2. The discrete fourier transform p.2-7-- C.3. The fast fourier transform p. 3-9-- C.4. Complex FFT on the Motorola DSP family p.4-32-- C.5. Optimizing Performance of the FFT P. 5-12-- C.6. Real -valued input FFT Algorithm p.6-23-- C.7. Two dimensional fourier and cosine transforms p.8-7-- C.8. Competitive analysis of FFT performances p.8-7-- C.9. Conclusion p.9-1--