1. The Dirac delta function and Heaviside step function 2. Fourier series, Parseval's theorem, FFT and Cooley-Tukey algorithm 3. Fourier integrals and Fourier series 4. Properties of the Fourier transform and Heaviside's step function 5. Complex signal, complex envelope and Hilbert transform 6. Correlation functions, spectral density, Wiener-Khinchine theorem 7. Linear, time-invariant systems 8. Transfer matrices and frequency filters 9. Laplace transforms, transfer functions, Nyquist criterion 10. Maxwell's equations, optical waveguides and Poynting's vector 11. Pulse propagation in optical fibers 12. Split step Fourier method and nonlinear Schrodinger equation 13. Introduction to modulation formats 14. Required bandwidth for heterodyne and homodyne detection 15. Bandpass noise 16. Bit error rate 17. Pulse shaping using optical Fourier transform 18. Spectrum magnification 19. Optical Fourier transformation, dispersion compensation, jitter suppression 20. Regeneration of WDM phase-modulated signals 21. Time-space duality, dispersion and diffraction, time lens 22. Couplers and their use for optical DFT 23. Multicarrier modulation, OFDM, DFT, Nyquist modulation 24. Optical orthogonal frequency division modulation