Appendices

Some signal processing and statistical appendices

Sometimes, just to understand something, I write an appendix…

• A derivation of Fourier transforms
• Two derivations of Laplace transforms and z-transforms
• A note on the real and complex cepstrum
• A derivation of the EM algorithm
• A derivation of the Kalman filter and Kalman smoother
• The origin of the multivariate normal distribution
• The Complex Gaussian distribution
• Convolution of two complex Gaussians
• Maximum likelihood and MAP derivations of linear prediction
• A derivation of a second order damped system
• How to derive a Student-t from a Gaussian
• A note on sparse conditional probability