This is a demonstration of the power of Stochastistic Gradient Descent for solving difficult non-convex optimization problems. Tensorflow is used for numerical implementation.
This project aims to determine the model parameters (poles and zeros) of AR (auto-regressive) systems in noise and ARMA (auto-regressive moving average) systems. To do so it:
- Determines an approximate frequency domain representation of the signal by BURG method.
- Parameterizes the poles and zeros.
- Build a loss fuction (or objective function) for matching the parameterized frequency domain representation to the original one.
- Because this is a highly non-convex optimization problem with local minima and the loss function is intractable, SGD is used to solve the optimiztion problem.
For more info regarding the math see "Math.pdf"
Demo:
- AR system in noise: https://www.youtube.com/watch?v=HT8WLNDcW-I
- ARMA system: https://www.youtube.com/watch?v=TSW2mzV_9lE
