Topics in Signal Processing

This is a collection of notes describing all the necessary mathematics needed for building numerical optimization based algorithms for signal processing.

The notes are hosted at tisp.indigits.com.

The topics covered include:

• Basic set theory
  • Sets, Relations, Functions
  • Sequences
  • Cartesian product, axiom of choice
• Elementary real analysis
  • Topology of the real line
  • Sequences and series
  • Extended real line
  • Real functions
  • Differentiable functions
  • Inequalities
• Metric spaces
  • Metric topology
  • Sequences
  • Functions and continuity
  • Completeness
  • Compactness
  • Subspaces
  • Real valued functions (closed functions, semicontinuity)
• Linear algebra
  • Vector spaces
  • Linear transformations
  • Inner product spaces
  • Dual spaces
  • Normed linear spaces
  • Euclidean space
  • Sequence spaces
  • Banach spaces
  • Hilbert spaces
  • Affine sets and transformations
• Multivariable calculus
  • Differentiation in n-dim spaces
  • Differentiation in Banach spaces
• Convex analysis and optimization
  • Convex sets and functions
  • Topology of convex sets
  • Separation theorems
  • Continuity of convex functions
  • Subgradients
  • Conjugate functions
  • Smoothness of convex functions
• Convex optimization
  • General concepts of mathematical optimization
  • Convex optimization formulations
  • Projection on convex sets
  • Duality
  • Linear programming
  • Quadratic programming
  • Optimization over differentiable objective functions
• Proximal operators

Building from source

The book has been written using jupyter-book. You can build the book yourself from the source.

Make sure that you have Python 3.8 or later installed.

Clone the repository

git clone https://github.com/shailesh1729/cvx-opt-book.git
cd cvx-opt-book

Install the dependencies

pip install -r requirements.txt

Build the book

jupyter-book build book

Jupyter book will write the book's HTML content to book/_build/html/ directory, so you can open index.html from there to view the local build.

Notes

• Check which version of Sphinx is installed.
• Jupyter-Book 0.13 doesn't seem to work well with Sphinx 5.x.
• It works well with Sphinx 4.5.0.

Publishing on gh-pages

GitHub-Pages is an alternative deployment of the book. The alternative deployment is hosted at indigits.com/tisp.

This section is relevant only for active contributors.

Make sure you have ghp-import installed.

pip install ghp-import

Run the ghp-import command from the root directory as follows:

ghp-import -n -p -f book/_build/html