Some well-written and self-contained introductory books for applied algorithms and DSP!

### ** Probability and Statistics**

by by Dimitri P. Bertsekas and John N. Tsitsiklis [Amazon] [DirectTextbook] – A clear and concise introduction to the elements of probability.**Introduction to Probability**– by David MacKay. [PDF] – Fun exploration of a slew of applied techniques in probability. Strong Bayesian focus.*Information Theory, Inference, and Learning Algorithms*

### **Signal Processing**

by Richard Lyons [Amazon] [DirectTextbook] [PDF] – Intuitive & visual introduction to digital signal processing by an experienced DSP consultant. Author of Signal Processing Magazine‘s Tips & Tricks column.*Understanding Digital Signal Processing*by Alan V. Oppenheim [Amazon] [DirectTextbook] [PDF] – Classic textbook written by my Ph.D. advisor. Solid mathematical foundation if combined with supplements below.*Discrete-Time Signal Processing*by Lloyd n. Trefethen and David Bau [PDF] – Introduction to the most useful matrix methods including least-squares, norms, SVD, QR decomposition. Good foundation for vector space signal processing, wavelets, etc…*Numerical Linear Algebra*by Martin Vetterli, Jelena Kovacevic & Vivek K Goyal [PDF] – Introduction to vector-space / linear algebra interpretation of DSP. (I also recommend Yoram Bresler’s ECE 513 notes).*Foundations of Signal Processing*by Martin Vetterli, Jelena Kovacevic & Vivek K Goyal [PDF] –**Fourier and Wavelet Signal Processing***The*textbook on wavelets. Good for multimedia, compression applications.**Fundamentals of Adaptive Filtering**

**Brief overview of many DSP topics:** http://ccrma.stanford.edu/~jos/sasp/

**Useful software tools: ** http://dsp.rice.edu/software

**Tips and tricks for efficient implementation:** http://www.dspguru.com/dsp/tricks

### Useful Papers on Special Topics

Introduction to Factor Graphs – Powerful graphical modeling tool unifying algorithms for HMMs, Vitterbi, Kalman Filters, Gaussian Belief Propogation, LDPC, and more.

On Graphical Models for Communications and Machine Learning: Algorithms, Bounds, and Analog Implementation by Justin Dauwels. Covers many topics in graphical models, multivariate-Gaussian belief propagation.

Unscented Kalman Filter – Discussion of Sigma Points — or approximating Gaussian moments through non-linear functions by passing points through the function at a few standard deviations.

**Filter Banks**

Multirate Digital Filters, Filter Banks, Polyphase Networks, and Applications: A Tutorial by P. P. Vaidyanathan – One of the first–but still a relevant–introduction to filter bank ideas. (Also see Vetterli’s book above)

**Adaptive Filters**

Frequency-Domain and Multirate Adaptive Filtering – Classic introduction to performing adaptive filtering in the frequency domain (FDAF). This can greatly improve convergence and reduce the computation (with FFT) of adaptive filtering on channels with long impulse responses.

Lower-Latency Frequency Domain Adaptive Filtering – Adaptation in frequency domain but actual filtering in time-domain to eliminate the latency penalty of a normal FDAF.

Soft-partitioned Frequency-Domain Adaptive Filtering – To eliminate gradient constraint step to further reduce computation of FDAF.

###### Dynamic Programming

Seam Carving for Content-Aware Image Resizing (Shai Avidan and Ariel Shamir, MERL) – Cool use of DP for content-aware image resizing and object removal.

** Philosophy **

* The Structure of Scientific Revolutions *by Thomas Khun

* Philosophical Investigations* by Ludwig Wittgenstein.