# Introduction to Statistical Signal Processing

There is a postdoc in my lab whose specialty is "statistical signal processing". He has a PhD in Electrical Engineering and he analyzes the neural data collected.

I am wondering what courses/topics I should start studying to follow in his footsteps. I'm not exactly looking for things like statistics and signal processing, I've had basic classes in both but still find it hard to understand his work.

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Sometimes there are courses entitled 'statistical signal processing', that's a good place to start :-) If your university doesn't have this, try looking for 'detection and estimation', or 'advanced signal processing'. If you don't have a university handy, you could try http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-432-stochastic-processes-detection-and-estimation-spring-2004/

Much statistical signal processing is linear, so you should learn as much linear algebra as you can. Stocastic processes is a foundational course. Control theory shares much with SSP, and would be very useful.

This should be enough for a start :-)

These classical references are a good start:

1. B. Porat, Digital Processing of Random Signals, Prentice-Hall, 1994. Library serial number 2144342.

2. A. Papoulis, Probability, Random Variables and Stochastic Processes, 3rd Ed. , McGraw-Hill, 1991. Library serial number 21111643.

3. S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, Prentice-Hall, 1993. Library serial number 2157997.

You could also try KT Wong's (University of Waterloo) lecture notes

You might also find some of this lecture series on Adaptive Signal Processing by Prof. M.Chakraborty on YouTube of use

Hi,

Assuming you are interested in doing research in the field, I will advice following a path built on a strong foundations in mathematics.

I know this, beacuse I just have finished teaching a course in Estimation & Detection and I can assure you that there is a strong correlation between the quality and novelty of the work and your knowledge of math.

What kind of math?

1. Linear Algebra:

You need to know about vector spaces and matrix algebra because; as someone else posted before, there is a lot of theory and algorithms that delve with this type of models. Some results that are often used are the Inverse Matrix Lemma, all that have to do with matrix decompositions.

2. Probability Theory and Stochastic Processes

This is also key. Statistical signal processing is about methods for detecting and estimating information (inference) using faulty observations (noisy) of phenomena that could also be random.

So you need to know how to handle this kind of object. A basic course in probability can give you a good starting point (one that covers random variables and random vectors, and hopefully talks a little bit about random sequences and processes), but it is desirable to take a second course, focused on random processes. You need to have some confidence with these ideas since it will allow you to understand many applications and practical implementations used in research and technology.

On a second tier I will also consider taking a course in Optimization, since the computation of estimators is mostly based in solving problems of maximization and minimization (maximum likelihood estimators, minimum mean square error estimator, etc.)

Of course, there is also the "algorithmic" point of view, where you concentrate more on statistical signal processing procedures for fast computation, convergence, low complexity, etc., but in the end the development os new ideas requires a good foundation in mathematics.

Note that your knowledge of the inner workings of a given phenomena is also key for producing the models you plan to use in a given setup. In that sense, the practical experience that you can obtain from a course in digital communications, digital signal processing, and even electronic circuits can be invaluable to give you an edge as a researcher.

If you have more questions, do not hesitate to contact me.

Cheers, Patricio

As tdc has cited, Papoulis (RIP to one of the leaders of this field) is one of the best books, but you may need to step into it first via something like http://www.amazon.com/Discrete-Time-Signal-Processing-2nd-Prentice-Hall/dp/0137549202 if you haven't had a good undergraduate/early graduate course in signal processing (I didn't, and it hurt a bit).

From a more statistical perspective (but still very valid for engineers) is http://www.amazon.com/Random-Data-Measurement-Procedures-Probability/dp/0470248777/ref=sr_1_1?s=books&ie=UTF8&qid=1323737134&sr=1-1. This is packed to the gills with info, so it's very slow reading.

Van Den Bos, Adriaan: "Parameter Estimation for Scientists and Engineers"