# A good textbook for designing signal filters

Since a couple of months ago I started being actively involved in the area of control of dynamical systems.

In most cases, designing a controller for a given dynamic system will require the employment of digital signal processing techniques, especially in the area of signal filters.

Since I do not have a background in control engineering, I wonder if any of you may provide me with suggestions of sound textbooks dealing with signal filters into some detail.

The textbooks should ideally encompass:

• Introduction to the most common filters in the area of DSP;
• Explanation of their main characteristics in both frequency and time domain;
• In which scenarios are they generally used (role or function of the filter).

Although being a naive question, I hope you may advise a couple of textbooks.

There are a lot of books out there, but if you are interested in Control and Signal Processing, I strongly suggest you take a look a Stephen Boyd Lectures from standford:

There's the first one, the entire course is really valuable and he is a great Teacher.

Appart from That here's a good list of my preferred books on Signal Processing, some are more introductory, and some are more advanced:

Basics:

• Signals And Systems - Oppenheim & Willsky

• Digital Signal Processing - Proakis & Manolakis

• Discrete Time Signal Processing - Oppenheim & Schafer

A bit more Advanced and Related to Control:

• Optimum Signal Processing - Sophocles J. Orfanidis

• Optimal Filtering - Brian D. O. Anderson & John B. Moore

• Optimal Control: Linear Quadratic Methods - Brian D. O. Anderson & John B. Moore

• Statistical Signal Procfessing - Louis L. Scharf

• Linear Estimation - Thomas Kailath, Ali H. Sayed & Babak Hassibi (Watch out this one is really tough)

• Spectral Analysis of Signals - Petre Stoica & Randolph Moses

And some about Adaptive processing (Useful in every area of signal processing and control):

• Adaptive Filter Theory - Simon Haykin

• Adaptive Filters - Ali H. Sayed

• Satistical And adaptive Signal Processing - Manolakis, Ingle & Kogon

And of course, the father of all Control Engineering Textbooks:

• Linear Systems - Thomas Kailath

From your question i cannot really guess your background, but if you have never studied any topic like LTI systems, Digital Systems or Control, i would say you have a couple of years ahead of you to really learn and dominate the topic. The books i listed are the most referenced books in university courses, and in general the ones that everyone studies. They are for the most part, very theoretical, a lot of math and stuff like that. But it's a must have for reference. If you are looking for more instant satisfaction i would say try to google some cookbooks about digital filters or control, with the basics of PID controllers, linear regulators, etc.

Hope it helps

• thanks for the prompt and precise response: well, I studied Mech.Eng. and only had an undergraduate class on LTI control for mechanical dynamic systems; therefore, I do have a clue about PID regulators, stability, design in frequency domain and time domain. All the rest, I'll to study throughout my doctoral studies. – fpe Jan 26 '14 at 0:17
• Ahh i See, well in that case, i would say that the "Kalman Filter" and its many variations is the central filter in DSP applied to Control. So any book that has that topic in depth would surely be of use to you. Linear Estimation from Kailath has a chapter on it, and any good book on Optimal or Robust control should mention it. – bone Jan 26 '14 at 2:42
• it was helpful for me – dato datuashvili Jan 26 '14 at 8:01

A great book to learn about digital signal processing in general ist "Understanding digital signal processing" from "Richard Lyons". Amazon-Link. It's easy to read and requiers no previous knowledge. You'll get comfortable with discrete signals, FFT, filters and so on very fast. All the mathematics that you need is described inside this book (you'll need no other references for mathematics). You may find a cheaper version of this book on eurobuch - good luck! Maybe, for designing the perfect filter you will need another book afterwards, but I think it's the rigth one to start with.

• You know, i've been recommended that book as well and i took a look at it and thought it lacked some depth on some topics. But seems Lyons is a very established and respected author. – bone Jan 31 '14 at 14:05
• The book may lack some depth, but it definitively doesn't lack comprehensibility. I think this matters for a beginner. If you got the main ideas in digital signal processing you can and should go on to s.th. more advanced. I think the chapters on the DFT/FFt and on complex signals really descriptive. The chapters on filters may be more detailed. – Semjon Mössinger Feb 2 '14 at 20:12

While all the books listed in other answers are recommended books, neverthless they are not specific for filters and skip basics. The main issue when learning digital filters is that most learners are uncomfortable moving from time domain to frequency domain. Then there is math one needs to deal with. Add to this lot of jargon specific to filters, this makes learning filters a very non-intuitive and hard exercise.

Before starting to learn digital filters, I think one needs to be at least comfortable with basic concepts and jargon of Analog Passive(RLC) Filters such as Impedance, Phasors, RMS, Frequency sweep, dB scale(octave/decade), Transfer function, filter order, Gain, Attenuation, Magnitude & Phase Frequency response(Bode Plots), -3dB(cut-off) frequency, roll-off, Passband/stopband, ripple, Bandwidth, resonance frequency, Quality Q factor(sharpness), tuning, s-domain(=jw), domain transformations(time-domain to s-domain to z-domain), Laplace transform, z-transform, Types of filters (Low pass, High pass, Bandpass, Bandstop, All pass), Basic 1st order/2nd order filters, applications of basic filters(audio, radio, anti-aliasing, etc.), designing filters for given specifications, filter stability analysis(pole-zero plot) etc.

In order understand some of the above concepts and jargon, the book I will suggest to read (in order are as follows:

1. The Art of Electronics by Paul Horowitz and Winfield Hill: sections 1.3-1-5.1, 1.7, 6.1-6.2 (50 pages) and Learning the Art of Electronics by Thomas Hayes and Paul Horowitz: sections 2N, 2L(lab), 2S, 2W, 3N.1-3N.4 (70 pages)
2. A Basic Introduction to Filters — Active, Passive, and Switched-Capacitor by Kerry Lacanette (24 Pages)
3. (Optional) Design and Analysis of Analog Filters: A Signal Processing Perspective - Chapters 1 and 2 (100 pages)

Once the above concepts are clear, you will gain an intuitive understanding of filter design. There after you can pick any of the recommended digital filter design books and I assure you that most of it will be a cakewalk. In any case, here is a book I recommend for making transition from passive analog to digital filters:

• Digital Filters for Everyone by Rusty Allred