The book from Alan V. Oppenhein and Ronald W. Schafer - Discrete-Time Signal Processing.

https://www.amazon.com/Discrete-Time-Signal-Processing-3rd-Prentice-Hall/dp/0131988425/ref=sr_1_1?ie=UTF8&qid=1522777158&sr=8-1&keywords=digital+signal+processing+oppenheim

Digital Signal Processing Book by Dimitris G. Manolakis and John G Proakis

The book recommended by @ Avinash Kumar is excellent.

You may want to consider, also:

M. Weeks, Digital Signal Processing Using Matlab and Wavelets, 2nd Ed., Jones & Bartlett Publishers, Boston-Toronoto-London-Singapore, 2011:

https://www.amazon.com/Digital-Signal-Processing-MATLAB-Wavelets/dp/0763784222

This book has lots of good examples.

Since you have training in mathematics, you find what Mathematica provides both helpful and amazing in the range and depth of the topics it covers. In Mathematica 11, for example, enter "signal processing" in the documentation menu bar to get an overview of what is available. See, for example, the LowpassFilter function that Mathematics provides. In addition to LowpassFilter, there are 11 other beautifully documented and illustrated filter funtions.

Another good book to consider is

R. Newbold, Practical Applications in Digital Signal Processing, Prentice-Hall, 2013:

https://www.amazon.com/Practical-Applications-Digital-Signal-Processing/dp/0133038386/ref=sr_1_1?s=books&ie=UTF8&qid=1522774800&sr=1-1&keywords=Practical+Applications++in+Digital+Signal+Processing

This book is good for neural signal processing https://mitpress.mit.edu/books/analyzing-neural-time-series-data

The book from Alan V. Oppenhein and Ronald W. Schafer - Discrete-Time Signal Processing.

https://www.amazon.com/Discrete-Time-Signal-Processing-3rd-Prentice-Hall/dp/0131988425/ref=sr_1_1?ie=UTF8&qid=1522777158&sr=8-1&keywords=digital+signal+processing+oppenheim

Maybe you'd also want to have a look at "Digital Signal Processing. A Practical Guide for Engineers and Scientists", by Steven W. Smith. It has very detailed explanations and programming code examples, and I, personally, found it an "easier" read than the (nevertheless very good, just more... theoretical?) book recommended by Avinash Kumar.

I think one of the best text books to learn digital signal processing is DSP first. I think it suits you very well and i personally used it and found it very help full. Please for more details about the book please follow the link: http://www.chegg.com/homework-help/dsp-first-2nd-edition-solutions-9780136019251

Best wishes

"Introduction to Signal Processing" by Sophocles Orfanidis has a lot of examples along with functions both in Matlab and C.

Try Understanding Digital Signal Processing (3rd Edition):

https://www.amazon.com/Scientist-Engineers-Digital-Signal-Processing/dp/0966017633/ref=pd_lpo_sbs_14_t_0?_encoding=UTF8&psc=1&refRID=S7RCTTEPHE7S0VPE5AG7

I obviously have not read all these books, but the fact that everybody recommends a different one leads me to the conclusion that all of them are probably good and it's just a matter of personal preference. Maybe just try finding reading samples online (the Amazon "look inside" function may be useful), compare the styles and go with your gut feeling. Everybody has a different learning style.

Understanding Digital Signal Processing (3rd Edition) 3rd Edition

by Richard G. Lyons

I would also weigh in with Manolakis and Proakis. Oppenheim and Schafer is also very good; one of the 'old' classics, highly theoretical. One of my all-time favorites with plenty of theory and examples across a broad range of signal types and disciplines is by Ifeachor, E.C. and Jervis, B.W. "Digital Signal Processing - A Practical Approach".

Good Luck.

You can download this great book for free:

The Scientist and Engineer's Guide to Digital Signal Processing

http://www.dspguide.com/pdfbook.htm

It is such a good book I ended up buying it anyway.

For a layman understanding in Digital signal processing by p.ramesh babu...

Digital Signal Processing: Principles, Algorithms & Applications

By:

John G Proakis and Dimitris G. Manolakis.

( PEARSON )

Though a lot of good texts has being recommended by different Researchers but "INTRODUCTION to Signal Processing" BY Sophocles J. Orfanidis of Rutgers University and Digital Signal Processing (Everything you need to know to get started) by Michael Parker of Altera Corporation are good texts for beginners.