Re: How to learn DSP
If you're are not a senior undergrad student or an engineer or a computer science graduate......i would recommend "SIGNALS & SYSTEMS MADE RIDICULOUSLY SIMPLE".. this is a wonderful book of less than 150 pages...and covers all the basic concepts with a minimum amount of maths. Otherwise with PROAKIS, or OPPENHEIM or SANJEET K. MITRA, you will need a whole LOT of mathematical techniques before you get to the real thing (around 2-3 months)...Still, if you do have a lot of time to give to DSP, I would recommend SANJEET K. MITRA alongwith its lab manual (that uses MATLAB).
MATLAB is a programming environment, specially suited for all sorts of engineering and maths intensive jobs. It provides you all lot of functionality with a very few lines of code (integration, plotting, etc....) In DSP, we usually use it to simulate our algorithms before we implement them on some hardware platform such as Digital Signal Processors or FPGAs. You can compute FFTs and find CONVOLUTIONs etc with single line of code. Thus, you can focus on your particular algorithm rather than having to write huge code for these basic mathematical operations (FFT, convolution, correlation etc) on your signals.
One wonderful book for MATLAB's latest version is by William J. Palm.