I'd Like to ask two questions :
What is the difference between studying Signal processing (both Deterministic and statistical) in Department of Electrical Engineering versus Department of Mathematics and statistics
What's All the mathematical topics (both time/n-domain and f/S f/Z domain ) which is a prerequisites of studying Signal Processing (Both continuous and discrete) or reading a book like "signals and systems" by "Alan Oppenheim" ??
Thanks All
i remember this question being asked on USENET at comp.dsp, but i don't remember all of my answer.
there are several mathematic disciplines that inform signal processing and formalize some of the concepts.
let's assume you have calculus of one and many variables and differential equations (any scientist or engineer should have those).
well, Complex Variables and Analysis of Complex functions to start with.
Linear Algebra: Matrices and Determinants
Fourier Series and Transforms
Probability, Random Variables, and Random Processes
Numerical Techniques
Metric Spaces and Functional Analysis
all those are useful math topics, sufficiently useful that i would recommend taking math classes in these if you end up in grad school in EE. there are many signal processing topics that make reference to one or more of the above math topics.
Well the main difference would be that studying engineering signal processing would be like studying applied signals, while going in the math direction would be studying just in the theory domain. Engineers don't always use "correct" math, but they use the math needed to get the job done. If you're interested in using the theory to build systems, go engineering, if you are more interested in learning the ins and outs of the theory, go math.
Engineering is applied science. But to apply any science, u have to develop a concept behind it, a theory. And mathematics is a tool to prove your theoretical assumption. Bcoz if u prove anything in mathematics, it can be implemented in real life. The signal processing is nothing but mathematical operation on real world signals and the amount of math in this subject is very heavy. So, in math department u get in very depth of what it is, how u show that in graphical data, how u prove it etc. An engineer then uses this proofs to apply in real life with few changes. A signal have few basic parameters like frequency/wavelength, amplitude/intensity etc. These parameters u show/model in mathematics using complex numbers and vectors which can be mathematically processed i.e. added, subtracted etc. to produced desired output. U need to learn basic differentiation, integration, summation then using that fouriour, z & s-domain (complex) analysis, wavelet, and time domain analysis like convolution etc. need to be learned.
Then it also depend on application or type of data like image processing, digital communication, etc. So, if u wish to learn specific application, start from basic for that application. Once u learn one application, learning another will be pretty easy.
Hope that helps.
