What maths does Digital-Signal Processing use? Does it apply to other areas?

[Tosh5457]

Hi, what mathematics does DSP use? And is it easy to use this knowledge to apply to other areas of study, where it's needed to study signals?

[rbj]

Algebra
Trigonometry
Calculus (incl. multivariable)
Differential equations (including Laplace transform and partial diff eq.)
Complex variables
Probability, random variables, and random processes
Applied matrix theory
Approximation theory (Newton's method, least squares, Remez, etc.)
Functional analysis (metric spaces, normed spaces, Hilbert spaces)

not saying you need all of these disciplines, but i have seen issues in DSP make reference to any of these mathematical fields.

within the EE discipline, you'll need:
Signals and systems (a.k.a. Linear system theory)
which has more about transforms.

DSP has application in:

Communications theory
Statistical communications
Control systems theory
maybe even analog electronics

so knowing something in those areas might be useful.

[Tosh5457]

Algebra
Trigonometry
Calculus (incl. multivariable)
Differential equations (including Laplace transform and partial diff eq.)
Complex variables
Probability, random variables, and random processes
Applied matrix theory
Approximation theory (Newton's method, least squares, Remez, etc.)
Functional analysis (metric spaces, normed spaces, Hilbert spaces)

not saying you need all of these disciplines, but i have seen issues in DSP make reference to any of these mathematical fields.

within the EE discipline, you'll need:
Signals and systems (a.k.a. Linear system theory)
which has more about transforms.

DSP has application in:

Communications theory
Statistical communications
Control systems theory
maybe even analog electronics

so knowing something in those areas might be useful.

I don't know the 2 I put in bold, would I have problems studying DSP? And what do you mean by applied matrix theory? I know linear algebra, is that enough?

And I want to apply it to financial markets, would it be easy to apply the knowledge from DSP to study financial markets? I've seen a guy doing it with success, but unfortunately he stopped going to the forums he was in, so I can't ask him. But I'm pretty sure he only used the price to generate signals and etc...

And sorry to bother you with this, but in a post he says he has to deal with multiplicative noise, which uses mathematics underlying non-stationary and non-gaussian filtering. He says his trading system is based on this. Do standard DSP books talk about multiplicative noise?