Does differential and partial differential equations subject has applications in Signal Processing? I have basic DSP background and know Matrix algebra and Fourier transforms very well, but I am not sure how differential equations would fit in.
I am asking this because I have the option of taking 2 graduate level diff. equations courses(linear, non-linear and dynamical systems) and am wondering if it would be insightful or practical.
I don’t think it will hurt or will be a waste of time.
You can think of SP in a number of ways and those ways overlap. It’s a technolgy, a science,a branch of mathematics, an engineering discipline, and your view is largely tied to your self image.
A lot of SP is based on physical models. A lot is based on hueristics.
SP overlaps. You might benefit from taking music or statistics. A lot of people take the longer path.
Differential equations are a way to describe a lot of phenomena that SP is used to sense and often control.
You should consider what motivates you.
To be honest a lot of what I took had to do with what was offered that semester. Getting that piece of paper on time was a huge practical consideration.
No. The core theory of signal processing does not benefit much from differential equations as much as it does from linear system theory. It's the applications of DSP that make use of them.
As you may anticipate, isolated bunch of DSP algorithms rarely make sense; they must be used within physical applications. And the mathematical nature of the physical laws is the differential equations. Acoustics, Optics, Electromagnetics, Thermodynamics, Mechanics, etc.. all physical phenomena are described by them.
Note that modern engineering techniques favor transform domain based methods (Laplace, Fourier, Z-) over the classical-time domain approach for their solutions, which is probably more emphasised in a pure mathematical treatment of them, yet one still obtains irreplaceable insight from the time domain handling of differential equations too.
