I'm studying CE and math. My computer engineering course is basically electronic/electrical engineering with extra software. I have a choice between the two subject combinations below. Additionally, 1. I'm studying two mechatronic control theory subject, and a mathematical control theory subject

^{1}, 2. I have the option to study a PDE subject , a non-linear dynamics (chaos) subject, or a image processing/computer vision subject 3. I'm studying algorithms and data structures, and have the option to study maching learning or high performance computing. Any advice is appreciated.**Subject combination 1***Digital signal processing*Advanced digital filtering: polyphase, multirate, all-pass, lattice & IIR filters. Signal conditioning, analog filter types, sigma delta converters. Fast algorithms; Cooley-Tukey FFT, mixed radix formulations, Good-Thomas algorithm. Autoregressive, moving average signals. DSP applications and programming.

*Applied math*Elements of vector analysis. Sturm-Liouville theory. Fourier transform & Green's functions. Generalised functions. Modelling with scalar & vector fields: perfect fluid flow & potential theory; convection-diffusion equations & spread of pollutants; elastic continua and vibrations.

**Subject combination 2***Operating systems architecture*Implementation and design techniques for operating systems. Core material includes advanced kernel-level and device driver programming techniques, how operating systems principles are realised in practice, principles and practice of operating system support for distributed and real-time computing, case studies and different approaches to operating system design and implementation, including different models of software ownership.

*Advanced mathematical control theory*edit: I just realized I could take applied math, DSP, and image processing/computer vision and advanced control theory if I give up operating systems architecture. Is this a good idea? Do the subjects complement each other?Topics from: state space control; linear systems; calculus of variations & Pontryagin principle; optimal control, quadratic optimisation, Riccati equations; stability; LQG, Kalman filtering; frequency domain theory; Matrix transfer functions, realisations; coprime factorisation; robust control.

**-----------***1*.Calculus of variations: critical points; Euler equations; transversality; corner conditions; Hamilton equations; Jacobi equations; Legendre sufficient condition; Weierstrass E-function. Control theory: Lagrange, Mayer & Bolza problems; Pontryagin maximal principle, legendre transformations, augmented Hamiltonians, transversality, bang-bang control, linear systems.

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