The semester has finally ended, and I didn’t fail any of my classes. I consider that a success! Immediately after finals, I once again picked up “Understanding Digital Signal Processing” by Richard Lyons; I plan on slowly working through all of the chapters in the book. I’ve just finished the discrete Fourier Transform section and learned a lot about leakage, the Nyquist criterion, windowing and a whole bunch of other weird digitization effects....

Following the book “Understanding Digital Signal Processing” by Richard G. Lyons. Discrete Sequences and Systems Definitions and Notation Signal Processing: the science of analyzing time-varying physical processes Analog refers to waveforms that are continuous in time and can take on a continuous range o amplitude values Comes from analog computers, where physical electronic differentiators and integrators were used to model differential equations Discrete: the time variable is quantized This means that the signal at intermediate values is unknown....

Almost done with the semester. Since finals are approaching, here’s a quick update: I’ve kept punting the camera module debugging. I tried ordering another module to see if it was a hardware issue, but it seems to have gotten lost in the mail? With regards to the GameTank verilog port, I’ve started porting over a 6502 CPU core into system verilog. The reasoning behind this is twofold: to get a better understanding of the 6502, and also to add a global enable to the module....

So I got checked out by my doctor, and it seems like the back pain that I experienced was just a very severe muscle spasm. I don’t show any signs of having a herniated disk, and I seems to have maintained full mobility and flexibility in my spine. I can even touch my toes again! Going forward, I’m going to need to be more cautious when doing stand-up, but other than that, I got off easy....

I managed to injure my lower back like an idiot this week. The day immediately after, I had difficulty walking and sitting without grimacing. Considering that I need to sit down for extended periods of time during the day, this was troubling. As a result, I fell down a spiral of Youtube videos and WebMD posts (not the best idea in hindsight…) to try and fix my problem. I managed to find some stretches (things like piriformis muscle stretch, child’s pose etc....

I spent most of January just relaxing. For me, “relaxing” involved writing a chess engine, trudging my way through an online FPGA course, and video games (what a strange definition). The chess engine went pretty well: I managed to get a working prototype in Typescript up and running. It’s butt-ugly and has a terrible UI, but it works. I made a half-hearted attempt to train a neural-net to act as the evaluation function during the tree search, but ran into issues with convergence....

Notes following this MIT course and is based on the xv6 toy operating system. Operating System Interfaces Processes and Memory Forking Exec Operating System Organization Abstracting Physical Resources CPU Modes Processes xv6 startup Security Page Tables Kernel Address space Xv6 Implementation Physical Memory Allocation Xv6 Physical Memory Implementation Process Address Space Sbrk (Xv6) Exec (Xv6) Real World Paging Traps and System Calls RISC-V traps User Space Traps Syscalls Kernel Space Traps Page Fault Exceptions Interrupts ad Device Drivers Console Input Console Output Timer Interrupts Locking Races Spinlocks Using Locks Deadlocks Spinlocks Scheduling Context Switching Scheduler Sleep and Wakeup Semaphores Lost Wake-Up Problem Pipes Process Locks Real World Scheduling File System Buffer Cache Layer Logging Layer Block Allocator Inode Layer Directory Layer Path Layer File Descriptor Layer Operating System Interfaces Operating systems serve a number of purposes Abstracts away lower level hardware, so that programs don’t have to care about what disk you are writing to Allows multiple programs to run “at the same time” Provide well defined interface for programs to interact with each other For the interface, we want a simple interface that is easy to implement, but allows high sophisticated operations to happen UNIX philosophy of composing many simple programs together helps keep this problem trackable Can divide operating system into kernel space and user space kernel space is the program which provides services to other programs....

Linear Regression You have a set of data $(x_{i},y_{i},\sigma_[i])$, where x is the independent variable, y is the dependent variable, and $\sigma$ is the uncertainty in the dependent variable You want to fit a line to the data ($\hat{y} = mx+b$) You also want the uncertainties of the parameters Why would you want to do this? To know the parameters of the model To extrapolate/interpolate values of the dataset that you don’t have How you do this depends on your viewpoint a frequentist approach would try to maximize the likelihood estimate (information theory) Suppose that you have a probability density for the data $y_{i}$ ranging from 1 to N Treat this density as a function of the parameters....

Logistics Thermodynamics 0th Law 1st Law Response Functions 2nd Law Entropy 3rd Law Thermodynamic Potentials Enthalpy Helmhotz Free Energy Gibbs Free Energy Grand Potential Probability Definitions Important Probability Distributions Kinetic Theory of Gases Liouville’s Theorem Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy (BBGKY) Boltzmann Equation H-Theorem Classical Statistical Mechanics Microcanonical Ensemble Two State System Example 0th Law 1st Law 2nd Law Ideal Gas Mixing Entropy The Canonical Ensemble Grand Canonical Ensemble Conserved Ensemble Notes Interacting Particles Cumulant Expansion Mean Field Theory of Condensation Critical Points Quantum Statistical Mechanics Dilute Polyatomic Gases Quantized Vibrational Modes Quantized Rotational Modes Blackbody Radiation Formalism Identical Particles Grand Canonical Formulation Degenerate Fermi Gas $f_{m}^{\eta}(z)$ Denegerate Bose Gas Logistics Book(s) Landau and Lifshitz Kardar Pathria Thermodynamics 0th Law Thermodynamic equilibrium means that each object in thermal contact with each other have the same temperature Ideal gases, as you cool them down, all converge to a single point, which defines absolute zero....

The Basics Hibert Space Review In an infinitely dimensional space, we have some abstract vector $\Psi$. We can choose coordinate axes such that all values can be taken by the position x, so that we can describe $\Psi$ as as set of components $\Psi(x)$ Could have also chosen p instead for our coordinate axes $(v,w) \geq 0$, where (a,b) denotes an inner product This is linear in the right argument, and anti-linear in the first argument (ie....