#aiGenerated --- I have a bunch of notes that I'd like to digitize but that I also have no desire to manually typset into LaTex. Enter AI!! Claude seems to do pretty good job at parsing text from images and typesetting it. I tested it out with some differential equations and some DSP notes. The results: $ \begin{align} \frac{dy}{dt} = -2ty + 4e^{-t^2} \\ P(t) &= 2t \\ \mu(t) &= e^{\int 2t\,dt} = e^{t^2} \\\\ \frac{dy}{dt} + 2ty = 4e^{-t^2} \\[0.5cm] e^{t^2}\frac{dy}{dt} + 2te^{t^2}y &= 4e^{-t^2}e^{t^2} \\[0.5cm] \frac{d}{dt}\left[e^{t^2}y\right] &= 4 \\[0.5cm] \int\frac{d}{dt}e^{t^2}y\,dt &= \int 4\,dt \\[0.5cm] e^{t^2}y &= 4t + C \\[0.5cm] y &= 4te^{-t^2} + Ce^{-t^2} \\[0.5cm] y(t) &= e^{-t^2}(4t + C) \end{align} $ ![[Pasted image 20250305231218.png]] And some [[convolution-notes|DSP Notes]]! I asked that these were formatted into an entire note and I'm *really* happy with the results. I would probably just ask for LaTex for equations and solved problems and a formatted Markdown note for everything else. Make sure you check for errors! --- ## Convolution Theorem: DFT of convolution is product of DFTs $y = h * x \quad \Rightarrow \quad Y[m] = H[m] \cdot X[m]$ ↓ apply inverse DFT to recover time-domain output signal. - can be used for filter analysis to understand how a given impulse response might effect a signal. (h) $H(m)$ is complex number in the frequency domain. $H[m] = Ae^{j\phi} \text{ ("gain")}$ $X[m] = Be^{j\theta} \text{ encodes magnitude and phase of a given sinusoid in the signal}$ $Y[m]$ has magnitude $AB$, phase $\phi+\theta$ $H[m]$ determines how much each sinusoidal component gets scaled by $A$ and delayed by $\phi$ --- All the notes I fed Claude were iPad screenshots. I'll try paper copies and report back since the screenshots were so promising. My next project will be finding a way to automate sending notes to Claude for typesetting and having the results auto-loaded into my Obsidian vault. ![[Pasted image 20250305232131.png|600]] ---