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-A Not-Too-Short, Not-Quite-Long Summary of Signal Processing#
-Author: Igor L.R. Azevedo - The University of Tokyo & University of Brasilia
-Email: igorlima1740@gmail.com
-GitHub: igor17400/dsp-174
-WHAT TO EXPECT:#
-This work aims to provide a summary of signal processing that achieves a balance, as indicated by the title—not overly concise yet not as exhaustive as a comprehensive textbook. My intention was to explore essential content with more depth than a typical summary offers, yet not as extensively as a canonical textbook. At the same time, the idea is to combine several high-quality tutorials available online, which might be helpful in understanding and gaining a clear vision of signal processing. While this isn’t just a collection of equations, it also isn’t a book or paper that aims to make a significant contribution. Ultimately, my goal is to present a practical approach to signal processing that may be useful for those trying to better understand this subject. In any case, I hope this proves helpful to someone beyond myself. If you’ve read this far, thank you, and stay safe!
-Getting Started#
-To use this summary just access the following link: igor17400/dsp-174.git
-Topics Covered#
-This summary includes, but is not limited to, the following signal processing topics:
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Fourier Transform and its applications
-Digital filters (FIR and IIR)
-Sampling and quantization
-Discrete-time signals and systems
-Frequency analysis
-Signal modulation techniques
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Contributing#
-Contributions to improve this summary are welcome! If you’d like to contribute:
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Fork the repository
-Create a new branch (
git checkout -b feature/your-feature-name)
-Make your changes
-Commit your changes (
git commit -am 'Add some feature')
-Push to the branch (
git push origin feature/your-feature-name)
-Create a new Pull Request
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License#
-This project is licensed under the MIT License - see the LICENSE file for details.
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I hope this proves to be helpful to someone other than just me!
-✧⁺⸜(^-^)⸝⁺✧
![\"rl_circuit\"](\"./figures/rl_circuit.png\")
\n",
- "\n",
- "RL circuit schematic\n",
- ":::\n",
- "\n",
- "That is,\n",
- "\n",
- "$$L\\frac{di(t)}{dt} + Ri(t) = 0 \\implies \\frac{di(t)}{dt} = -\\frac{R}{L} i(t) = a i(t), \\text{ where } a = -\\frac{R}{L}$$\n",
- "\n",
- "The current is then:\n",
- "\n",
- "$$i(t) = i(0) e^{-\\frac{Rt}{L}}$$\n",
- "\n",
- "With that in mind, since such signals are common in engineering, let's proceed with a more general form of such a signal.\n",
- "\n",
- "$$ x(t) = Ce^{at} $$\n",
- "\n",
- "where $ C $ and $ a $ can be