https://github.com/zazi2002/signals-and-systems-simulations
Signals & Systems course simulations exploring different aspects of signal processing, system behavior, and sampling theory, using both theoretical and practical approaches.
https://github.com/zazi2002/signals-and-systems-simulations
audio-processing fourier-analysis image-processing laplace-transform matlab sampling
Last synced: 3 days ago
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Signals & Systems course simulations exploring different aspects of signal processing, system behavior, and sampling theory, using both theoretical and practical approaches.
- Host: GitHub
- URL: https://github.com/zazi2002/signals-and-systems-simulations
- Owner: ZaZi2002
- Created: 2024-09-06T17:33:40.000Z (6 months ago)
- Default Branch: main
- Last Pushed: 2024-09-06T20:50:55.000Z (6 months ago)
- Last Synced: 2024-12-28T10:44:37.135Z (about 2 months ago)
- Topics: audio-processing, fourier-analysis, image-processing, laplace-transform, matlab, sampling
- Language: MATLAB
- Homepage:
- Size: 39.1 MB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Signals & Systems Simulations
This repository contains MATLAB-based simulations and analyses for three key homework assignments in signals & systems. Each homework explores different aspects of signal processing, system behavior, and sampling theory, using both theoretical and practical approaches.
## Homework 1: Fourier Series Analysis and Music Note Generation
This homework focuses on the Fourier series and its applications in signal decomposition and reconstruction. Key tasks include:
- **Fourier Coefficients Calculation**: Finding and analyzing the Fourier coefficients for different signals.
- **Music Note Generation**: Using windowing techniques to generate and compare musical tones.
- **Signal Comparisons**: Exploring the effects of windowing on different time-domain signals and observing the corresponding frequency-domain characteristics.
## Homework 2: Laplace Transform and Transfer Function Analysis
This homework explores the Laplace domain for analyzing control systems, specifically focusing on transfer functions. Major components include:
- **Transfer Function Representation**: Defining transfer functions using MATLAB and analyzing system dynamics.
- **Pole-Zero Mapping**: Plotting the poles and zeros of the transfer function to study system stability.
- **Inverse Laplace Transform**: Calculating and interpreting the inverse Laplace transform of complex systems.
## Homework 3: Sampling Theorem and Audio Processing
This homework examines key concepts of digital signal processing, including sampling theory and its application to audio signals. Key tasks include:
- **Sampling and Aliasing**: Understanding Nyquist criteria, performing downsampling, and analyzing the effects of aliasing on sampled signals.
- **Audio Resampling**: Manipulating audio signals by upsampling and downsampling, and evaluating the resulting audio quality and spectral content.
- **Fourier Analysis of Audio Signals**: Applying FFT and visualizing the frequency spectrum of audio files.
## Requirements
- MATLAB R2023 or later.