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Signal Processing Course Description

Course Title: Introduction to Signal Processing with AI

Course Summary

This course offers an engaging introduction to the field of signal processing, emphasizing practical applications and interactive learning through the extensive use of MicroSims generated by AI. Students will learn the fundamental principles of signal processing, including analysis and manipulation of signals, filtering, Fourier transforms, and digital signal processing (DSP) algorithms. Through innovative interactive web-based simulations, visualizations, and real-world applications powered by AI, the course seeks to make the complexities of signal processing accessible to students with varying backgrounds in mathematics. This course concludes with capstone projects that use low-cost microcontrollers that include powerful signal processing functionality.

Credits: 3

Detailed Course Description

This course provides a comprehensive introduction to signal processing, a core area in electrical engineering, with a special focus on real-world applications and accessibility for students with diverse backgrounds. Leveraging the power of generative AI, students will interactively explore key concepts in signal processing, such as signal classification, time and frequency domain representations, Fourier and Laplace transforms, sampling theory, and digital filtering. The curriculum includes AI-powered simulations, hands-on labs, and projects that allow students to visualize and manipulate signals, enhancing their conceptual understanding and confidence.

Through AI-generated learning resources and simulations, students will experiment with various signal processing applications, such as audio filtering, image processing, communications, and biomedical signal analysis. The use of AI ensures that content is tailored to individual learning paces and styles, making complex mathematical concepts more intuitive and engaging.

Prerequisites

  • Introductory Electrical Engineering or Physics: Students should have foundational knowledge in electrical circuits and systems.
  • Basic Calculus and Linear Algebra: Comfort with differential and integral calculus and matrix operations is beneficial, though the course provides AI-driven tools to support students with minimal math background.
  • Programming Basics: Familiarity with basic programming concepts in Python or MATLAB is recommended, as assignments involve signal processing simulations.

Topics Covered

  1. Signals - Fundamental concept of information carriers
  2. Systems - Devices/processes that transform signals
  3. Continuous-Time Signals - Signals defined for all time values
  4. Discrete-Time Signals - Signals defined at discrete time intervals
  5. Analog Signals - Continuous amplitude signals
  6. Digital Signals - Quantized amplitude signals
  7. Sampling - Converting continuous to discrete-time signals
  8. Nyquist-Shannon Sampling Theorem - Minimum sampling rate requirement
  9. Aliasing - Distortion from inadequate sampling
  10. Quantization - Converting continuous to discrete amplitude
  11. Fourier Transform - Converting signals to frequency domain
  12. Discrete Fourier Transform (DFT) - Discrete version of Fourier transform
  13. Fast Fourier Transform (FFT) - Efficient DFT algorithm
  14. Frequency Domain - Representation of signals by frequency components
  15. Time Domain - Representation of signals over time
  16. Complex Numbers - Essential for signal representation
  17. Euler's Formula - Connection between exponentials and sinusoids
  18. Phasors - Rotating vector representation of sinusoids
  19. Convolution - Operation for system response calculation
  20. Impulse Response - System's output to impulse input
  21. Transfer Function - Frequency domain system characterization
  22. Linear Systems - Systems obeying superposition principle
  23. Time-Invariant Systems - Systems with constant parameters
  24. Causality - System output depends only on past/present inputs
  25. Stability - Bounded output for bounded input
  26. Low-Pass Filters - Passes low frequencies, attenuates high
  27. High-Pass Filters - Passes high frequencies, attenuates low
  28. Band-Pass Filters - Passes specific frequency band
  29. FIR Filters - Finite Impulse Response filters
  30. IIR Filters - Infinite Impulse Response filters
  31. Z-Transform - Discrete-time equivalent of Laplace transform
  32. Pole-Zero Analysis - System characterization via poles and zeros
  33. Frequency Response - System output vs. frequency
  34. Amplitude Modulation - Encoding information in signal amplitude
  35. Spectral Analysis - Analyzing frequency content of signals
  36. Power Spectral Density - Power distribution across frequencies
  37. Autocorrelation - Signal similarity with time-shifted version
  38. Adaptive Filters - Filters that adjust parameters automatically
  39. Least Mean Squares (LMS) - Adaptive filter algorithm
  40. Wavelets - Time-frequency localized basis functions
  41. Short-Time Fourier Transform (STFT) - Time-varying frequency analysis
  42. Signal-to-Noise Ratio (SNR) - Signal quality metric
  43. Random Processes - Stochastic signal models
  44. Multirate Signal Processing - Processing at multiple sampling rates
  45. Signal Compression - Reducing data rate while preserving information
  46. Convolutional Neural Networks (CNNs) - Deep learning for signal processing
  47. Spectrogram - Visual representation of frequency vs. time
  48. Window Functions - Functions for controlling spectral leakage
  49. Digital Signal Processors (DSPs) - Hardware for signal processing
  50. Machine Learning in Signal Processing - AI techniques for signal analysis

Topics Not Covered

  1. Advanced Deep Neural Networks
  2. Reinforcement Learning
  3. Graph Embeddings

Learning Objectives

Based on the 2001 Bloom Taxonomy of Learning Objectives

Remembering

  1. Define key signal processing terms and concepts, including signals, systems, noise, filters, and transformations.
  2. Recall common signal processing algorithms, including convolution, Fourier transform, and sampling theory.
  3. Recognize the types and characteristics of signals (analog, digital, continuous, discrete).

Understanding

  1. Explain the importance of signal processing in various real-world applications, such as communications, audio engineering, and image processing.
  2. Describe the principles of time and frequency domain analysis and their relevance to signal interpretation.
  3. Summarize the role of sampling, quantization, and aliasing in digital signal processing.

Applying

  1. Apply Fourier analysis to break down complex signals into frequency components, using AI-driven simulations to aid understanding.
  2. Use convolution to understand system response to various input signals.
  3. Implement basic filtering techniques on real-world datasets, such as audio or biomedical signals, using generative AI-generated coding examples and templates.

Analyzing

  1. Differentiate between types of filters (e.g., low-pass, high-pass, band-pass) and determine their impact on signals.
  2. Examine how signal characteristics vary in time and frequency domains using interactive AI simulations.
  3. Interpret results from digital filters applied to noisy signals, exploring the effects of different filter parameters.

Evaluating

  1. Assess the effectiveness of various filtering techniques for specific applications, such as audio signal processing, image denoising, and communication channel equalization.
  2. Compare signal processing outcomes from AI-driven simulations and real-world data, identifying sources of error and noise.
  3. Critique the accuracy and limitations of different signal representations and transformations, especially for high-noise or high-complexity signals.

Creating

  1. Design custom signal processing algorithms to address real-world problems, using AI to simulate and test these solutions.
  2. Develop simulations that visualize the effects of different processing techniques on signals, customizing for different types of input (e.g., audio, medical data).
  3. Construct projects that demonstrate how generative AI can enhance the comprehension and application of signal processing concepts for students from various mathematical backgrounds.

Course Highlights

  • AI-Powered Simulations: The course employs AI-generated simulations and visualizations that allow students to interactively explore the effects of different signal processing techniques.
  • Project-Based Learning: Students will work on individual and group projects that apply signal processing concepts to real-world challenges, with AI tools helping generate custom content and suggestions.
  • Adaptable Content: The generative AI component provides adaptive exercises, supplementary examples, and explanations, allowing students with varying levels of mathematical knowledge to succeed.
  • Engagement with Real Data: Students will process real-world datasets (e.g., audio files, medical data) to see firsthand how signal processing is used across industries.
  • Career-Relevant Skills: By course completion, students will be equipped with foundational skills in signal processing and practical experience with AI tools, preparing them for roles in engineering, data science, and applied technology.