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Signal Processing Concept List

This document contains 200 concepts for the "Introduction to Signal Processing with AI" course. Each concept is labeled in Title Case with a maximum of 32 characters.

Mathematical Foundations (1-25)

  1. Real Numbers
  2. Complex Numbers
  3. Imaginary Unit
  4. Euler's Formula
  5. Phasors
  6. Vectors
  7. Matrices
  8. Linear Algebra
  9. Differential Calculus
  10. Integral Calculus
  11. Differential Equations
  12. Partial Derivatives
  13. Probability Theory
  14. Random Variables
  15. Statistical Distributions
  16. Mean and Expected Value
  17. Variance
  18. Standard Deviation
  19. Trigonometry
  20. Exponential Functions
  21. Logarithmic Functions
  22. Series and Sequences
  23. Eigenvalues and Eigenvectors
  24. Inner Product
  25. Norms and Metrics

Signal Fundamentals (26-50)

  1. Signals
  2. Systems
  3. Continuous-Time Signals
  4. Discrete-Time Signals
  5. Analog Signals
  6. Digital Signals
  7. Periodic Signals
  8. Aperiodic Signals
  9. Even Signals
  10. Odd Signals
  11. Energy Signals
  12. Power Signals
  13. Unit Step Function
  14. Unit Impulse Function
  15. Sinusoidal Signals
  16. Exponential Signals
  17. Signal Operations
  18. Time Shifting
  19. Time Scaling
  20. Signal Amplitude
  21. Signal Frequency
  22. Signal Phase
  23. Signal Duration
  24. Signal Energy
  25. Signal Power

System Properties (51-70)

  1. Linear Systems
  2. Nonlinear Systems
  3. Time-Invariant Systems
  4. Time-Varying Systems
  5. Causality
  6. Non-Causal Systems
  7. Stability
  8. Unstable Systems
  9. Memory Systems
  10. Memoryless Systems
  11. Invertible Systems
  12. System Response
  13. Impulse Response
  14. Step Response
  15. Frequency Response
  16. Transfer Function
  17. System Identification
  18. Feedback Systems
  19. Feedforward Systems
  20. System Interconnections

Convolution and Correlation (71-80)

  1. Convolution
  2. Discrete Convolution
  3. Circular Convolution
  4. Convolution Theorem
  5. Correlation
  6. Autocorrelation
  7. Cross-Correlation
  8. Correlation Coefficient
  9. Matched Filter
  10. Wiener Filter

Sampling and Quantization (81-95)

  1. Sampling
  2. Sampling Rate
  3. Sampling Theorem
  4. Nyquist Rate
  5. Nyquist Frequency
  6. Aliasing
  7. Anti-Aliasing Filter
  8. Oversampling
  9. Undersampling
  10. Quantization
  11. Quantization Error
  12. Quantization Noise
  13. Uniform Quantization
  14. Non-Uniform Quantization
  15. Signal Reconstruction

Fourier Analysis (96-115)

  1. Fourier Series
  2. Fourier Coefficients
  3. Fourier Transform
  4. Inverse Fourier Transform
  5. Discrete Fourier Transform
  6. Inverse DFT
  7. Fast Fourier Transform
  8. FFT Algorithms
  9. Radix-2 FFT
  10. Cooley-Tukey Algorithm
  11. Frequency Domain
  12. Time Domain
  13. Spectrum
  14. Magnitude Spectrum
  15. Phase Spectrum
  16. Power Spectrum
  17. Spectral Analysis
  18. Spectral Leakage
  19. Window Functions
  20. Windowing Techniques

Transforms (116-130)

  1. Laplace Transform
  2. Z-Transform
  3. Inverse Z-Transform
  4. Region of Convergence
  5. Poles
  6. Zeros
  7. Pole-Zero Plot
  8. Pole-Zero Analysis
  9. S-Plane
  10. Z-Plane
  11. Discrete Cosine Transform
  12. Wavelet Transform
  13. Discrete Wavelet Transform
  14. Continuous Wavelet Transform
  15. Short-Time Fourier Transform

Filter Design (131-155)

  1. Filters
  2. Low-Pass Filters
  3. High-Pass Filters
  4. Band-Pass Filters
  5. Band-Stop Filters
  6. Notch Filters
  7. Comb Filters
  8. All-Pass Filters
  9. FIR Filters
  10. IIR Filters
  11. Filter Order
  12. Filter Coefficients
  13. Filter Stability
  14. Filter Design Methods
  15. Butterworth Filter
  16. Chebyshev Filter
  17. Elliptic Filter
  18. Bessel Filter
  19. Window Method
  20. Frequency Sampling Method
  21. Bilinear Transform
  22. Impulse Invariance
  23. Filter Banks
  24. Multirate Filters
  25. Polyphase Filters

Adaptive Processing (156-165)

  1. Adaptive Filters
  2. Adaptive Algorithms
  3. Least Mean Squares
  4. Normalized LMS
  5. Recursive Least Squares
  6. Kalman Filter
  7. Adaptive Noise Cancellation
  8. Echo Cancellation
  9. Adaptive Equalization
  10. System Identification

Stochastic Processes (166-175)

  1. Random Processes
  2. Stochastic Signals
  3. White Noise
  4. Colored Noise
  5. Gaussian Noise
  6. Signal-to-Noise Ratio
  7. Noise Reduction
  8. Statistical Signal Processing
  9. Power Spectral Density
  10. Wiener-Khinchin Theorem

Advanced Topics (176-190)

  1. Multirate Signal Processing
  2. Decimation
  3. Interpolation
  4. Upsampling
  5. Downsampling
  6. Signal Compression
  7. Lossy Compression
  8. Lossless Compression
  9. Transform Coding
  10. Huffman Coding
  11. Time-Frequency Analysis
  12. Spectrogram
  13. Wigner-Ville Distribution
  14. Ambiguity Function
  15. Compressed Sensing

Applications and AI (191-200)

  1. Digital Signal Processors
  2. FPGA Implementation
  3. Real-Time Processing
  4. Audio Signal Processing
  5. Image Processing
  6. Video Processing
  7. Machine Learning in DSP
  8. Convolutional Neural Networks
  9. Deep Learning for Signals
  10. AI-Driven Signal Analysis

Total Concepts: 200

Note: These concepts are designed to build upon each other and will be organized with dependency relationships in the next phase of learning graph generation.