Signals & systems
Undergraduate · Engineering
Syllabus focus
Topics typically covered
Standard syllabus
Continuous-time signals and systems
- Signal classifications: energy, power, periodic, aperiodic
- Elementary signals: unit step, impulse, exponentials, sinusoids
- System properties: linearity, time-invariance, causality, stability
- Convolution integral for LTI systems
- Impulse response and frequency response relationships
- Fourier series for periodic signals
- Continuous-time Fourier transform pairs and properties
- Frequency spectrum interpretation and filtering concepts
- Laplace transform definition and region of convergence
- Transfer functions and pole-zero plots from Laplace domain
Discrete-time and sampling
- Sampling theorem and aliasing
- Discrete-time signals and sequences
- Linear convolution for discrete systems
- Z-transform and its properties
- Difference equations and digital filters
- FIR and IIR filter structures
- DFT and FFT for spectral analysis
- Relationship between Laplace, Fourier, and Z-transforms
- Reconstruction with ideal and practical hold circuits
- Stability and ROC for discrete-time systems
STEM / applied
Applications in communications and control
- AM/FM modulation concepts at block-diagram level
- Filtering for noise rejection and channel separation
- Feedback loop analysis using frequency response
- MATLAB/Python for signal processing labs
- Audio and image signal processing examples
- Digital filter design: cutoff and ripple trade-offs
- Windowing for spectral leakage control
- Correlation and matched filtering intro
- State-space realization from transfer functions
- Lab: oscilloscope, spectrum analyzer, and filter demos
Advanced topics survey
- Multirate signal processing and decimation
- Wavelets and time-frequency analysis (overview)
- Adaptive filters and LMS algorithm intro
- Random signals: autocorrelation and power spectral density
- LTI systems driven by noise and SNR
- Control system bandwidth from Bode plots
- Biomedical signals: ECG and EEG feature extraction
- Radar and sonar pulse compression (conceptual)
- Hardware: ADC/DAC resolution and quantization noise
- Capstone: design a digital filter for a sensor signal
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Continuous-time signals and systems
Signal classifications: energy, power, periodic, aperiodic
Coming soon - Discrete-time and sampling
Sampling theorem and aliasing
Coming soon
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.