Signals & systems
Undergraduate · Engineering
Syllabus focus
Standard syllabus · STEM / applied
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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
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.