Course Title: Introduction to Signal Processing
Course Description: This course introduces the principles and techniques of signal processing, covering topics such as digital signal processing, Fourier analysis, filtering, and spectral analysis. Students will learn about signal representation, transformation, and manipulation in both time and frequency domains.
Course Outline:
- Week 1: Introduction to Signals
- Definition of signals and systems
- Continuous-time vs. discrete-time signals
- Analog vs. digital signals
- Week 2: Signal Representation and Sampling
- Signal representation using mathematical functions
- Sampling theorem and Nyquist frequency
- Aliasing and anti-aliasing filters
- Week 3: Time-Domain Analysis
- Convolution and correlation
- Time-domain properties of signals (energy, power, periodicity)
- Autocorrelation and cross-correlation functions
- Week 4: Fourier Transform
- Fourier series and Fourier transform
- Properties of Fourier transform
- Inverse Fourier transform
- Week 5: Discrete Fourier Transform (DFT)
- Introduction to DFT and its computation
- Fast Fourier Transform (FFT) algorithms
- Applications of DFT in signal analysis
- Week 6: Frequency-Domain Analysis
- Frequency response of systems
- Filtering techniques (low-pass, high-pass, band-pass filters)
- Windowing and spectral leakage
- Week 7: Z-Transform and Transfer Functions
- Z-transform and its properties
- Transfer functions and system analysis
- Digital filter design using Z-transform
- Week 8: Digital Signal Processing (DSP)
- Basics of digital signal processing
- FIR (Finite Impulse Response) and IIR (Infinite Impulse Response) filters
- Real-time DSP and applications
- Week 9: Spectral Analysis
- Power spectral density (PSD)
- Welch and periodogram methods for spectral estimation
- Spectrogram and time-frequency analysis
- Week 10: Advanced Topics and Applications
- Multirate signal processing
- Adaptive signal processing techniques
- Signal processing applications in audio, image, and video processing
Course Assignments:
- Signal representation and analysis exercises
- Sampling and aliasing simulations
- Fourier transform and DFT calculations
- Filter design and frequency response analysis
- DSP algorithm implementation projects
- Spectral analysis and spectrogram generation tasks
- Application-based signal processing projects
Course Materials:
- Textbook: “Digital Signal Processing” by John G. Proakis and Dimitris G. Manolakis
- Signal processing software (MATLAB, Python libraries like NumPy, SciPy)
- Online tutorials and resources on signal processing
- DSP hardware and simulation tools (DSP boards, Simulink)
- Case studies and real-world examples of signal processing applications
Assessment:
- Weekly problem sets and quizzes
- Midterm and final exams covering theory and applications
- Signal processing algorithm implementation projects
- Spectral analysis and filtering assignments
- Final project demonstrating an application of signal processing techniques
Prerequisites: Basic understanding of calculus, linear algebra, and programming concepts (MATLAB or Python) would be beneficial but not mandatory.