4: Signal Processing

Learning Objectives

1. Introduce the continuous-time analog signal and its frequency analysis using Laplace transforms.
2. Discuss discrete-time digital signal and its frequency analysis using both discrete Fourier transforms (DFT) and fast Fourier transforms (FFT). In addition, be familiar with the discrete-time \(z\)-transform of signal and discrete-time system models in \(z\)-transform that is important for digital filter and controller design.
3. Define signal conversions between analog and digital signals, along with realization hardware for analog-to-digital (A/D) and digital-to-analog (D/A) converters. Understand data conversion between binary and decimal numbers. For graduate-level courses, provide the single and double precision floating-point representation in microprocessors.
4. Describe low-pass, high-pass, band-pass, and band-kill (notch) filter design for both analog and digital signals. Also describe their implementation and characteristics.
5. Introduce Nyquist-Shannon sample theory, sample aliasing, and anti-aliasing filter design.
6. Define the digital interface between the physical and information domains using pulse-train signals such as pulse-width-modulation and frequency modulation methods.
7. Introduce advanced filter design such as moving average, Chebyshev, and Butterworth filters.