Introduction to continuous-time signals and systems.
- Signals and systems:
- basic definitions/concepts
- review of complex analysis
- signal properties
- system properties
- basic signal transformations
- elementary signals
- signal representations using elementary signals
- Linear time-invariant (LTI) systems:
- convolution
- properties of convolution
- representation of signals using impulses
- impulse response and convolution representation of LTI systems
- properties of LTI systems
- response of LTI systems to complex exponential signals
- Fourier series:
- Fourier series definition
- finding Fourier series representations of signals
- convergence of Fourier series
- properties of Fourier series
- Fourier series and frequency spectra
- Fourier series and LTI systems
- Fourier transform:
- Fourier transform definition
- convergence of Fourier transform
- Fourier transform properties
- Fourier transform of periodic signals
- frequency spectra of signals
- frequency response of LTI systems
- applications
- Laplace transform:
- Laplace transform definition
- relationship between Laplace transform and Fourier transform
- region of convergence
- finding the inverse Laplace transform
- properties of the Laplace transform
- analysis of systems using the Laplace transform
- solving differential equations using the unilateral Laplace transform
- Define various properties of systems (such as linearity, time invariance, causality, memory, invertibility, and BIBO stability) and determine if a system has each of these properties;
- Identify basic properties of convolution and compute the convolution of functions;
- Explain the significance of convolution in the context of LTI systems;
- State the basic properties of the Fourier and Laplace transforms and use these properties in problem solving;
- Compute forward/inverse Fourier and Laplace transforms of functions and find Fourier series representations of periodic functions;
- Use the Fourier transform and/or Laplace transform to design and analyze simple systems (e.g., filtering/equalization systems, amplitude modulation systems, and feedback control systems);
- Use the Laplace transform to solve differential equations;
- Demonstrate competency in working with both time- and frequency-domain representations of signals and systems;
- Explain the relationships amongst the various representations of LTI systems (e.g., differential equation, frequency response, transfer function, impulse response);
- Identify basic types of frequency-selective filters (i.e., lowpass, highpass, and bandpass);
- Explain the fundamentals of sampling and the implications of the sampling theorem; and
- Use MATLAB effectively for problem solving.