This course aims to equip students with the ability to express continuous and discrete-time signals mathematically. Students will gain an understanding of input-output relationships in linear time-invariant systems, perform convolution, and apply Fourier series to represent periodic signals. Students will also analyze Fourier transforms for continuous and discrete-time signals, recognizing their frequency characteristics. Finally students will learn to formulate conditions for proper signal sampling to prevent aliasing.
Upon successful completion of the course, students will be able to:
(1) Express the mathematical representations of continuous and discrete-time signals,
(2) Explain the input-output relationships in linear time-invariant systems and the steps needed to perform convolution,
(3) Apply the concepts of Fourier series representation to represent continuous-time and discrete-time periodic signals,
(4) Analyze the Fourier transform of a continuous-time signal, understanding its frequency content and spectral characteristics,
(5) Evaluate the Fourier transform for discrete-time signals, identifying their frequency components and spectral properties,
(6) Formulate the necessary conditions for properly sampling a continuous-time signal to avoid aliasing (sampling theorem).
(1) McClellan, J. H., Schafer, R. W., & Yoder, M. A. (2003). Signal Processing First. 2nd Edition, Pearson/Prentice Hall.
(2) Tervo, R. J. (2013). Practical Signals Theory with MATLAB Applications. 1st Edition, Wiley.