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F: LTI Systems

This module is a review of the concepts of linear time-invariant systems, and also a refresher of your Matlab skills.

Required readings

  • Lee and Varaiya, Section 8.1, LTI Systems
  • Lee and Varaiya, Section 8.2, Finding and using the frequency response
  • Lee and Varaiya, Section 11.1, Sampling
  • Lee and Varaiya, Section 11.2, Reconstruction
  • Lee and Varaiya, Section 11.3, The Nyquist-Shannon sampling theorem

Other readings

  • Kadi, Session 1, Introduction, sampling and reconstruction
  • Smith, Chapter 3, ADC and DAC
  • Smith, Chapter 5, Linear Systems
Exercises and problems
  1. Graphically illustrate sampling of a 1 kHz sinewave at 8 kHz, in both the time and frequency domains. In the time domain, show multiplication of the sine wave with a pulse train; in the frequency domain, show convolution of the corresponding signals.
  2. Write the mathematical equations for the above.
  3. Graphically illustrate ideal reconstruction of the 1 kHz sinewave (that is, using a "brickwall" filter at 4 kHz), in both the time and frequency domains.
  4. Write the mathematical equations for the above.
  5. Repeat (1) and (2) with a 7 kHz sinewave.
  6. Explain linearity and time-invariance both mathematically and by using block diagrams.
Lab exercises
  • Lee and Varaiya, Lab 1, Arrays and Sound
  • Lee and Varaiya, Lab 11, Sampling and Aliasing
  • Lee and Varaiya, Lab 2, Images

Other resources