ECE 429

By the end of this course, the student will be able to:

1. State and apply the definitions of the following system properties: linearity, time invariance, causality, and BIBO stability.
2. Describe the distinctions between analog, continuous-time, discrete-time and digital signals, and describe the basic operations involved in analog-digital (A/D) and digital-analog (D/A) conversion.
3. State and apply the definition of a periodic discrete-time signal.
4. State the sampling theorem and explain aliasing.
5. Apply simple discrete-time signals to filters to obtain the output response.
6. Convolve discrete-time signals.
7. Calculate the z-transform X(z) of a simple signal x(n) (such as an exponential and sinusoid): specify the region of convergence (ROC) of X(z).
8. Apply z-transform theorems.
9. Given the transfer function H(z) and ROC of an LTI system, find the system poles (and zeros) and state whether or not the system is BIBO stable.
10. Compute the discrete-time Fourier transform (DTFT) of a signal.
11. Use the frequency response of a discrete-time system.
12. Knowing the poles and zeros of a transfer function, make a rough sketch of the gain response.
13. Design digital filters.
14. Apply DFT properties to compute the DFT and IDFT of simple signals.
15. Design the parameters associated with DFT implementation (sampling rate and record length) to provide an accurate analysis of the frequency and strength of dominant frequency components present in some given, unknown signal (e.g., for spectral analysis of a signal).
16. Explain the need for zero padding and tapered windows when doing spectral analysis of real-world signals. Explain the terms picket fence effect and spectral leakage.
17. Compare the characteristics (advantages and disadvantages) of IIR and FIR filters.
18. Explain (using frequency domain sketches) the application of oversampling and subsequent decimation for recording in digital audio systems.