Sampling as a modulation process; aliasing; the sampling theorem; the Z-transform and discrete-time system analysis; direct and computer-aided design of recursive and nonrecursive digital filters; the Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT); digital filtering using the FFT; analog-to-digital and digital-to analog conversion; effects of quantization and finite-word-length arithmetic.
Prerequisite: ENEE322; and completion of all lower-division technical courses in the EE curriculum.
Semesters OfferedFall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023
- Understand how analog signals are represented by their discrete-time samples, and in what ways digital filtering is equivalent to analog filtering
- Master the representation of discrete-time signals in the frequency domain, using the notions of z-transform, discrete-time Fourier transform (DTFT) and discrete Fourier transform (DFT)
- Learn the basic forms of FIR and IIR filters, and how to design filters with desired frequency responses
- Understand the implementation of the DFT in terms of the FFT, as well as some of its applications (computation of convolution sums, spectral analysis)
- Uniform sampling: sampling as a modulation process; aliasing; ideal impulse sampling; sampling theorem; sampling bandpass signals
- Data reconstruction by polynomial interpolation and extrapolation: zero-order hold; first order hold; linear point connector
- The z-transform: definition; inverse; useful transform relationships; Parseval's theorem; difference equations
- Analysis of sampled-data systems by transform methods: transfer functions for discrete-time systems; sinusoidal steady-state frequency response; structures for realizing transfer functions; stability; decimation and interpolation
- The design of transfer functions for digital filtering: bilinear transformation method for IIR filters; Fourier series, windowing and the Remez algorithm for FIR filters
- Effects of quantization and finite word length arithmetic in digital filters
- The discrete Fourier transform (DFT): definition of the DFT and its inverse; transform relationships; cyclic convolution and correlation; fast Fourier transform (FFT); filtering long sequences using the FFT