Credits: 3

### Description

Prerequisite: ENEE322; and completion of all lower-division technical courses in the EE curriculum.
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.

### Semesters Offered

Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019

### Learning Objectives

• 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)

### Topics Covered

• 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