Credits:
Semesters Offered
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