1 / 9

ECE310 – Lecture 17

ECE310 – Lecture 17. Sampling Theorem 03/31/01 – 04/02/01. Why Discrete?. The use of digital computers Analog filters -> digital filters Cellular phone: analog & digital mode Digital television. Sample. A question

colby-james
Télécharger la présentation

ECE310 – Lecture 17

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ECE310 – Lecture 17 Sampling Theorem 03/31/01 – 04/02/01

  2. Why Discrete? • The use of digital computers • Analog filters -> digital filters • Cellular phone: analog & digital mode • Digital television

  3. Sample • A question • For a certain continuous-time signal, how many samples are enough to describe the signal accurately? • Shannon’s theorem • The sampling rate required to exactly reconstruct a signal from its samples is more than twice the highest frequency at which the FT of the signal is non-zero • Band-limited signal

  4. How Does It Come From? • Impulse sampling – the product of a signal and a comb function • FT of the impulse-sampled signal • fs frequency domain period

  5. Cont’d - Example

  6. The Alias Page 9-9, 9-12, 9-13

  7. Nyquist Frequency and Rate • fs: frequency domain period • fm: the highest frequency is called the Nyquist frequency (folding frequency) • 2fm: the minimum rate at which a signal can be sampled and still be reconstructed from its samples is called Nyquist rate • If fs > 2fm, then it’s oversampled • If fs < 2fm, then it’s undersampled • Alias: shifted versions of the original spectrum • If the alias overlap, the discrete-time signal is said to be ‘aliased’

  8. Reconstruct Time-Domain Signal • Filter the impulse-sampled signal using • an ideal lowpass filter with a cutoff frequency at fc, where fm<fc<fs-fm • and a gain of Ts

  9. Cont’d • When fs=2fm, fc must be equal to fm. This works only when the signal’s spectrum does not have an impulse at fm

More Related