Download presentation

Presentation is loading. Please wait.

1
DCSP-11 Jianfeng Feng Jianfeng.feng@warwick.ac.uk http://www.dcs.warwick.ac.uk/~feng/dsp.html

2
1. Data transmission 2. Information theory

3
3. Signal Representation idea: time vs. Frequency ( continuous FT)

4
Sequences and their representation A sequence is an infinite series of real numbers { x(n) }, which is written { x(n) } = {…, x(-1),x(0),x(1),x(2), …,x(n), … }

5
Sequences and their representation A sequence is an infinite series of real numbers { x(n) }, which is written { x(n) } = {…, x(-1),x(0),x(1),x(2), …,x(n), … } This can be used to represent a sampled signal, i.e. x(n) = x(nT), where x(t) is the original (continuous) function of time. (might prefer x[n]) Q: we can not work on x(t), how about x(n)?

6
Discrete Time Fourier Transform (DTFT) The basic tool of signal analysis is the Fourier transform (DTFT)

7
Definition and properties: The DTFT gives the frequency representation of a discrete time sequence with infinite length.

8
Definition and properties: The DTFT gives the frequency representation of a discrete time sequence with infinite length. X( ): frequency domain x(n): time domain

10
Find the DC term ? Calculate the power spectrum?

11
the unit impulse

12
Computation of the DTFT It is well known that the whole Fourier approach to signal analysis is based on the expansion of a signal in terms of sinusoids or, more precisely complex exponentials. In this approach we begin analyzing a signal by determining the frequencies contributing to its spectrum in terms of magnitudes and phases.

13
For example, if a sequence is a sinusoid x(n)=cos( 0 n) of infinite length, its DTFT yields two `delta' functions,

Similar presentations

OK

The Nyquist–Shannon Sampling Theorem. Impulse Train Impulse Train (also known as "Dirac comb") is an infinite series of delta functions with a period.

The Nyquist–Shannon Sampling Theorem. Impulse Train Impulse Train (also known as "Dirac comb") is an infinite series of delta functions with a period.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on review of related literature in research Ppt on programmable logic array Ppt on shell structures theory Ppt on business plan of a coffee shop Ppt on technical analysis of stocks Ppt on non agricultural activities in jamaica Ppt on power system stability using facts devices Ppt on chromosomes and genes and alleles Ppt on cross docking advantages Ppt on business etiquettes training wheels