Ch 1 lecture 4

Ch 1 lecture 4 - EE 3120 Linear Systems Analysis Lecture 4...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE 3120 Linear Systems Analysis Lecture 4 Frequencies of Analog and Digital Sinusoids ( ) sin o f t t ϖ = 2 o P π ϖ = T [ ]: ( ) sin o f k f kT kT ϖ = = 0, 1, 2,... k = Analog sinusoid is periodic with fundamental (smallest) period P where: (repeats itself every P seconds) If we sample it with a sampling period: This is a discrete-time sinusoid. for [ ] f k [ ] [ ] f k f k N = + ( , ) k- [ ] [ ] [ 2 ] [ 3 ] [ ] f k f k N f k N f k N f k nN = + = + = + = + [ ] f k A D-T signal is periodic with period N , where N is a positive integer if: for all k where for any k and every positive integer n . is periodic with period N. f is also periodic with period 2N, 3N … The smallest N is the fundamental period . and EE 3120 Linear Systems Analysis Lecture 4 Frequencies of Analog and Digital Sinusoids sin o t ϖ is periodic for every , its sampled sequence is NOT necessarily periodic for every and every sampling period T. o ϖ sin o kT ϖ is periodic, then there exists a positive integer N such that sin sin ( ) sin( ) o o o o kT k N T kT NT ϖ ϖ ϖ ϖ = + = + sin sin cos cos sin o o o o o kT kT NT kT NT ϖ ϖ ϖ ϖ ϖ = + for all k. This holds IFF cos 1 o NT ϖ = sin o NT ϖ = and i.e. 2 o NT n ϖ π = 2 o T n N ϖ π = 2 o n N for some integer n is rational o T ϖ π is irrational This equality will only hold if o ϖ or T are multiples of some rational and π o ϖ if For integer n and positive integer N : EE 3120 Linear Systems Analysis Lecture 4 Frequencies of Analog and Digital Sinusoids sin 0.01 k π 0.01 1 2 100 o T n N ϖ π π π = = = 2 2 200 200 0.01 o n n N n T π π ϖ π = = = = 1 n = period choosing N = 20...
View Full Document

{[ snackBarMessage ]}

Page1 / 14

Ch 1 lecture 4 - EE 3120 Linear Systems Analysis Lecture 4...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online