Signals and Systems

Signals and Systems - Signals and Systems Summer 2009 Dr....

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Click to edit Master subtitle style 10/6/09 Signals and Systems Summer 2009 Dr. Jean Andrian
Background image of page 1

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

View Full DocumentRight Arrow Icon
10/6/09 Reading assignment: Signals and Systems by Haykin and Van Veen Chapter 1, sections 1.1 to 1.8
Background image of page 2
10/6/09
Background image of page 3

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

View Full DocumentRight Arrow Icon
10/6/09
Background image of page 4
10/6/09
Background image of page 5

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

View Full DocumentRight Arrow Icon
10/6/09
Background image of page 6
10/6/09
Background image of page 7

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

View Full DocumentRight Arrow Icon
10/6/09 Even and odd signals CT signal x(t) is said to be an even signal if x(-t)=x(t) for all t X(t) is said to be an odd signal if x(-t)=-x(t) for all t DT signal x[n] is even if x[-n]=x[n] for all n And odd if
Background image of page 8
10/6/09 Any signal x(t) can be decomposed into a sum of even and odd components xe(t) and xo(t) such that x(t)= xe(t)+xo(t) where xe(t)= ½[x(t)+x(-t)] and xo(t)= ½[x(t)-x(-t)]
Background image of page 9

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

View Full DocumentRight Arrow Icon
10/6/09 A complex-valued signal is said to be conjugate symmetric if x(t)= x*(-t) x(t)= a(t) + j b(t) x*(t)= a(t) – j b(t) x*(-t)= a(-t)+ j b(-t) True if a(t)=a(-t) and b(-t)=-b(t) that is the real part is even and the imaginary part is
Background image of page 10
10/6/09 Periodic signals A CT periodic signal x(t) is a function of time that satisfies the condition x(t)= x(t + T) for all t, T>0 and is the smallest number such that the condition is satisfied. T is called the period and f = 1/T is called the fundamental frequency of the signal. The frequency is measured in hertz (Hz). The angular frequency is measured in radians per second, and is defined by
Background image of page 11

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

View Full DocumentRight Arrow Icon
Periodic signals (cont.) A DT periodic signal x[n] is such that x[n] = x[n + N] for integers n, where N is the smallest positive integer. N is called the fundamental period of the DT signal x[n]. The fundamental angular frequency or, simply, the fundamental frequency of x[n] is defined by Ω = 2π/N, which is measured in radians. Note that N must be an integer therefore Ω
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/10/2009 for the course EEL 3135 taught by Professor Andrian during the Summer '09 term at FIU.

Page1 / 155

Signals and Systems - Signals and Systems Summer 2009 Dr....

This preview shows document pages 1 - 13. Sign up to view the full document.

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