{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Cours2 - Chapter 2 Signal Representation ELEC 2880 Modem...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 2: Signal Representation ELEC 2880: Modem Design () Chapter 2: Signal Representation ELEC 2880: Modem Design 1 / 18
Image of page 1

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

View Full Document Right Arrow Icon
Complex baseband signal Why is it useful? For bandpass signal, such as modulated signal Simple, low pass representation Used for performance computation Also used in actual signal processing Course structure Reminder of basic principles/equations Application to elements in communication chain Modulation Filters Random noise Typical example: Sinusoid in AWGN () Chapter 2: Signal Representation ELEC 2880: Modem Design 2 / 18
Image of page 2
Analytical Signal Let x ( t ) be a real signal Bandpass: | X ( w ) | = 0 for | ω - ω 0 | > π B Analytical Signal x a ( t ): Keep positive frequencies ( ω 0) with factor 2 x ( t ) = { x a ( t ) } Add imaginary part to cancel negative frequencies () Chapter 2: Signal Representation ELEC 2880: Modem Design 3 / 18
Image of page 3

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

View Full Document Right Arrow Icon
Complex baseband representation X(w) X a (w) E x (w) () Chapter 2: Signal Representation ELEC 2880: Modem Design 4 / 18
Image of page 4
Complex baseband representation Complex baseband, also called complex envelope: E x ( ω ) = X a ( ω + ω 0 ) e x ( t ) = e - j ω 0 t x a ( t ) Depends on choice of ω 0 (not unique!) Equivalent representation, contains all information x ( t ) = { e x ( t ) e j ω 0 t } () Chapter 2: Signal Representation ELEC 2880: Modem Design 5 / 18
Image of page 5

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

View Full Document Right Arrow Icon
Rice components Rice components defined as e x ( t ) = x 1 ( t ) + jx 2 ( t ) If ω 0 well chosen, they have same bandwidth as complex baseband (but not same shape) x 1 ( t ) = { e x ( t ) } = [ e x ( t ) + e * x ( t )] / 2 X 1 ( ω ) = [ E x ( ω ) + E * x ( - ω )] / 2 They represent I/Q components: (! sign) x ( t ) = x 1 ( t ) cos( ω 0 t ) - x 2 ( t ) sin( ω 0 t )
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern