{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Introduction_1 - System and Signals Input Signal x(t System...

This preview shows pages 1–6. Sign up to view the full content.

10/20/10 1 System and Signals System h(t) Input Signal x(t) Response y(t) [ ] ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 1 jw Y t y jw H jw X jw Y OR t h t x t Y - = = = Signals Deterministic Random [o/p of radio receiver when there e.g. is no broadcasting, the o/p of speaker when no body is talking, etc] t A t x π 50 sin ) ( = Now, if the input is random How can we measure the output? We can use, for example, Convolution

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

View Full Document
10/20/10 2 Energy and Power Signals: Let be the instantaneous voltage and current respectively, then the energy is : ) ( ) ( t i and t v Classification of is a voltage across The energy dissipated by the signal during the interval is given by: ) 1 ( ) ( resistor for t v ) ( t v 1 - 2 , 2 T T - = 2 2 2 ) ( T T T v dt t v E dt t v E resistor for dt t v R dt t i t v E v v - - - = = = 2 2 ) ( 1 ) ( 1 ) ( ) (
10/20/10 3 And the average power is: - = 2 2 2 ) ( 1 T T T v dt t v T P Now is an energy signal if : is finite, i.e: , where: ) ( t v v E v E 0 2 2 2 2 ) ( lim V dt t v E T T T v - = = While is a power signal if: where, ) ( t v v P 0 - = 2 2 2 ) ( 1 lim T T T v dt t v T E ( Limited can be dropped )

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

View Full Document
10/20/10 4 ( 29 signal power is t v finite A T T A dt t T A dt t A T P t A t v Ex T T T T T T v ) ( 2 2 2 cos 1 2 lim cos 1 lim cos ) ( : 2 2 2 2 2 2 2 2 2 = = + = = = - - In general, periodic signal is a power signal Parseval’s Theorem: - - -∞ = = = = = energy dw t v dt t v E signal power C dt t v T P v T n n 2 2 2 2 ) ( 2 1 ) ( ) ( 1 π
10/20/10 5 energy per unit frequency ( jouls/Hz ). It is called energy spectral density ( or energy density ). Thus, to find the energy, we have to integrate over the frequency band of the signal. Notice, the energy depends on the magnitude squared of the signal ( independent of the phase of the signal ).

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

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

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern