HW 08: Difference between revisions

From Class Wiki
Jump to navigation Jump to search
No edit summary
Line 3: Line 3:
===Answer 1===
===Answer 1===
Frequency: The frequency is doubled
Frequency: The frequency is doubled

Amplitude:
Amplitude:

Phase:
Phase:

===Question 2===
===Question 2===
Suppose <math>x(t)=\int_{-\infty}^{\infty}\Omega(\beta)\,\Phi(\beta,t)\,d\beta</math> and <math>\int_{-\infty}^{\infty}\Phi^*(\beta,t)\,\Phi(\lambda,t)\,dt=\delta(\beta-\lambda)</math> where <math>x(t)\,\!</math> is any real function of t. If we have a linear time invariant system where an input of <math>\Phi(\lambda,t)\,\!</math> produces an output of <math>\Psi(\lambda,t)\,\!</math>.
Suppose <math>x(t)=\int_{-\infty}^{\infty}\Omega(\beta)\,\Phi(\beta,t)\,d\beta</math> and <math>\int_{-\infty}^{\infty}\Phi^*(\beta,t)\,\Phi(\lambda,t)\,dt=\delta(\beta-\lambda)</math> where <math>x(t)\,\!</math> is any real function of t. If we have a linear time invariant system where an input of <math>\Phi(\lambda,t)\,\!</math> produces an output of <math>\Psi(\lambda,t)\,\!</math>.

Revision as of 14:38, 7 December 2008

Question 1

If the sound track of a movie was played into a high fidelity playback system at twice the correct speed, what happens to a sine wave's frequency, amplitude and phase, relative to what happens at the correct speed? Explain your answers.

Answer 1

Frequency: The frequency is doubled

Amplitude:

Phase:

Question 2

Suppose and where is any real function of t. If we have a linear time invariant system where an input of produces an output of .

  • How do you find if you are given ?
  • What is the output due to ?

Answer 2

Question 3

If a signal x(t) only has frequency components near DC, for , then x(t) is known as a baseband signal. When x(t) is a baseband signal, is known as a double sideband (DSB) signal. Sometimes a double sideband signal is used to send information over a radio frequency communications link. The transmitter and receiver are shown below.

  • Find the Fourier Transform of the DSB signal, .
  • What is the lowest that can be used and still have the communications system work?
  • How does the bandwidth of v(t) compare to the bandwidth of x(t)?
  • What does the spectrum of w(t) look like and how does it compare to that of x(t)? A graph would be appropriate showing the spectrum of x(t) and that of w(t).

Answer 3