HW 08: Difference between revisions

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*The bandwidth of v(t) is 1/2 that of x(t). The cosine splits the (amplitude? of the) signal up in half and moves it up and down by f_0.
*The bandwidth of v(t) is 1/2 that of x(t). The cosine splits the (amplitude? of the) signal up in half and moves it up and down by f_0.
*The spectrum of w(t) is 1/2 of x(t) at the center frequency. At +/- 2*f_0, 1/4th of x(t).

Revision as of 01:55, 9 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: The amplitude remains the same

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

x(t) is the original signal
v(f) is x(t) after a low pass filter (cutoff frequency = f_max), multiplied by cos(2\pi f_0 t)
w(t) is v(t) multiplied by cos(2\pi f_0 t)
  • The bandwidth of v(t) is 1/2 that of x(t). The cosine splits the (amplitude? of the) signal up in half and moves it up and down by f_0.
  • The spectrum of w(t) is 1/2 of x(t) at the center frequency. At +/- 2*f_0, 1/4th of x(t).