HW 08: Difference between revisions
(New page: ===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, rel...) |
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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. |
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. |
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===Answer 1=== |
===Answer 1=== |
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Frequency: The frequency is doubled |
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Amplitude: |
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Phase: |
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===Question 2=== |
===Question 2=== |
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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>. |
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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).
