Question

P3.3) State whether each of the following statements is TRUE or FALSE. Please show your work. a) Let $f(t)$ be a band-limited signal with bandwidth 300Hz. Then signal $f(2t)$ is band-limited with bandwidth 150Hz. b) If $x(t)$ is a real signal then the magnitude of the Fourier transform $X(\omega)$ is an even function. c) Let $x(t) = cos(2t)$ be the input signal to an LTI system with impulse response $h(t)$, where $h(t)$ is a real signal. Then the output of the system is equal to $Acos(4t-\theta)$ for some $A$ and $\theta$.

          P3.3) State whether each of the following statements is TRUE or FALSE. Please show your work.
a) Let $f(t)$ be a band-limited signal with bandwidth 300Hz. Then signal $f(2t)$ is band-limited with bandwidth 150Hz.
b) If $x(t)$ is a real signal then the magnitude of the Fourier transform $X(\omega)$ is an even function.
c) Let $x(t) = cos(2t)$ be the input signal to an LTI system with impulse response $h(t)$, where $h(t)$ is a real signal. Then the
output of the system is equal to $Acos(4t-\theta)$ for some $A$ and $\theta$.

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P3.3) State whether each of the following statements is TRUE or FALSE. Please show your work.
a) Let f(t) be a band-limited signal with bandwidth 300Hz. Then signal f(2t) is band-limited with bandwidth 150Hz.
b) If x(t) is a real signal then the magnitude of the Fourier transform X(ω) is an even function.
c) Let x(t) = cos(2t) be the input signal to an LTI system with impulse response h(t), where h(t) is a real signal. Then the
output of the system is equal to Acos(4t-θ) for some A and θ.

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Prabhu Ramji

Step 1

Band-limited means that the signal has no frequency components above a certain frequency. In this case, the bandwidth is 300Hz, so the highest frequency component in f(t) is 300Hz. Now, let's consider the signal f(2t). This means that the time axis is compressed Show more…

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Text: Signals and Systems P3.3 State whether each of the following statements is TRUE or FALSE. Please show your work. a) Let f() be a band-limited signal with bandwidth 300Hz. Then the signal f(2t) is band-limited with bandwidth 150Hz. b) If x(t) is a real signal, then the magnitude of the Fourier transform X(w) is an even function. c) Let x(t) = cos(2t) be the input signal to an LTI system with impulse response h(t), where h(t) is a real signal. Then the output of the system is equal to A cos(4t - 0) for some A and 0.

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