Given a continuous time signal x(t). Sample the signal with a sampling rate of F=100 samples/s. x(t) = cos(2π40t) ● What is the frequency of the cosine in Hz? What is the frequency of the cosine in rad/s? What is the frequency of the sampled cosine in normalized rad/s?

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Given a continuous time signal x(t). Sample the signal with a sampling rate of F₁=100 samples/s.
x(t) = cos(2π40t)
● What is the frequency of the cosine in Hz?
●
●
●
What is the frequency of the cosine in rad/s?
What is the frequency of the sampled cosine in normalized rad/s?
What is the frequency of the sampled cosine in normalized Hz?
Using N = 50, what is the DFT of the sampled signal? What are the indexes where the DFT is non-
zero?
In MATLAB, generate the sampled signal and plot the magnitude of the DFT with index k on the
x-axis.
In MATLAB, plot the magnitude of the DFT with Hz on the x-axis.
Transcribed Image Text:Given a continuous time signal x(t). Sample the signal with a sampling rate of F₁=100 samples/s. x(t) = cos(2π40t) ● What is the frequency of the cosine in Hz? ● ● ● What is the frequency of the cosine in rad/s? What is the frequency of the sampled cosine in normalized rad/s? What is the frequency of the sampled cosine in normalized Hz? Using N = 50, what is the DFT of the sampled signal? What are the indexes where the DFT is non- zero? In MATLAB, generate the sampled signal and plot the magnitude of the DFT with index k on the x-axis. In MATLAB, plot the magnitude of the DFT with Hz on the x-axis.
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