As shown in the figure below, the input signal m(t) is multiplied with a sinusoidal pulse p(t) to generate the system output r(t). Its FT M (jw) is given below. M(jw) m(t) X r(t) p(t) = cos(wet) -2 (500) -500m (a) In this system, the frequency we is set to we = 27 (500) rad/s, that is, p(t) = cos(27 (500)t). What is the relationship between the Fourier transforms of m(t) and r(t), i.e., what is the relationship between M(jw) and R(jw)? 500 +2 (500) (b) Given M(jw) shown above, make a fully-labeled sketch of R(jw). (c) If m(t) is to be sampled digitally, what is the Nyquist sampling rate in Hertz?
As shown in the figure below, the input signal m(t) is multiplied with a sinusoidal pulse p(t) to generate the system output r(t). Its FT M (jw) is given below. M(jw) m(t) X r(t) p(t) = cos(wet) -2 (500) -500m (a) In this system, the frequency we is set to we = 27 (500) rad/s, that is, p(t) = cos(27 (500)t). What is the relationship between the Fourier transforms of m(t) and r(t), i.e., what is the relationship between M(jw) and R(jw)? 500 +2 (500) (b) Given M(jw) shown above, make a fully-labeled sketch of R(jw). (c) If m(t) is to be sampled digitally, what is the Nyquist sampling rate in Hertz?
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Transcribed Image Text:Problem PS8-4
As shown in the figure below, the input signal m(t) is multiplied with a sinusoidal pulse p(t) to generate the
system output r(t). Its FT M (jw) is given below.
M(jw)
m(t)
X
r(t)
p(t) = cos(wet)
2
-2T (500) -500m 0 500m +2T (500)
(a) In this system, the frequency we is set to we = 2(500) rad/s, that is, p(t) = cos(27 (500)t). What is the
relationship between the Fourier transforms of m(t) and r(t), i.e., what is the relationship between M (jw)
and R(jw)?
(b) Given M (jw) shown above, make a fully-labeled sketch of R(jw).
(c) If m(t) is to be sampled digitally, what is the Nyquist sampling rate in Hertz?
(d) The frequency we is changed to we = 27 (250) rad/s. Make a fully-labeled sketch of R(jw).
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