Consider the quantity H(f) defined below: 1 H(f)= 1+j2f(RC) H(f) is the frequency response of a simple circuit containing a a resistor with resistance R and a capacitor with capacitance C. The circuit is a real linear time-invariant system. For the rest of this problem, you can assume that RC = 2(1000). The input to this circuit is a sinusoidal voltage x(t) = A cos(2 ft). The output is the voltage across the capacitor is y(t). (a) Make a plot of the magnitude of the frequency response, |H(f), for 0
Consider the quantity H(f) defined below: 1 H(f)= 1+j2f(RC) H(f) is the frequency response of a simple circuit containing a a resistor with resistance R and a capacitor with capacitance C. The circuit is a real linear time-invariant system. For the rest of this problem, you can assume that RC = 2(1000). The input to this circuit is a sinusoidal voltage x(t) = A cos(2 ft). The output is the voltage across the capacitor is y(t). (a) Make a plot of the magnitude of the frequency response, |H(f), for 0
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I need help with this problem and an explanation of the solution for the image described below. (Introduction to Signals and Systems)

Transcribed Image Text:Consider the quantity H(f) defined below:
1
H(f)=
1+j2f(RC)
H(f) is the frequency response of a simple circuit containing a a resistor with resistance R and a
capacitor with capacitance C. The circuit is a real linear time-invariant system. For the rest of this
problem, you can assume that RC = 2(1000). The input to this circuit is a sinusoidal voltage x(t) =
A cos(2 ft). The output is the voltage across the capacitor is y(t).
(a) Make a plot of the magnitude of the frequency response, |H(f), for 0 <f < 100,000. You
can make this plot using a variety of methods: plotting a set of points on graph paper using a
calculator to compute the points, Python, Matlab, Excel, or whatever programming language you
wish. Comment on the shape of the plot.
(b) Make a plot of the phase of the frequency response, LH(f), for 0 < f< 100,000. You can make
this plot using a variety of methods: plotting a set of points on graph paper using a calculator to
compute the points, Python, Matlab, Excel, or whatever programming language you wish. Your
plot should show the phase in degrees, rather than radians. As w increases does the phase approach
a limiting value?
(c) Consider the following input signals. Determine the outputs for each case. You may make rea-
sonable approximations.
(i) a(t) = cos(2π(0.1)t)
(ii) x(t) = cos(2π (1000)t)
(iii) e(t) = cos(2π(105)t)
(d) Based on these calculations, can you tell something about what this system does to sinusoids of
different frequencies?
(e) If the input to this system is the sinusoid x(t) = A cos(2π ft), can the output y(t) ever be larger
than the input x(t)? Why or why not?
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