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ECE 108 – Fall 2013 – Homework #7

Assume that an input signal, f(t), is sampled in two ways. First, suppose it is ideally sampled by
multiplying with an impulse train, creating a new signal g(t). Second, suppose it is sampled using
standard technology (S/H is used to create the stair step waveform we have discussed), creating a
second new signal, s(t). Oh yeah, remember that ù = 2ðf.

1) Assuming that the sampling rate in creating g(t) and s(t) is 20KHz, draw the spectrum out to
50KHz of these signals given that f(t) = cos(2000ðt). Accurately compute the weight of each of the
impulses in the spectra.

2) Now assume that f(t) = cos(38000ðt) and recompute the weight of each of the impulses in the
spectra (same conditions as in prob. 1)

3) In the problem 1 scenario, assume that each signal, g(t) and s(t) is filtered by an ideal lowpass
filter whose gain is 1 from 0 to 5KHz and 0 beyond that. Give the exact mathematical form of the
steady state response at the output of the respective filters.

4) Redo problem 3 assuming that the ideal filters have unity gain out to 25KHz and 0 beyond that.

5) Redo problem 1 assuming that f(t) is the 10KHz square wave that is 1 from -25ìsec to +25ìsec
and 0 from 25ìsec to 75ìsec, etc.. Hint: There is an easy way to do this! Think about g(t) and
s(t)……

ECE 108 – Fall 2013 – Homework #10

out inSolve for the transfer function, H(s) = V / V , in the circuit below, assuming that the op amp is

1 2ideal. Let both capacitors be 0.1ìF, R = 500, and R = 2K in all of the following. Determine the
poles of the system. Draw the Bode plot for the circuit. What kind of filter is this (your choices are

inlowpass, highpass, bandpass, or bandstop)? Now find the steady state response to the input V =

in2sin(10,000t). Find the Laplace transform of the response to V = 2u(t)sin(10,000t). Find the zero-

instate response to the input, V = 2u(t), where u(t) is the step function. Find the zero-state response

into the input, V = 2u(t)sin(10,000t).