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# Decompsotion of time domain signals into frequency component

a. A square wave signal with voltage levels 0 volts and 2.0 volt at a frequency of 1.00 MHz
is multiplied by a sine wave at a frequency of 5.0 MHz. Which of the following frequencies are
present at the output of the multiplier - there may also be other frequencies not listed below.

1.0 MHz 2.0 MHz 3.0 MHz 4.0 MHz 5.0 MHz 6.0 MHz

b. A radio transmitter operates at a carrier frequency of 99.1 MHz. The transmitter has an
intermediate frequency of 10.0 MHz. A local oscillator is required in the transmitter to
provide the up-conversion from 10.0 MHz to 99.1 MHz. Compute the oscillator frequency.

c. A square wave with amplitudes 0 V and 1.0 V, and a period of 1.0 ms is applied to an
ideal high pass filter with a cut on frequency of 1500 Hz.
Which of the following sine waves are present at the filter output, where ωo = 2000 PI radians/s:

2/PI cos (wt ) 2/PI cos (2wt) 2/3PI cos (3wt) 1/3 cos 3 (wt) 1/2PI cos 4 (wt).

#### Solution Preview

a. Multiplying 2 signal components (pure sinusoids) together results in sum and difference components.

Consider two signals of angular frequency w1, w2 with w1 > w2.

S1= cos(w1*t), S2= cos(w2*t) normalized to amplitude of 1V

Which gives

S1*S2 = cos(w1*t).cos(w2*t) = 0.5{cos(w1+w2)*t + cos(w1 - w2)t} for w1 > w2

We would therefore expect frequencies to appear from the multiplier at 5 + 1 = 6 MHz and 5 -1 = 4 MHz,
...

#### Solution Summary

A number of questions are posed on time domain signals and superpoistion of such signals, resultant frequency domain signals are determined in the solution.

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