Decompsotion of time domain signals into frequency component

Please provide necessary explanations leading to the answer.

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

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.

A spectrum analyzer is connected to an unknown signal. The spectrum analyzer displays the voltage level of signals in volts vertically and frequency horizontally. The spectrum of the unknown signal creates the following display:
A vertical line at a frequency of 50 kHz with a magnitude of 1.80 V
A vertical line at a fr

An ideal low-pass filter is described in the frequency-domain by
H_d(e^(jw)) = 1 . e^(-jaw) , |w| <= w_c
0 , w_c < |w| <= PI
where w_c is called the cutoff frequency and a (denoting symbol alpha) is called the phase delay.
Determine the ideal impulse response h_d(n) using the

Laplace transforms enable interpretation and manipulation of different signals by viewing these signals as either timedomainsignals/pulse or else frequencydomain representations. A number of examples are presented in these solutions showing how such tranforms may be maniupluted to better understand circuit driving forces. A n

A spectrum analyzer is connected to an unknown signal. The spectrum analyzer displays the power level of signals in dBm vertically and frequency horizontally. The spectrum of the unknown signal creates the following display:
A continuous spectrum that is completely filled so no lines are visible.
The spectrum has a sin X

A discrete timedomain signal x(n) - u(n) - u(n-10) is decomposed and plotted. It is then examined in the z domian by appropriate transformation and algebraic manipulation. From the z transform representation the poles and zeros are determined and plotted in the z domain

A waveform v(t) has a Fourier transform which extends over the range -F to +F in the frequencydomain. The square of the waveform v(t), that is, v(t) v(t), then has a Fourier transforms which extends over the range:
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Answers:
a) -F to +F
b) -2F to +2F
c) -3F to +3F
d) -4F to +

A Ku band satellite link has a carrier frequency of 14.125 GHz and carries a symbol stream at Rs = 40 Msps. The transmitter and receiver have ideal RRC filters with ? = 0.25.
a. What is the RF bandwidth occupied by signal?
b. What is the frequency range of the transmitted RF signal?

I am trying to get a feel for Fourier transforms and would like some help.
Please show all work/explanations.
1. Let g(t) = x(2t) - x*(2t- 1/2T0), assume that X(jw) is known
Find G(jw) in terms of X(jw).
2. Let x(t) = 10sin(200t)/t
a) Find X(jw)
b) Let x(t) be the input to a continuous LTI system with impulse response