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These are the first 8 terms in the Fourier series of the periodic square wave shown in [link] .
Run the model by selecting
Start under the
Simulation menu.
A graph will pop up that shows the synthesized square wave signaland its spectrum.
This is the output of the
Spectrum Analyzer .
After the simulation runs for a while,the
Spectrum Analyzer element will update
the plot of the spectral energy and the incoming waveform.Notice that the energy is concentrated in peaks corresponding
to the individual sine waves.Print the output of the
Spectrum Analyzer .
You may have a closer look at the synthesized signal
by double clicking on the
Scope1 icon.
You can also see a plot of all the individual sine wavesby double clicking on the
Scope2 icon.
Synthesize the two periodic waveforms defined in the
"Synthesis of Periodic Signals" section of the background exercises.
Do this by setting the frequency, amplitude, and phaseof each sinewave generator to the proper values.
For each case, print the output of the
Spectrum Analyzer .
Spectrum Analyzer output
for each of the three synthesized waveforms.For each case, comment on how the synthesized waveform
differs from the desired signal, and on the structureof the spectral density.
Double click the icon labeled
Modulator to bring up a system as shown in
[link] .
This system modulates a triangular pulse signal with a sine wave.You can control the duration and duty cycle of the triangular
envelope and the frequency of the modulating sine wave.The system also contains a spectrum analyzer which plots
the modulated signal and its spectrum.
Generate the following signals by adjusting the
Time values and
Output values of the
Repeating Sequence block and the
Frequency of the
Sine Wave . The
Time values vector
contains entries spanning one period of the repeating signal.The
Output values vector
contains the values of the repeating signal at the times specifiedin the
Time values vector. Note that the
Repeating Sequence block
does NOT create a discrete time signal. It creates a continuous time signalby connecting the output values with line segments.
Print the output of the
Spectrum Analyzer for each signal.
Notice that the spectrum of the modulated signal consists of of a comb of impulses in the frequency domain,arranged around a center frequency.
Spectrum Analyzer for each signal.
Answer following questions:1) What effect does changing the modulating frequency
have on the spectral density?2) Why does the spectrum have a comb structure and what
is the spectral distance between impulses? Why?3) What would happen to the spectral density if the period of the
triangle pulse were to increase toward infinity? (in the limit)
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