# 0.3 Lab 3 - frequency analysis  (Page 3/4)

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$x\left(t\right)=0+\sum _{\genfrac{}{}{0pt}{}{k=1}{k\phantom{\rule{0.166667em}{0ex}}\text{odd}}}^{13}\frac{4}{k\pi }sin\left(2\pi kt\right)\phantom{\rule{4pt}{0ex}}.$

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 .

Hand in plots of the 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.

## Modulation property

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.

1. Triangular pulse duration of 1 sec; period of 2 sec; modulating frequency of 10 Hz (initial settings of the experiment).
2. Triangular pulse duration of 1 sec; period of 2 sec; modulating frequency of 15 Hz.
3. Triangular pulse duration of 1 sec; period of 3 sec; modulating frequency of 10 Hz.
4. Triangular pulse duration of 1 sec; period of 6 sec; modulating frequency of 10 Hz.

Notice that the spectrum of the modulated signal consists of of a comb of impulses in the frequency domain,arranged around a center frequency.

Hand in plots of the output of the 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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William
currently
William
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nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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learn
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da
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Bhagvanji
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Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
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Kamaluddeen
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narayan
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ya I also want to know the raman spectra
Bhagvanji
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Damian
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Professor
I think
Professor
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Alexandre
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Rafiq
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Damian
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LITNING
scanning tunneling microscope
Sahil
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Santosh
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Rafiq
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Mahi
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Rafiq
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Anam
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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Bob
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brayan
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Damian
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
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