Study Objective:
Understanding the Fourier Theory-Frequency Domain and Time DomainIntroduction:
Communications systems are normally studied using sinusoidal voltage waveforms to simplify the analysis. In the real world, electrical information signals are normally non-sinusoidal voltage waveforms, such as audio signals, video signals, or computer data. Fourier theory provides a powerful means of analyzing communications systems by representing a non-sinusoidal signal as a series of sinusoidal voltages added together. Fourier theory states that a complex voltage waveform is essentially a composite of harmonically related sine or cosine waves at different frequencies and amplitudes determined by the particular signal voltage wave-shape. Any non-sinusoidal periodic waveform can be broken down into a sine or cosine wave equal to the frequency of the periodic waveform, called the fundamental frequency, and a series of sine or cosine waves that are integer multiples of the fundamental frequency, called harmonics. This series of sine or cosine waves is called a Fourier series.Useful equations:
EMBED Equation.3 (1)EMBED Equation.3 (2)
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EMBED Equation.3 (4)
Square wave Fourier series:
EMBED Equation.3 (5)
Triangular wave Fourier series:
EMBED Equation.3 (6)
Experiment Items:
Item one (1): square wave signal
Experiment Procedures
Connect the circuit shown in fig. 1, then run the simulation. This circuit will generate square wave from these sinusoidal sources.
Now draw the oscilloscope and spectrum analyzer output.
Start closing the switches one by one and notice the effect of each one on the signal waveform and spectrum then record that.
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Fig. (1)
1.2 comparesion with ideal square signal
(1) Modify the circuit in fig. 1 to be look like that in the fig. 2 and compare the output of the two cases.
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Item two (2): Triangular wave signal
2.1 Experiment Procedures(1) Draw the circuit in the fig. 3. This circuit will generate triangular wave, run the simulation, then check and draw the output waveform and spectrum.
Study the effect of each switch on the output and record that.
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Fig. (3)2.2 Experiment Procedures
Now connect function generator as shown in fig. 4, to produce a triangular wave to make a comparison between the signals.EMBED Multisim.Document
Fig. (4)
Discussion:
What is the relationship between the fundamental sine wave frequency and the square wave frequency (f)?Comment on the effect of the switches on the output for the two waves.
What do you learn from this experiment?
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Experiment No. (4)
Fourier Theory-Frequency Domain and Time Domain