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In this project, a matlab function will be used to show how a finite number of Fourier Series coefficients can approximate a periodic signal.  
 
In this project, a matlab function will be used to show how a finite number of Fourier Series coefficients can approximate a periodic signal.  
  
When there are only 1 non-zero term, the time and frequency domain are shown below:
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<gallery>
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File:code.png|square.m
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</gallery>
  
[[Image:code.png]]
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When there are only 1 non-zero term, the time and frequency domain are shown below:
  
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<gallery>
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File:time1.jpeg|1.time
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File:1freq.jpg|1.freq
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</gallery>
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When 2 non-zero terms
 
When 2 non-zero terms
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<gallery>
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File:time2.jpg|2.time
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File:freq2.jpg|2.freq
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</gallery>
 
   
 
   
 
   
 
   
 
When 5 non-zeros terms
 
When 5 non-zeros terms
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<gallery>
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File:time5.jpg|5.time
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File:freq5.jpg|5.freq
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</gallery>
 
   
 
   
 
   
 
   
 
When there are 25 non-zero terms
 
When there are 25 non-zero terms
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<gallery>
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File:time25.jpg|25.time
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File:freq25.jpg|25.freq
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</gallery>
 
   
 
   
 
   
 
   
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A circuit is built to measure the Fourier series  of a Square wave
 
A circuit is built to measure the Fourier series  of a Square wave
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<gallery>
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File:square_circuit.png|circuit
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</gallery>
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For example, we set s(t) to be square wave with A = 3V, T0 = 0.5*10^-6s  
 
For example, we set s(t) to be square wave with A = 3V, T0 = 0.5*10^-6s  
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<gallery>
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File:square_wave.png|s(t)
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</gallery>
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The frequency domain of output shown in spectrum analyzer will be:
 
The frequency domain of output shown in spectrum analyzer will be:
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<gallery>
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File:output_frequency_domain.jpg|freq_domain
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 +
</gallery>
 
   
 
   
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The time domain of output shown in oscilloscope will be:
 
The time domain of output shown in oscilloscope will be:
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<gallery>
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File:output_time_domain.png|time_domain
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 +
</gallery>
 
   
 
   
  

Latest revision as of 16:42, 21 April 2018


Approximating Periodic Signals with Finite Fourier Series

In this project, a matlab function will be used to show how a finite number of Fourier Series coefficients can approximate a periodic signal.

When there are only 1 non-zero term, the time and frequency domain are shown below:

When 2 non-zero terms


When 5 non-zeros terms


When there are 25 non-zero terms


Conclusion: From the above diagrams we are able to distinguish that: As the number of Fourier Series Coefficients increases, the output of approximated periodic signal is more accurate.


A circuit is built to measure the Fourier series of a Square wave


For example, we set s(t) to be square wave with A = 3V, T0 = 0.5*10^-6s


The frequency domain of output shown in spectrum analyzer will be:


The time domain of output shown in oscilloscope will be:




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