| (5 intermediate revisions by the same user not shown) | |||
| Line 3: | Line 3: | ||
=Approximating Periodic Signals with Finite Fourier Series= | =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. | |
| + | |||
| + | <gallery> | ||
| + | File:code.png|square.m | ||
| + | </gallery> | ||
| + | |||
| + | When there are only 1 non-zero term, the time and frequency domain are shown below: | ||
| + | |||
| + | <gallery> | ||
| + | File:time1.jpeg|1.time | ||
| + | File:1freq.jpg|1.freq | ||
| + | </gallery> | ||
| + | |||
| + | When 2 non-zero terms | ||
| + | |||
| + | <gallery> | ||
| + | File:time2.jpg|2.time | ||
| + | File:freq2.jpg|2.freq | ||
| + | </gallery> | ||
| + | |||
| + | |||
| + | When 5 non-zeros terms | ||
| + | |||
| + | <gallery> | ||
| + | File:time5.jpg|5.time | ||
| + | File:freq5.jpg|5.freq | ||
| + | </gallery> | ||
| + | |||
| + | |||
| + | When there are 25 non-zero terms | ||
| + | |||
| + | <gallery> | ||
| + | File:time25.jpg|25.time | ||
| + | File:freq25.jpg|25.freq | ||
| + | </gallery> | ||
| + | |||
| + | |||
| + | 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 | ||
| + | |||
| + | <gallery> | ||
| + | File:square_circuit.png|circuit | ||
| + | |||
| + | </gallery> | ||
| + | |||
| + | |||
| + | |||
| + | For example, we set s(t) to be square wave with A = 3V, T0 = 0.5*10^-6s | ||
| + | |||
| + | |||
| + | <gallery> | ||
| + | File:square_wave.png|s(t) | ||
| + | |||
| + | </gallery> | ||
| + | |||
| + | The frequency domain of output shown in spectrum analyzer will be: | ||
| + | <gallery> | ||
| + | File:output_frequency_domain.jpg|freq_domain | ||
| + | |||
| + | </gallery> | ||
| + | |||
| + | |||
| + | The time domain of output shown in oscilloscope will be: | ||
| + | |||
| + | <gallery> | ||
| + | File:output_time_domain.png|time_domain | ||
| + | |||
| + | </gallery> | ||
| + | |||
Latest revision as of 15:42, 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.
square.m
When there are only 1 non-zero term, the time and frequency domain are shown below:
1.time
1.freq
When 2 non-zero terms
2.time
2.freq
When 5 non-zeros terms
5.time
5.freq
When there are 25 non-zero terms
25.time
25.freq
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
circuit
For example, we set s(t) to be square wave with A = 3V, T0 = 0.5*10^-6s
s(t)
The frequency domain of output shown in spectrum analyzer will be:
freq_domain
The time domain of output shown in oscilloscope will be:
time_domain
