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:
- Frequency time domain.jpg
freq_domain
The time domain of output shown in oscilloscope will be:
time_domain
