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Suppose we have a sine voltage supplied to a resistive load. When I perform a Fourier transform to this signal in the frequency domain what do I get? All values of g(a) will be 0 except for the frequency of my sine signal?

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    \$\begingroup\$ In pure math you can have a sine voltage which has never started, it has been on from minus eternity and goes on to plus eternity. That sine voltage has just a single frequency component. All practical sinewaves start and stop. One should tell when these things happen and what kind of startup and winding down transients there happens. One popular solution is to calculate Fourier transforms only during a certain time interval and assume the signal during that interval has repeated & repeats eternally. In Fourier transform math one also meets obscurities: negative frequency and complex numbers \$\endgroup\$
    – user287001
    Oct 15 at 17:13
  • \$\begingroup\$ Yes, you will have infinite amplitude spikes at the positive and negative frequency, and it will be zero everywhere else. This is for the continuous time Fourier transform, not the discrete transform. \$\endgroup\$
    – mkeith
    Oct 16 at 3:13
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Yes, that is correct. Since there are no harmonics in a sine (other than the fundamental) there will only be that frequency in the transform.

enter image description here

Figure 1. This fabulous illustration of the Fourier Transform by Lucas V. Barbosa on Wikipedia's Fourier transform page shows the transformation of a periodic waveform from the time domain to the frequency domain. The frequency plot shows the relative strength of the harmonics with clarity that could not be obtained from staring at the time plot.

  • It should be apparent that the more square the time domain waveform is then the more harmonics you will have and these should be visible in the frequency domain.
  • It should also be clear that the amplitude decreases with the increasing frequency.

For your question it should also be clear that you only have the fundanmental (largest blue sine signal) in the composite signal and therefore only have the first frequency line in the Fourier transform.

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    \$\begingroup\$ Love the animation junction! \$\endgroup\$ Oct 15 at 19:10
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The sine function can be Fourier transformed only using distributions and the result is a summation of two Dirac's delta distributions centered at +f and -f, multiplied by i where i is the imaginary unit.

That distribution is imaginary.

Take a look here:

https://math.stackexchange.com/questions/106476/fourier-transform-of-sine-and-cosine-function.

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