Question

I've been getting confused with how to actually take a wave and convert into a fourier spectrum and was wondering if I could get an explanation?

Answer 1

To the this topic, we must have knowledge of following terms

Time Period: Duration of time of one cycle in a repeating unit. It is denoted by ' T '.

Frequency: It is defined as the number of occurances of a repeating unit per unit time. It is denoted by ' f '.

It is the inverse of the time period.

For a well defined signal, it is very easy to get the time period and frequency but for a random signal we have

frequency range.

According to Fourier, any kind of periodic singal can be decomposed into sine and cosine whose frequency is the integer multiple of fundamental frequency.

For example: Let be a periodic signal with fundamental frequency , then can be expressed as   

  

The Fourier series expression can be expressed as

......( 1 )

where coefficients can be solved as

,

,

  .

If we want to write fourier series in exponential form, we have

....... ( 2 )

where    ........( 3 )

Now we discuss over the fourier spectrum,

Fourier Spectrum is defined as a plot of the magnitude coefficients versus their corresponding frequencies.

To get the the coefficients, i would suggest to use the equation ( 3 ). It will be provide you coefficients in the form of n.

Then just take the modulus of the coefficients and plot them corresponding to their frequencies.