Fourier Transform: Frequency to Time Domain Relationship

[romsofia]

Is it going from the frequency domain to the time domain? Also, is there a relationship between the Fourier series and transform?

Thanks for your help!

 

[zhermes]

Is it going from the frequency domain to the time domain?

That is one possible application, although there are many others. That is the general idea though.

Also, is there a relationship between the Fourier series and transform?

Yes. The Fourier series expresses a function as an infinite series of discrete terms. The Fourier transform uses the same idea, except it converts the function to a continuous spectrum of terms. That's why the equation switches from a Sum, to an Integral.

 

[mathman]

Fourier series represent functions which are defined on a finite interval and periodic over the rest of the real line. Fourier integrals represent functions which are defined (and integrable in some sense, usually L1 or L2) over the entire real line.

 

[romsofia]

That is one possible application, although there are many others. That is the general idea though.


Yes. The Fourier series expresses a function as an infinite series of discrete terms. The Fourier transform uses the same idea, except it converts the function to a continuous spectrum of terms. That's why the equation switches from a Sum, to an Integral.

Fourier series represent functions which are defined on a finite interval and periodic over the rest of the real line. Fourier integrals represent functions which are defined (and integrable in some sense, usually L1 or L2) over the entire real line.

Thank you both for your help :D