Question

Explain qualitatively how the Fourier transform can be used to analyse the frequency components present in a time-varying signal. If a signal has a finite duration ΔT, what implication does this have for the range of frequencies present in the signal?

Answer 1

any periodic signal can be decomposed into a sum of integrals of sine waves having differnt frequncies. each of this repersents a frequency compoenet. any given signal can be converted between teh tiem and frequency domains by using these fourier transoforms. the spectrum of thses frequency components repsrent the frequency domain of the signal.

Any kind of wave can be easily be tranformed into sinusoidal signals using these transformation functions,as they reduces the complexity.

if the signal has a finite duration of deltat, then the range of frequencies will take the form,

here s(t) is the transform function and t is the initial time.