Fourier Transform of Basic Signals (Complex Exponential Signal)

Signal and System: Fourier Transform of Basic Signals (Complex Exponential Signal)
Topics Discussed:
1. Fourier transform of e^jω₀t.

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[AshwaniYadavIIT]

*Easy Solution: Apply shifting property in frequency domain*
consider x(t) = 1 . e^jw0t
FT{dc value} = FT{1} = 1.2PI.delta(w)
using frequency shifting property we can write
FT{1.e^jwot} = 1.2PI.delta(w - w0)

Hope it helps! XD

[rationalthinker]

Where did you get d(w-wo) ??? It just magically appeared in your head and you decided to use it?

[PankajKumareeb]

The fourier transform of 1 is 2πdelta(w), so using property of frequency shifting e^jw0t has fourier transform e^[j(w-w0)]

[c.cody.]

professor how do we know that x'(t) = delta (w -w0) ? because in the previous video about F.T. of DC value 1 you stated that x"(t) = delta (w) only so why is it different this time?

[ninepuchar]

May I ask, here omega(w) is angular velocity(rad/s) or frequency(Hz)?

[দূরন্তপথ-চ৯গ]

find the output of an LTI system for a complex exponential input x(t) = e^(jωt).



Solution plz

[venkateswarluguntaka]

Sir why you considered X'(w)= del(w-w0), is it necessary to consider del or we can consider other functions

[anirudhnarva]

can we consider 1 and its furiers transform and multiply both sides with e ^j (omega not) t and apply frequency shifting property

[vhvines]

x(t) = e^jw0t u(t) if that is the question then the answer will be the same as shown in video if not kindly provide solution for it

[kondababuamaradi]

draw magnitude and phase spectrum of above signal

[solomonp]

Sir please provide answers to previous homework problems in comment section of respective videos.

[therandomgamerofficial]

Can any one tell me with steps on how to find the Fourier Transform of e^j2pifct??

[manishadas]

sir how did u consider that value of x'(w) all of a sudden?? plz answer i am confused