Fourier Transform of Basic Signals (Complex Exponential Signal)

[@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

[@thiruvazhidhinesh1903]

Yeahhhh broo

[@starkendeavours7072]

Easiest solution! Lovely bro.🤞🏻

[@rationalthinker9612]

Way better rationalization, he literally just pulled that other crap right out of his butt with zero explanation as to why he decided to randomly pick d(w-wo)

[@SagarKumar-zv8vq]

What does XD mean..? 🤔

[@kuntalparashar3376]

@@SagarKumar-zv8vq happiness or laughter

[@rationalthinker9612]

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.3886]

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?

[@venkateswarluguntaka7370]

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

[@sreeharshaparuchuri6115]

yes, it is necessary to consider the del function as it is zero at everywhere but w0, thus we can easily evaluate the integral.

[@ninepuchar1]

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

[@phanindrareddy4885]

Superb sir and awesome

[@anirudhnarva3141]

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

[@tokkachaitanya2233]

kathal mingakunda notes rasko

[@anirudhnarva3141]

@@tokkachaitanya2233 ninja nee pan nuv chusko

[@tokkachaitanya2233]

Bayya..sorry...chill@ok na

[@tokkachaitanya2233]

@@anirudhnarva3141 bayya...sorry chill...ok na

[@kondababuamaradi2073]

draw magnitude and phase spectrum of above signal

[@manishadas7434]

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

[@babayaga1698]

He is giving an example of taking Fourier transformation of signal x(t') , as x(w') then using inverse Fourier transformation

[@manishadas7434]

i couldnt still catch up..but i might understand gradually

[@mihirvaghela2185]

You don't need to do this actually.. We know Fourier transform of 1 is 2π*del(w) Now here by using frequency shifting property i.e x(t) * e^(j*Wo*t) = X(W-Wo) If we simply multiply exponential term to 1 then on the other side we will get 2π*Del(W-Wo) minus sign because we multiplied e^(j*Wo*t)

[@ShivamSharma-db7xn]

@@mihirvaghela2185: So where did 2π at the beginning go for the expression of X'(w)?

[@ShivamSharma-db7xn]

Cuz, then further solution steps wouldn't be required then??

[@therandomgamerofficial]

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

[@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

[@solomonp8960]

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

[@HEMANTPORWAL-t7d]

1000th like

[@athalal.ghufaily7275]

What does the j notates?

[@snehasishbanerjee1525]

@athal it means it is complx term

[@vloggetts]

it's sometimes used instead of i but it means the same thing

[@vigneshsivashankar156]

Electrical engineers use j to represent the square root of 1 because 'i' represents current