the Fourier Transform

property of sinusoid

Hello everyone ^^

Why I can say "The Fourier transform tells us " how much sinusoid" there is in the waveform at a given frequency "w""

Form Linear circuit analysis by Artice M. David

thanks a lot

cause in fourier transform u can get x(f) then just substitute by the freq. u want and thats it u get the amplitude at a certain frequency

hi
By Fourier transform we have simple caculation for linear circuit analysis.∫

∫f(t)dt----------->jwF(w)
d/dt(f(t) -------->1/jw F(w)

Hi

As you have posted
Why I can say "The Fourier transform tells us " how much sinusoid" there is in the waveform at a given frequency "w""

Form Linear circuit analysis by Artice M. David


First start it this way, when you find the fourier series for a periodic signal is given as

F = A0 + ∑B0×sin(wt) + ∑B1×cos(wt)

You see that when you perform fourier transform of a periodic signal you get the spectral components in terms of a DC signal , a sin wave and a cosine wave.
So whatever may be the signal it can be decomposed into its spectral components which are only sin and cosine.
For example fourier transform of square waves gives only odd harmonics of sine wave. You can generate a square wave by adding all the odd harmonics of sine wave.

Thanks
Shaikh Sarfraz

Added after 28 seconds:


Hi

As you have posted
Why I can say "The Fourier transform tells us " how much sinusoid" there is in the waveform at a given frequency "w""

Form Linear circuit analysis by Artice M. David


First start it this way, when you find the fourier series for a periodic signal is given as

F = A0 + ∑B0×sin(wt) + ∑B1×cos(wt)

You see that when you perform fourier transform of a periodic signal you get the spectral components in terms of a DC signal , a sin wave and a cosine wave.
So whatever may be the signal it can be decomposed into its spectral components which are only sin and cosine.
For example fourier transform of square waves gives only odd harmonics of sine wave. You can generate a square wave by adding all the odd harmonics of sine wave.

Thanks
Shaikh Sarfraz

when u take a signal of frequency fc,then it is always advisable to assume it to be sinusoidal signal.The special property of sinusoid is that the output of a linear system fed with sinusoid is also a sinusoid.That is why fourier transform also gives sinusoidal components.