neptune
Member
Hello,
I have a confusion on how fourier transform works fourier transform is defined as
F(ω) = ∫ f(t).e-jωt dt limits -∞ to ∞
which can be expanded to F(ω) = ∫ f(t). (cosjωt + jsinωt) dt
these cosine and sine wave are extrapolated on F(t) signal , their resultant is calculated by adding sin and cosine waves amplitude to f(t)'s amplitude at a all time t.
then in step 2 frequency ω is varied, and then again resultant is calculated by above process , we repeat this process to plot frequency and amplitude graph of a given signal f(t).
Q1 - is my basic understanding correct ?
Q2 - why do we use imaginary term j with sine wave , cant we simply use sine wave here. (sine and cosine are orthogonal functions out of phase by 90 degrees)
I have a confusion on how fourier transform works fourier transform is defined as
F(ω) = ∫ f(t).e-jωt dt limits -∞ to ∞
which can be expanded to F(ω) = ∫ f(t). (cosjωt + jsinωt) dt
these cosine and sine wave are extrapolated on F(t) signal , their resultant is calculated by adding sin and cosine waves amplitude to f(t)'s amplitude at a all time t.
then in step 2 frequency ω is varied, and then again resultant is calculated by above process , we repeat this process to plot frequency and amplitude graph of a given signal f(t).
Q1 - is my basic understanding correct ?
Q2 - why do we use imaginary term j with sine wave , cant we simply use sine wave here. (sine and cosine are orthogonal functions out of phase by 90 degrees)