How do you calculate the Fourier transform of a function?
For a general real function, the Fourier transform will have both real and imaginary parts. We can write f˜(k)=f˜c(k)+if˜ s(k) (18) where f˜ s(k) is the Fourier sine transform and f˜c(k) the Fourier cosine transform. One hardly ever uses Fourier sine and cosine transforms. We practically always talk about the complex Fourier transform.
Is the Fourier transform real or imaginary?
Fourier transform is purely imaginary. For a general real function, the Fourier transform will have both real and imaginary parts. We can write f˜(k)=f˜c(k)+if˜ s(k) (18) where f˜ s(k) is the Fourier sine transform and f˜c(k) the Fourier cosine transform. One hardly ever uses Fourier sine and cosine transforms.
How is delay interpreted in the Fourier transform?
Translation (that is, delay) in the time domain is interpreted as complex phase shifts in the frequency domain. In the second row is shown g(t), a delayed unit pulse, beside the real and imaginary parts of the Fourier transform.
What is the difference between Fourier transform and wavelet transform?
These can be generalizations of the Fourier transform, such as the short-time Fourier transform or fractional Fourier transform, or other functions to represent signals, as in wavelet transforms and chirplet transforms, with the wavelet analog of the (continuous) Fourier transform being the continuous wavelet transform.
What is the Fourier pair of G(T) and G(F)?
In addition, g can be obtained from G via the inverse Fourier Transform: Equation [2] states that we can obtain the original function g (t) from the function G (f) via the inverse Fourier transform. As a result, g (t) and G (f) form a Fourier Pair: they are distinct representations of the same underlying identity.