Difference between revisions of "Talk:Video/The imaginary number i and the Fourier Transform"
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Fourier transform integral | Fourier transform integral : | ||
<math>\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-i 2\pi \xi x}\,dx,\quad \forall\ \xi \in \mathbb R.</math> | <math>\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-i 2\pi \xi x}\,dx,\quad \forall\ \xi \in \mathbb R.</math> | ||
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We have a signal called x(t) in time we will represent it in terms of the time domain. We also can represent it in another way which is called x(f) we will represent it in terms of the frequency domain and This is why we called transformation. Fourier Transform is an equivalent representation of the signal. | We have a signal called x(t) in time we will represent it in terms of the time domain. We also can represent it in another way which is called x(f) we will represent it in terms of the frequency domain and This is why we called transformation. Fourier Transform is an equivalent representation of the signal. | ||
Convolution equation : | |||
<math>(f * g)(t) := \int_{-\infty}^\infty f(\tau) g(t - \tau) \, d\tau.</math> | <math>(f * g)(t) := \int_{-\infty}^\infty f(\tau) g(t - \tau) \, d\tau.</math> | ||
Revision as of 00:14, 27 July 2022
Fourier transform integral :
Example for Fourier transform: We have a signal called x(t) in time we will represent it in terms of the time domain. We also can represent it in another way which is called x(f) we will represent it in terms of the frequency domain and This is why we called transformation. Fourier Transform is an equivalent representation of the signal.
Convolution equation :
