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- Convolution theorem
- Let $\mathfrak{F}$, $*$, and $\cdot$ denote the Fourier transform, convolution, and point-wise multiplication, respectively. The convolution theorem states

- Discrete Fourier transform
- The discrete Fourier transform is derived from the Fourier series. The Fourier series is expressed as

- Fourier transform of the Gaussian function
- The Fourier transform of Eq. \eqref{eq:gaussian} can be written as

- GISC 4360K - Digital Image Processing
- Fourier transform

- Introduction to the discrete Fourier transform
- The Fourier transform is a special case of the Fourier series where $T\rightarrow\infty$.

- Shift theorem
- Let $\mathfrak{F}$ denote the Fourier transform. The shift theorem states