Howtosignalprocessing
- Which of the following is the correct statement of Fourier slice theorem?
- Which theorem states that the Fourier transform of a projection is a slice of the 2 D Fourier transform of the region from which the projection was obtained?
- What are the limitations of Fourier Theorem?
- What does the Fourier theorem say?
Which of the following is the correct statement of Fourier slice theorem?
The Fourier Slice Theorem states that the Fourier transform of a projection of a function f(x,y) (1), seen from an angle θ, equals the slice of the fourier transform of f(x,y), F(f(x,y)) = F(ωx, ωy), under that angle θ.
Which theorem states that the Fourier transform of a projection is a slice of the 2 D Fourier transform of the region from which the projection was obtained?
The Fourier-slice theorem or the central slice theorem relates the 1D Fourier transform of a projection with the 2D Fourier transform of the region of the image from which the projection was obtained. The resulting equation is known as the Fourier-slice theorem.
What are the limitations of Fourier Theorem?
A limitation of the Fourier transform is that it's not truly realizable in practice - we can never sample a function for every x∈R! This can be mitigated by the way we do integrals numerically: we do Riemann sums, which naturally require sampling your function anyway!
What does the Fourier theorem say?
FOURIER THEOREM
A mathematical theorem stating that a PERIODIC function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which has specific AMPLITUDE and PHASE coefficients known as Fourier coefficients.
