Regarding the Fourier transform, which of the following characteristics are true

Question

Regarding the Fourier transform, which of the following characteristics are true? the Fourier transform of the sum of two functions FT(f +g) is equal to the sum of the Fourier transforms of the two functions FT(f) + FT(g). the Fourier transform of a convolution of two signals FT(f*g) is equal to the Fourier transform of the first signal divided by the Fourier transform of the second FT(l)/FT(g). the Fourier transform of a Gaussian is also a Gaussian. Answers a and c are true. Answers a, b and c arc true. Which of the following statements is true about the interaction of electromagnetic radiation with matter? Photoelectric absorption involves the interaction of a photon with the nucleus of an atom. Rayleigh scattering involves an inelastic collision of a photon with an outer-shell electron with negligible binding energy, after which that electron is ejected from the atom. the main phenomena associated with X-ray imaging are Rayleigh scattering at low photon energies and pair production at high photon energies. the main phenomena associated with X-ray imaging arc photoelectric absorption at low photon energies and Compton scattering at high photon energies. None of these statements are true.

Explanation / Answer

Answer for Question 1:

Fourier transform of the sum of two functions FT(f+g) is equal to the sum of the Fourier
transforms of the two functions FT(f) + FT(g)

The Fourier transform of a gassian is also a Gaussian

Ans: Option D..i.e both and c are true

Answer for Question 2:

Answer is Option a and d..

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