Plot Components of the FT

The Fourier transform, named for Joseph Fourier, is a mathematical transformation used to transform signals between the time (or space) domain and the frequency domain, which has many applications in physics and engineering.

FT uses an input function consisting of a real and an imaginary part. The output function resulting from the FT will thus also have a real and an imaginary component. The characteristics of the image that we are going to analyse: -Amplitude: measure of the maximum variation of the displacement or other physical quantity that varies periodically or quasi-periodically in time. It is the distance between the farthest point of a wave and the equilibrium or middle point.

-Power Spectral density (PSD)= refers to the spectral energy distribution that would be found per unit time, since the total energy of such a signal over all time would generally be infinite. Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process), identical to what would be obtained by integrating over the time domain, as dictated by Parseval's theorem. The formula os the psd in matlab is: 10*log10(abs(fftshift(fft2(gray))).^2 )

-Real and imaginary part= The images are real functions and their Fourier transforms are complex functions with real part and imaginary part (as it can be seen in the formula of the FT)

-Phase: The phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the number of periods spanned by that variable.

In the interface, at the left side, you have images of the power density spectrum, the real and the imaginary part of the image,at in the right side you can choose which function (the amplitude, the psd, the real part, the imaginary part and the phase) you want to plot, you cant overlap plots, but you can see all of them in a logaritmic or linear way DEMO: