A signal f is a function of the location (x,y), given by: f = sin[2(u₀x+v₀y)]+2, where u₀ and v₀ are the spatial frequencies (/mm) of x and y directions, respectively. The response of an imaging system to the input signal f is given by: g(x,y) = 0.5sin[2(u₀x+v₀y)]+1. Seat the frequencies, u₀ and v₀, to the inverse number of 7 and 11 respectively. u₀=1/7 (/mm) and v₀=1/11 (/mm). Then, calculate f in the range of 0 x,y 150 mm (1mm step) using Matlab.

• Attach your Matlab code in your answer.
• to create [x,y] data, you may use meshgrid.

(a) Obtain 2-D spatial frequency spectrum of the signal f using fft2 and show its magnitude (you may use abs) in image display. To set the center of the image display at the origin of the spatial frequency domain, i.e. (0,0), use fftshift. Label the axis, Frequency, u [1/mm], Frequency, v [1/mm], respectively.

(b) What is the range of the spatial frequency domain (u and v) obtained? Justify your answer.

(c) What are the frequency components of the signal f observed in the spectrum obtained in (d)?