11.3.8 Convolution of Functions

Condition: function \ (f \) is a broken one, connecting the points \ (a, b, c, d, e, f \). To the left of the point \ (a \) and to the right of the point \ (f \) it is zero. The function \ (G \) is set by the formula: \ (G (x) = \ Operatorname {RECT} X \). Find: a) transformation of Fourier functions \ (f \), using the converting Fourier of standard functions rect \ (x \) and \ (\ lambda (x) \), as well as the properties of Fourier transformation; b) the transformation of the Fourier of the package \ (f * g \). \ (A (0.2), b (1.1), C (2.1), \ quad D (4.3), \ quad E (5.3), \ Q