11.3.8 Convolution of functions

Condition: The function \( f \) is a broken line 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 equal to zero. The function \( g \) is given by the formula: \( g(x)=\operatorname{rect} x \). Find: a) the Fourier transform of the function \( f \), using the Fourier transform of the standard functions rect \( x \) and \( \Lambda(x) \), as well as the properties of the Fourier transform; b) Fourier transform of convolution \( f * g \). \( A(0,2), B(1,1), C(2,1), \quad D(4,3), \quad E(5,3), \q