Answer Happy

1. Based on Figure 1, calculate the Fourier Transform of the functions and validate whether the results indicate the symmetry property of even functions. x₁ (1) 2 -2 0 Figure 1 2. Figure 2, shows the convolution systems consisting of the input, x(t), output response, y(t), and the impulse response, h(t). The convolution of the input, x(t), and the impulse response, h(t) produces the output response, y(t). Sometimes the convolution integral is difficult to solve analytically in the time domain. By using the property, the output response can be obtained by using the Continuous-Time Fourier Transform (CTFT). In simple words, the convolution between two signals in the time domain is equivalent to the multiplication of the CTFTs of the two signals in the frequency domain. Based on that, if x(t) = e¯¹u(t) and h(t) = e-²tu(t) verify the results of the output response, y(t) = (e-t-e-²t)u(t) using the CTFT approach. x(t). h(t) Y(1) Figure 2 2