Problem 2 The periodic triangular wave shown below has Fourier series coefficients ak sin(kr/2) ak=13(km)2eP,k≠0 k=0 Consider the LTI system with frequency response HGw) depicted below y() 23-2-91g192g2 Determine values of A1, A2, A3, 01, Q2, and @3 of the LTI filter H(u)such that y(t)=1-cos At the beginning, it is worth noting that the output y(t) contains only a dC component and a single sinusoid with a frequency of 3. H(jw)is a linear system so the output will only have frequency components that exit in the input. Knowing that the input a (t) has a dC component and a fundamental frequency of wo= 3, let's dissect y(t) into a DC component� � � Problem 2 The periodic triangular wave shown below has Fourier series coefficients ak. x(t) � �2 sin(kω/2)e−jk�/2 ⎧ , k ≤= 0 j(kω)2 1 ak = ⎧� 1 , k = 0. 2 · · · · · · −4 −2 0 2 4 t Consider the LTI system with frequency response H(j�) depicted below: H(j�) x(t) H( ) j� y(t) −�3 −�2 −�1 �1 �2 �3 � A1 A2 A3 Determine values of A1, A2, A3, �1, �2, and �3 of the LTI filter H(j�) such that 3ω y(t) = 1 − cos t . 2 At the beginning, it is worth noting that the output y(t) contains only a DC component and a single sinusoid with a frequency of 3 2 � . H(j�) is a linear system so the output will only have frequency components that exit in the input. Knowing that the input x(t) has a DC component and a fundamental frequency of �0 = 2 , let’s dissect y(t) into a DC component 5