We consider the elementary signals of the form x(t)=a0 2 + a1·cos2pt + b1·sin2pt + a2·cos4pt +...

We consider the elementary signals of the form x(t)=a0 2 + a1·cos2pt + b1·sin2pt + a2·cos4pt + b2·sin4pt + a3·cos6pt + b3 ·sin6pt + a4 2 ·cos8pt. Construct a low-pass ?lter by means of a digital ?lter: Sampling to the order 8, digital ?ltering of the discrete 8-periodic signal, trigonometric interpolation of the output values. The result of the ?ltering of x(t)=a0 2 + a1·cos2pt + b1·sin2pt + a2·cos4pt + b2·sin4pt + a3·cos6pt + b3 ·sin6pt + a4 2 ·cos8ptshould be ˜ x(t)=˜ a0 2 +˜ a1 ·cos2pt+˜ b1 ·sin2pt+˜ a2 ·cos4pt+˜ b2 ·sin4pt+˜ a3 ·cos6pt+˜ b3 · sin6pt+ ˜ a4 2 ·cos8pt = a0 2 + a1 ·cos2pt+ b1 ·sin2pt+ a2 ·cos4pt+ b2 ·sin4pt. (a) Find the impulse response h = : h0,h1,...,h7 : of the digital ?lter to be constructed. (b) A little test: Sample x(t) = cos6pt to the order 8, ?lter the sample values by Th and verify that the result is indeed the zero vector.