6. Given a long, causal impulse response h(n), we want to develop an IIR filter transfer...

Transcribed Image Text:

6. Given a long, causal impulse response h(n), we want to develop an IIR filter transfer function H(z) where a + bz + cz" H(z) = 1+dz +ez? (a) Give a difference equation that generates h(n) using the coefficients of H(z). (b) Using the proper values of n in part (a), give the equations for h(0), h(1), and h(2). Solving the equation for h(0), give the value for one of the coefficients in H(z). (c) Give as many additional equations for h(n), so that the numbers of equations for h(n) equals the number of unknowns in H(z). (d) Write the set of linear equations from parts (b) and (c) in matrix vector form, Ax = b remembering that values of h(n) are knowns and that the coefficients of H(z) are unknowns. 6. Given a long, causal impulse response h(n), we want to develop an IIR filter transfer function H(z) where a + bz + cz" H(z) = 1+dz +ez? (a) Give a difference equation that generates h(n) using the coefficients of H(z). (b) Using the proper values of n in part (a), give the equations for h(0), h(1), and h(2). Solving the equation for h(0), give the value for one of the coefficients in H(z). (c) Give as many additional equations for h(n), so that the numbers of equations for h(n) equals the number of unknowns in H(z). (d) Write the set of linear equations from parts (b) and (c) in matrix vector form, Ax = b remembering that values of h(n) are knowns and that the coefficients of H(z) are unknowns.

Answer rating: 100% (QA)

Sal Given data abzCz2 Id2ez2 O To find or delermme th... View the full answer