Sufficiently i 2kn m qk qne qk qne n 0km ii

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Unformatted text preview: = 0 ; n<0 15 15 Algorithm: Given the coefficients q[n] of the polynomial Q(z): i. Compute the M-point DFT of q[n] for a point sufficiently large M. sufficiently -i 2πkn M Q[k] = ∑ q[n]e Q[k] q[n]e n ; 0≤k<M ii. Take the logarithm. ^ Q[k] = ln (Q[k]) Q[k] ln iii. Determine the complex cepstrum of q[n] by Determine cepstrum of computing the IDFT. computing M - 1^ i 2π nk 1 ^ q[n] = ∑ Q[k] e M Q[k] M k=0 16 16 ½^ q[0] ^ q[n] 0 ; n=0 ; n>0 ; n<0 678 678 ^ r[n] = 678 ^ iv. Find the causal part of q[n]. v. Determine the DFT of r[n] by computing the Determine exponent of the DFT of ^ r[n]. exponent M-1 ^ –i 2π kn ^ R[k] = exp (R[k]) = exp ( ∑ r[n]e M kn) ; 0 ≤ k < M R[k] k=0 17 17 vi. Determine the DFT of h0[n], by including half the [n], zeros at z = -1. 2π k – i M )p H0[k] = R[k] (1 + e vii. Compute the IDFT to get h0[n]. vii. h0[n] = [n] 1 M-1 ∑ H [k] M k = 0 0[k] 2π ei M nk 18 18...
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