Question 24.35: Use the d.f.t. to find the circular autocorrelation of the s......
Use the d.f.t. to find the circular autocorrelation of the sequence f[n] = 8, 3, – 1, 2.
Step-by-Step
It is straightforward but tedious to show that the d.f.t. of f[n] is
F[k]=12,9-\mathrm{j}, 2,9+\mathrm{j}Then, the conjugate of F[k] \text { is } \overline{F[k]}=12,9+\mathrm{j}, 2,9-\mathrm{j} \text {, } and
F[k] \overline{F[k]}=144,82,4,82Finally, taking the inverse d.f.t. gives the sequence 78, 35, -4, 35 which you can verify is the circular autocorrelation of f[n] = 8, 3, – 1, 2.
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