Question 24.34: Find the circular correlation f ⊛ g when f[n] = 8, -9, 3, 2 ......
Find the circular correlation f ⊛ g when f[n] = 8, -9, 3, 2 and g[n] = 11, 4, -1, -5.
Step-by-Step
Either directly from the definition of the d.f.t., or by using a computer package, we can show that
F[k]=4,5+11 \mathrm{j}, 18,5-11 \mathrm{j} \quad G[k]=9,12-9 \mathrm{j}, 11,12+9 \mathrm{j}The conjugate of G[k] \text { is } \overline{G[k]}=9,12+9 \mathrm{j}, 11,12-9 \mathrm{j} \text {. } Then
F[k] \overline{G[k]}=36,-39+177 \mathrm{j}, 198,-39-177 \mathrm{j}Either directly, or using a computer package, taking the inverse d.f.t. yields the sequence
39,-129,78,48
which is the required circular correlation. You may like to verify this by directly calculating f ⊛ g.
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