Recall that I({x_k})= {x_k} and S({x_k}) = {X_k-1}.

Which signals from Table 1 are in the kernel of I - cS for a fixed nonzero scalar c ≠ 1?

Data from in Table 1

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TABLE I Examples of Signals Signals Name delta unit step constant alternating Fibonacci exponential Symbol 8 V X α F Ec Vector (..., 0, 0, 0, 1, 0, 0, 0, ...) (..., 0, 0, 0, 1, 1, 1, 1, ...) (..., 1, 1, 1, 1, 1, 1, 1, ...) (...,-1, 1,-1, 1, 1, 1,-1, ...) (...,2,-1, 1, 0, 1, 1, 2, ...) (...,c-2, c-¹, cº, c¹, c²,...) k = 0 Formal Description {dk}, where d = {uk, where uk = {C}, where ck = 1 {a}, where ak = {f}, where fk = 1 0 ifk = 0 if k 0 ifk ≥ 0 if k < 0 (-1) k 0 1 fk-1 + fk-2 fk+2 fk+1 {ek}, where ek = ck if k = 0 if k = 1 if k > 1 ifk < 0