Mathematics II20795 marksNumerical: linear independence of signalsApplications to difference equations
Verify that 1k, -2k, 3k are linearly independent signals.
Verify that $1k$, $-2^k$, $3^k$ are linearly independent signals. [5]
Three discrete-time signals: - $f1(k) = 1^k$ - $f2(k) = (-2)^k$ - $f3(k) = 3^k$ Task: verify they are linearly independent. Signals are linearly independent if $$C1 f1(k) + C2 f2(k) + C3 f3(k) = 0 \quad \text{for all } k$$ forces $C1 = C2 = C3 = 0$. $$C1(1)^k + C2(-2)^k + C3(3)^k = 0 \quad \foral...