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Given the sequence v(n) and its z-transform V(z), determine the z-transform of the following sequences:

v₁(n) = v(−n)

User Killa
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1 Answer

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Final answer:

To find the z-transform of v₁(n) = v(-n), substitute n with -n in the original z-transform V(z), resulting in V(z⁻¹) due to the time-reversal property of the z-transform.

Step-by-step explanation:

The z-transform of a sequence v(n) is a powerful tool in analyzing and solving difference equations and systems in the discrete-time domain. When trying to find the z-transform of the time-reversed sequence v1(n) = v(-n), one can use the property of time reversal in z-transforms. To find the z-transform of v1(n), we would substitute n with -n in the original z-transform V(z). Mathematically, if V(z) is the z-transform of v(n), then the z-transform of v1(n) is V(z-1). This is because z-transform involves zn terms, and reversing time would replace n with -n, hence introducing a reciprocal of z in the power.

User Rectangletangle
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