5. y[n] = E-0x[n – k] 6. y[n] = Ek--1 x[kn] 7. y[n] = E--2 x[kn – k] %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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For the systems below. Check all the systems properties( memory, inevitability, causality, time Invariant, linearity, and stability) and justify your answers.

Below are equations representing discrete-time signal processing operations:

5. \( y[n] = \sum_{k=0}^{2} x[n-k] \)

6. \( y[n] = \sum_{k=-1}^{1} x[kn] \)

7. \( y[n] = \sum_{k=-2}^{0} x[kn-k] \)

Each equation describes how the output signal \( y[n] \) is computed as a weighted sum over the input signal \( x \) at different indices, using specific index transformations and range limits for the summation.
Transcribed Image Text:Below are equations representing discrete-time signal processing operations: 5. \( y[n] = \sum_{k=0}^{2} x[n-k] \) 6. \( y[n] = \sum_{k=-1}^{1} x[kn] \) 7. \( y[n] = \sum_{k=-2}^{0} x[kn-k] \) Each equation describes how the output signal \( y[n] \) is computed as a weighted sum over the input signal \( x \) at different indices, using specific index transformations and range limits for the summation.
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