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2- Which of the following sequences cannot be a valid Auto Correlation Sequence (ACS)? For each case, explain why the sequence cannot be an ACS? 1 0.5 04 -0.5 -1 + 0.5 -0.5 -1 0.5 0 0 -0.5 -1 Y ان -3 -2 -1 ♡ H N ork of % (c) (e) 1 1 2 3 2 3 2 4 0.5 -0.5 -1 0.5 -0.5 -1 0.5 04 -0.5 7 £ ?? !!.. 1 2 3 रु० (b) (d) of (f) 1 2 1 2 3 3

2- Which of the following sequences cannot be a valid Auto Correlation Sequence (ACS)? For each case, explain why the sequence cannot be an ACS? 1 0.5 04 -0.5 -1 + 0.5 -0.5 -1 0.5 0 0 -0.5 -1 Y ان -3 -2 -1 ♡ H N ork of % (c) (e) 1 1 2 3 2 3 2 4 0.5 -0.5 -1 0.5 -0.5 -1 0.5 04 -0.5 7 £ ?? !!.. 1 2 3 रु० (b) (d) of (f) 1 2 1 2 3 3

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Question:** Which of the following sequences cannot be a valid Auto Correlation Sequence (ACS)? For each case, explain why the sequence cannot be an ACS. **Graph Descriptions:** Each graph is a discrete signal plot showing sequences on the y-axis against the `k` values on the x-axis ranging from -4 to 4. - **Graph (a):** - Symmetric about `k=0` - `k=0` value is 1 - Peaks at `k=-1` and `k=1` are 0.5 - Values decrease symmetrically as `k` moves toward -3 and 3 - **Graph (b):** - Symmetric about `k=0` - `k=0` value is 1 - Peaks at `k=-3` and `k=3` are 0.5 - No intermediate peaks; values at k=-2, -1, 1, and 2 are zero - **Graph (c):** - Symmetrical about `k=0` - `k=0` value is 1 - Peaks at `k=-2`, `k=0`, and `k=2` are 0.5 - **Graph (d):** - Symmetrical about `k=0` - `k=0` value is 1 - Peaks at `k=-1` and `k=1` are 0.5 - Zeroes at other points - **Graph (e):** - Symmetrical about `k=0` - Peaks at `k=-3`, `k=0`, and `k=3` are 0.5 - Values decrease symmetrically - **Graph (f):** - Symmetrical about `k=0` - `k=0` value is 1 - Peaks at `k=-2`, `k=0`, and `k=2` are 0.5 **Note:** The determination of a valid ACS generally depends on properties such as being real, symmetric, and non-negative definite. Each sequence needs to be evaluated based on these criteria.
Transcribed Image Text:**Question:** Which of the following sequences cannot be a valid Auto Correlation Sequence (ACS)? For each case, explain why the sequence cannot be an ACS. **Graph Descriptions:** Each graph is a discrete signal plot showing sequences on the y-axis against the `k` values on the x-axis ranging from -4 to 4. - **Graph (a):** - Symmetric about `k=0` - `k=0` value is 1 - Peaks at `k=-1` and `k=1` are 0.5 - Values decrease symmetrically as `k` moves toward -3 and 3 - **Graph (b):** - Symmetric about `k=0` - `k=0` value is 1 - Peaks at `k=-3` and `k=3` are 0.5 - No intermediate peaks; values at k=-2, -1, 1, and 2 are zero - **Graph (c):** - Symmetrical about `k=0` - `k=0` value is 1 - Peaks at `k=-2`, `k=0`, and `k=2` are 0.5 - **Graph (d):** - Symmetrical about `k=0` - `k=0` value is 1 - Peaks at `k=-1` and `k=1` are 0.5 - Zeroes at other points - **Graph (e):** - Symmetrical about `k=0` - Peaks at `k=-3`, `k=0`, and `k=3` are 0.5 - Values decrease symmetrically - **Graph (f):** - Symmetrical about `k=0` - `k=0` value is 1 - Peaks at `k=-2`, `k=0`, and `k=2` are 0.5 **Note:** The determination of a valid ACS generally depends on properties such as being real, symmetric, and non-negative definite. Each sequence needs to be evaluated based on these criteria.
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