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ECE 5345 Gaussian Random Processes copyright R.J. Marks II.

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Presentation on theme: "ECE 5345 Gaussian Random Processes copyright R.J. Marks II."— Presentation transcript:

1 ECE 5345 Gaussian Random Processes copyright R.J. Marks II

2 Multi-Dimensional Gaussian Random variables
pdf and characteristic function: copyright R.J. Marks II

3 Multi-Dimensional Gaussian Random variables
Expanded characteristic function: copyright R.J. Marks II

4 Multi-Dimensional Gaussian Random variables
Theorem: If a Gaussian RP is WSS, it is also SSS Proof: The process is WSS. Thus Choose k points {ti|1 i  k}. The elements of the K matrix are copyright R.J. Marks II

5 Multi-Dimensional Gaussian Random variables
For k points to {ti|1 i  k}, we have copyright R.J. Marks II

6 Multi-Dimensional Gaussian Random variables
If we shift the k points to {ti- |1 i  k}. The elements of the K matrix are then quod erat demonstrandum copyright R.J. Marks II

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