1. copyright Robert J. Marks II
ECE 5345
Analysis & Processing of Random Signals
copyright Robert J. Marks II

2. Analysis & Processing of Random Signals
Power Spectral Density of a WSS process is the Fourier transform of its autocorrelation
“Spectral” a function of frequency
“Power Density” Integration gives power
copyright Robert J. Marks II

3. Power Spectral Density
Inverse Transform:
“Spectral” a function of frequency
“Power Density” Integration gives power
copyright Robert J. Marks II

4. Power Spectral Density
Properties
follows from even autocorrelation
follows from even autocorrelation
proof to follow
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5. Power Spectral Density
Properties
thus
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6. Power Spectral Density
The power in a specified frequency band is obtained by integrating the PSD
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7. Power Spectral Density
Example: Random telegraph signal
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8. Power Spectral Density
Example: Random telegraph signal
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9. Power Spectral Density of Discrete RP’s
Let X[n] be WSS. The PSD is the DTFT of the autocorrelation.
SX(f) has the PSD properties except integration is from (-1/2, 1/2). Like all DTFT’s, SX(f) is periodic with period one.
copyright Robert J. Marks II

10. Power Spectral Density
Types of Noise
Continuous White Noise
Discrete White Noise
Laplace Noise
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11. copyright Robert J. Marks II
Types of Noise
Continuous White Noise
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12. copyright Robert J. Marks II
Types of Noise
Continuous White Noise
Thermal Noise.
Infinite Power!
White Gaussian Noise
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13. copyright Robert J. Marks II
Types of Noise
Discrete White Noise
Notes: Finite Power. Not samples from CWN.
copyright Robert J. Marks II

14. copyright Robert J. Marks II
Types of Noise
Discrete White Noise
Source: iid sequence.
Finite Power.
Not samples from CWN.
copyright Robert J. Marks II