Mathematical Representation of Noise
-
Upload
satishkumar8421 -
Category
Documents
-
view
361 -
download
51
Transcript of Mathematical Representation of Noise
![Page 1: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/1.jpg)
Principles of Communication Systems, Third Edition
Herbert Taub, Donald L Schilling, Goutam Saha
Course : Digital Communications
Topic : Mathematical Representationof Noise
1
Department of ECE
Raghu Institute of Technology
![Page 2: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/2.jpg)
Sources of Noise
• Thermal Noise
• Shot Noise
• Additive Noise
• Multiplicative Noise (fading)
• Gaussian Noise
![Page 3: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/3.jpg)
Noise: Frequency Domain Representation
![Page 4: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/4.jpg)
Noise : Power Spectrum
![Page 5: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/5.jpg)
Noise Represetation
![Page 6: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/6.jpg)
Filtering Gaussian Noise
![Page 7: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/7.jpg)
Noise : Spectral Component
![Page 8: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/8.jpg)
Noise : Narrowband Filter Response
![Page 9: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/9.jpg)
Noise PSD : Effect of Filter
![Page 10: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/10.jpg)
Mixing Noise with Sinusoid
![Page 11: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/11.jpg)
Mixing Noise with Noise
![Page 12: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/12.jpg)
Linear Filtering of Noise
![Page 13: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/13.jpg)
Noise and Low Pass Filter
RC Low Pass Filter:
Ideal Low Pass Filter:
![Page 14: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/14.jpg)
Noise and Band Pass Filter
![Page 15: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/15.jpg)
Noise and Differentiator
A differentiator follows
![Page 16: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/16.jpg)
Noise and Integrator-1
An integrator follows
![Page 17: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/17.jpg)
Noise and Integrator-2
![Page 18: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/18.jpg)
Quadrature Components of Noise
It is sometimes more advantageous to represent Narrowband noise centred around f0 as
Now,
![Page 19: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/19.jpg)
PSD of Quadrature Components
![Page 20: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/20.jpg)
![Page 21: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/21.jpg)
Probability Density of Quadrature Components and Time Derivatives
![Page 22: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/22.jpg)
Noise : Orthonormal Coordinates
![Page 23: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/23.jpg)
Irrelevant Noise Components and Optimum Receiver
![Page 24: Mathematical Representation of Noise](https://reader033.fdocuments.us/reader033/viewer/2022061119/546a769bb4af9f38018b45c5/html5/thumbnails/24.jpg)
End of Chapter 7