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Chapter 8. Impact of Noise

Chapter 8. Impact of Noise. Husheng Li The University of Tennessee. White Noise. When the noise spectrum is flat, we call it white noise. The spectral density is given by. Filtered (Colored) Noise. When passed through a LTI filter with transfer function H(f), we have

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Chapter 8. Impact of Noise

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  1. Chapter 8. Impact of Noise Husheng Li The University of Tennessee

  2. White Noise When the noise spectrum is flat, we call it white noise. The spectral density is given by

  3. Filtered (Colored) Noise When passed through a LTI filter with transfer function H(f), we have Example: noise passed through RC network

  4. Noise Equivalent Bandwidth What about the RC circuit? Average noise power: Noise equivalent bandwidth: The filtered noise is

  5. Illustration of Equivalent Bandwidth

  6. Bandpass Noise Bandpass noise results when white noise passes through a bandpass filter.

  7. SNR Destination SNR The predetection signal-to-noise ratio is given by We also define a system parameter (W is the low pass filter bandwidth)

  8. Quadrature Components The bandpass noise can be written as The power spectral densities are identical lowpass functions related to G_n(f):

  9. Impact on AM (Synchronous Detection) For DSB, the detected signal is given by Then, the destination SNR is given by

  10. Impact on AM (Synchronous Detection) For generic AM, we have For SSB, we have For VSB, we have

  11. Summary The message and noise are additive at the output if they are additive at the input. If the predetection noise spectrum is reasonably flat over the transmission band, then the destination noise spectrum is essentially constant over the message band. Relative to (S/N)_D, SSB has no particular advantage over DSB. Making due allowance for the wasted power in unsuppressed-carrier systems, all types of linear modulation have the same performance as baseband transmission on the basis of average transmitted power and fixed noise density.

  12. Envelop Detection When envelop detector is used for the demodulation of AM, the noise can affect the amplitude.

  13. Two Extreme Cases When the SNR is high, we have When the SNR is low, then the signal modulates the noise.

  14. Threshold Effect There is some value of SNR above which message corruption is negligible and below which system performance rapidly deteriorates. We define the threshold level as that value of SNR_R for which A_c>A_n with probability 0.99. The threshold effect is usually not a serious limitation for AM broadcasting.

  15. Angle Modulation with Noise Now (S/N)_R is often called carrier-to-noise ratio (CNR). The phasor construction shows

  16. Noise Spectrum in PM and FM FM PM When the signal is 0, the noise is given by

  17. SNR Gain of PM and FM Both PM and FM give SNR gains over the base band transmissions:

  18. Threshold Effect in FM When the system is operating near the threshold, small variations of received signal power cause sizable changes in the output signal --- one moment it is there and the next moment it is gone.

  19. Comparison of Continuous Waveform Modulations

  20. Review for Final Exam Nyquist criterion Aliasing Flat top sampling and aperture effect PAM, PPM and PDM (how to generate them? How to recover the original signal? What is the superhet principle? What are the frequency conversion procedure? How to determine the image frequency? Specifications of frequencies Tradeoff in spectrum analyzer What types of multiple access schemes do we have? What are their major concerns?

  21. Review How to derive the dynamics of phase locked loop? How to analyze the steady state of phase locked loop? Need to write down the details What if there is no carrier in the signal (say, DSB) for phase locked loop? What are the SNR properties of AM, FM and PM (just need to remember the qualitative conclusions)? What happens to the noise when envelop detection is used for demodulating AM signals? What are the noise spectrum shapes of FM and PM?

  22. Review

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