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  Example: noise passed through RC network

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

Illustration of Equivalent Bandwidth

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

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

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

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

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

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.

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

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

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  The threshold effect is usually not a serious limitation for AM broadcasting.

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

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

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

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.

Comparison of Continuous Waveform Modulations

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?

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?

Review