Chapter 8. Impact of NoiseHusheng LiThe University of Tennessee

White NoiseWhen the noise spectrum is flat, we call it

white noise.

The spectral density is given by

Filtered (Colored) NoiseWhen passed through a LTI filter with transfer

function H(f), we have

Example: noise passed through RC network

Noise Equivalent BandwidthAverage noise power:

Noise equivalent bandwidth:

The filtered noise is

What about the RC circuit?

Illustration of Equivalent Bandwidth

Bandpass NoiseBandpass noise results when white noise

passes through a bandpass filter.

SNRThe predetection signal-to-noise ratio is given

by

We also define a system parameter (W is the low pass filter bandwidth)

Destination SNR

Quadrature ComponentsThe 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 DetectionWhen envelop detector is used for the

demodulation of AM, the noise can affect the amplitude.

Two Extreme CasesWhen the SNR is high, we have

When the SNR is low, then the signal modulates the noise.

Threshold EffectThere 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.

Angle Modulation with NoiseNow (S/N)_R is often called carrier-to-noise

ratio (CNR).

The phasor construction shows

Noise Spectrum in PM and FMWhen the signal is 0, the noise is given by

PM FM

SNR Gain of PM and FMBoth PM and FM give SNR gains over the base

band transmissions:

Threshold Effect in FMWhen 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