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:
What about the
RC circuit?
 The filtered noise is

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 0.99.
 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