### Chapter8

```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
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
 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
 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
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
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
 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
```