Transcript 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
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 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