Communication Theory Flashcards
noise
unwanted signal pertubation that is always present
internal noise
thermal, shot, flicker
external noise
atmospheric, extra-terrestrial, man-made
noise power from thermal noise
Pn = kT 𐤃f
k variable value
1.38e-23
𐤃f =
bandwidth
RMS voltage
en = sqrt(4kT𐤃fR)
noise power with a resistor
Pn = (en/2)^2/R
converting to dB
10log(P1/P2)
20log(V1/V2)
noiseless system NR = ? NF = ?
NR = 1 NF = 0
NR =
(S/N)in / (S/N)out
NF =
10log(NR)
Noise ratio for cascaded system
NR = NR1 + NR2-1/P1 + … NRn-1/(P1P2…Pn)
what stage dominates in a cascading system
first
SNR max =
input signal / power of thermal noise
effective noise =
noise performance
effective noise =
Te = Pn/(PgkB)
relationship between noise ratio and noise temperature
F = 1+ Te/To Te = To(F-1)
all amplifiers introduce
some noise
bandwidth =
range of frequencies
bandpass filters
remove noise and channel interference
modulation
impressing the signal onto a carrier wave so it can be transmitted at the carrier frequency
when the carrier frequency is ____________ transmition signal is ____________
higher, lower
passband filters
- excludes excess noise
- modulates on a higher frequency without interference
- multiple transmitters can operate at the same time without frequency
modulation equation
v(t) = Vp*sin(wt+phi)
Vp
amplitude
sin(wt)
frequency
phi
phase
modulation can be
analogue or digital
AM
change in amplitude
FM
change in carrier frequency
PM
change in phase
FM and PM are also called
angle modulation
amplitude is related to the
modulating signal
carrier constant of AM signal
Accos(2pi*ft)
amplitude modulated carrier wave =
m(t)cos(2pift)
amplitude modulation pros/cons
pros: used for envelope detection -> simple and cheap
cons: transmitter needs a lot of power -> expensive
amplitude modulation equation
AM = [Ac+m(t)]cos(2pift)
in AM, message signals can be recovered using
envelope detection
modulation does what to the spectrum
shifts it either right or left
upper sideband limit
USB = fc+fm
lower sideband limit
LSB = fc-fm
fc>= W
avoids overlap
fc=W
main carrier frequency
fc/W >1
avoid distortion
AM envelope condition
(Ac+m(t))>0
envelope detection condition as mp is peak amplitude
Ac>= mp
AM modulation index
u = mp/Ac
inequality for envelope detection based off modulation index
0<=u<=1
coherent detection condition
Ac<mp
u>1
prerec for undistorted envelope
u<=1
tone modulation index
u = Am/Ac
modulation index for multi-tones
u = u1+u2+…+un
efficiency power
n = useful/total
n = Ps/(Dc+Ps)
n = Pm/(Ac^2+Bn)
tone modulation power efficiency
n = u^2/(2+u^2) * 100%
am coherent
translates frequency of sidebands back to baseband
DSB-AM coherent detection oscillation
oscillating source needs to be oscillating at the same frequency as the carrier source
RC conditions
RC>1/fc
RC<1/W
RC for an AM envelope =
RC = sqrt(1/Wfc)
W = message signal bandwidth
clearly defined envelope conditions
wc>2piW
wc= 2pif
DC components can be
blocked by high pass filters
ripples can be reduced by
low pass filters
Voice AM examples
emergency services, taxi, military, airport
generalised carrier signal
x(t) = Ac cos(wt+θ)
angular frequency
wi = dθ(t)/dt
phase angle
θ(t) = integral from -infinity to t (wi(a))da
varying the angle
encodes info of phase on carrier signal
phase deviation
𐤃θ = km(t)
peak phase
𐤃θ = |km(t)|
FM angular frequency
wi = wc +km(t)
frequency deviation
𐤃f = k/2pi * m(t)
power of AM modulated wave
power = Ac^2 /2
power of an am modulated wave is dependent on
amplitude
max frequency deviation in FM
𐤃w max = kf*mp
𐤃f = k/2pi * mp
bandwidth of an angle modulated signal is
finite
bessel functions
Jn(D) = (-1)^n*Jn(D)
as bandwidth increases in the FM spectrum
spread increases
power of carrier frequency decreases
AM signals
low bandwidth
low efficiency
no info in the carrier transmission
FM signals
complex
high efficiency
wide bandwidth
better noise performance
multiplexing
combines signals from different sources
sideband filters help
avoid overlap
FDM example
broadcast radio
FDM
signals seperated in frequency
occuplied limited portion of channel
occupy allocated frequency always
band-limited to avoid overlap
TDM
seperated in time
access to the entire channel
fraction of total time is allocated
used to multiplex digital signals
Xfm =
Accos(2pi(fct)) + Am/2cos(2pi(fc+fm)t)+Am/2cos(2pi(fc-fm)t)