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S H A R L E N E K A T Z
D A V I D S C H W A R T Z
J A M E S F L Y N N
I and Q Components inCommunications Signals
and Single Sideband
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OVERVIEW
Description of I and Q signal representation
Advantages of using I and Q components
Using I and Q to demodulate signals
I and Q signal processing in the USRP Single Sideband (SSB)
Processing I and Q components of a SSB signal in the
USRP
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Standard Representation of CommunicationsSignals
Modulation Time Domain Frequency Domain
AM
DSB
FM
XAM(f)
f
-fc fc
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Overview of I and Q Representation
I and Q are the In-phase and Quadraturecomponents of a signal.
Complete description of a signal is:
x(t) can therefore be represented as a vector withmagnitude and phase angle.
Phase angle is not absolute, but relates to somearbitrary reference.
( ) ( ) ( )x t I t jQ t
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Overview of I and Q Representation
In Digital Signal Processing (DSP), ultimatereference is local sampling clock.
DSP relies heavily on I and Q signals for processing.
Use of I and Q allows for processing of signals nearDC or zero frequency. If we use real signals (cosine) to shift a modulated signal to
baseband we get sum and difference frequencies
If we use a complex sinusoid to shift a modulated signal tobaseband we ONLY get the sum
This avoids problems with images
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Overview of I and Q Representation
Nyquist frequency is twice highest frequency, nottwice bandwidth of signal.
For example: common frequency used in analog
signal processing is 455 kHz. To sample in digitalprocessing, requires 910 kS/s. But if the signalbandwidth is only 10 kHz. With I & Q, samplingrequires only 20 kS/s.
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Overview of I and Q Representation
I and Q allows discerning of positive and negativefrequencies.
If :
Then:
( )H f a jb
( )H f a jb
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Overview of I and Q Representation
Representing familiar characteristics of a signal with Iand Q:
Amplitude:
Phase:
Frequency:
2 2( ) ( ) ( )A t I t Q t
1 ( )( ) tan( )
Q tt
I t
2 2
( ) ( )( ) ( )( )
( )( ) ( )
Q t I t I t Q tt t tf t
t I t Q t
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DEMODULATION
AM:
SSB:
FM:
PM:
2 2( ) ( ) ( )x t i t q t
( ) ( )x t i t
11 ( ) ( 1) ( ) ( 1)( ) tan( ) ( 1) ( ) ( 1)
i t q t q t i t x t
t i t i t q t q t
1 ( )( ) tan ( )
q tx t i t
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Overview of I and Q Representation
The traditional FM equation:
The analytic equation:
Modulation and Demodulation methods are differentwhen I and Q representation is used
( ) cos( ( ) )FM c mx t t k x t dt
( ) ( ) cos( ) ( )sin( )FM c cx t I t t jQ t t
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USRP DAUGHTER BOARD
I
Q
cos c t
sin c t
LPF
LPF
ADC
ADC
AMP
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FPGA
I
Q
complexmultiply
sin ftn
cos ftn
decimate
decimate
n = samplenumber
I
Q
To USBand PC
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Complex Multiply
I
Qcos (ftn )
cos (ftn )I
Q
(A + j B) * (C + j D) = AC BD + j (BC + AD)
I + j Q
cosft +
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Sideband Modulation
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Wheres the intelligence?
A signal carries useful information only when it changes.
Change ofANYcarrier parameter produces sidebands.
The intelligence or information is in the sidebands.
Why not just send the sidebands or just a sideband?
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AM Review
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AM review:
Carrier is modulated by varying amplitude linearlyproportional to intelligence (baseband) signal amplitude.
Block Diagram
m x +
Accosct
x(t) xAM(t)=Ac [1+mx(t)]cosct
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AM: Time Domain
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AM in the Time Domain
Unmodulated
carrier
100% modulatedcarrier
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AM: Frequency Domain
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AM in the Frequency Domain
carrier
uppersideband
lowersideband
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Double Sideband Modulation (DSB)
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Lets just transmit the sidebands
m x
Accosct
x(t) +
X
xDSB(t) = Ac*m*x(t)*cosct
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DSB: Time Domain
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Double Sideband in the Time Domain
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DSB: Frequency Domain
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Double Sideband in the Frequency Domain
carrier was here
uppersideband
lowersideban
d
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Example of a DSB Signal
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DSB Spectrum
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Note: the upper and lower sidebands are the same
Do we need both of them?carrier was here
uppersideband
lowersideband
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SSB Signals
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A sideband signal is obtained by adding a sidebandfilter to capture the upper or lower sideband.
x
Accosct
x(t)Lower
SidebandFilter
Low Pass Filter
f
f f
f
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Example of a USB Signal
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Comparison of DSB and SSB
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Power: SSB requires half of the power of DSB
Bandwidth: SSB requires half of the bandwidth ofDSB
Complexity: SSB modulators/demodulators aremore complex
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SSB Example
Start with arbitrary waveform in baseband:
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SSB Example
Modulate as Upper Sideband Signal:
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SSB Example
I
Q
cos c t
sin c t
LPF
LPF
ADC
ADC
AMP
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SSB Example
I
Q
cos c t
sin c t
LPF
LPF
ADC
ADC
AMP
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SSB Example
I
Q
cos c t
sin c t
LPF
LPF
ADC
ADC
AMP
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SSB Example
I
Q
cos c t
sin c t
LPF
LPF
ADC
ADC
AMP
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SSB Example
I
Q
cos c t
sin c t
LPF
LPF
ADC
ADC
AMP
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SSB Example
I
Q
complexmultiply
sin ftn
cos ftn
decimate
decimate
n = samplenumber
I
Q
To USBand PC
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SSB Example
I
Q
complexmultiply
sin ftn
cos ftn
decimate
decimate
n = samplenumber
I
Q
To USBand PC
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SSB Example
I
Q
complexmultiply
sin ftn
cos ftn
decimate
decimate
n = samplenumber
I
Q
To USBand PC
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SSB Example
I
Q
complexmultiply
sin ftn
cos ftn
decimate
decimate
n = samplenumber
I
Q
To USBand PC
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Practical SSB Reception
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Example above assumed no other signals on theband and perfectly synchronized oscillators
Need to isolate (filter) the signal of interest and deal
with oscillators slightly out of sync GRC tutorial demonstrates Weavers Method of
demodulating SSB that solves these problems