I and Q Components in
Communications Signals
and Single Sideband
1
SHARLENE KATZ
DAVID SCHWARTZ
JAMES FLYNN
7/22/2010
OVERVIEW
2
 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 Communications
Signals
3
Modulation Time Domain
Frequency Domain
AM
XAM(f)
-fc
fc
f
DSB
FM
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Overview of I and Q Representation
4
 I and Q are the In-phase and Quadrature
components of a signal.
 Complete description of a signal is:
x(t )  I (t )  jQ(t )
 x(t) can therefore be represented as a vector with
magnitude and phase angle.
 Phase angle is not absolute, but relates to some
arbitrary reference.
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Overview of I and Q Representation
5
 In Digital Signal Processing (DSP), ultimate
reference is local sampling clock.
 DSP relies heavily on I and Q signals for processing.
Use of I and Q allows for processing of signals near
DC 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 to
baseband we ONLY get the sum
This avoids problems with images
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Overview of I and Q Representation
6
 Nyquist frequency is twice highest frequency, not
twice bandwidth of signal.
For example: common frequency used in analog
signal processing is 455 kHz. To sample in digital
processing, requires 910 kS/s. But if the signal
bandwidth is only 10 kHz. With I & Q, sampling
requires only 20 kS/s.
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Overview of I and Q Representation
7
 I and Q allows discerning of positive and negative
frequencies.
 If : H ( f )  a  jb

Then:
H ( f )  a  jb
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Overview of I and Q Representation
8
Representing familiar characteristics of a signal with I
and Q:
• Amplitude:
• Phase:
A(t )  I 2 (t )  Q 2 (t )
 Q(t ) 
 (t )  tan 

I
(
t
)


1
• Frequency:
f (t ) 
 (t )

t
I (t )
Q(t )
I (t )
 Q(t )
t
t
2
2
I (t )  Q (t )
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DEMODULATION
9
 AM:
x(t )  i 2 (t )  q 2 (t )
 SSB:
x(t )  i (t )
 FM:
 1  1  i(t )q(t  1)  q(t )i(t  1) 
x(t )    tan 

i
(
t
)
i
(
t

1)

q
(
t
)
q
(
t

1)
 t 


 PM:
 q(t ) 
x(t )  tan 

i
(
t
)


1
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Overview of I and Q Representation
10
 The traditional FM equation:
xFM (t )  cos(ct  k  xm (t )dt )
 The analytic equation:
xFM (t )  I (t ) cos(ct )  jQ(t )sin(ct )
 Modulation and Demodulation methods are different
when I and Q representation is used
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USRP DAUGHTER BOARD
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AMP
LPF
ADC
I
LPF
ADC
Q
cos ωc t
sin ωc t
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FPGA
12
cos ωf tn
I
Q
complex
multiply
n = sample
number
decimate
I
decimate
Q
To USB
and PC
sin ωf tn
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Complex Multiply
13
cos (ωf tn )
I
Q
cos (ωf tn )
I
Q
(A + j B) * (C + j D) = AC – BD + j (BC + AD)
I+jQ
cosft +
sinft
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Sideband Modulation
14
 Where’s the intelligence?
 A signal carries useful information only when it changes.
 Change of ANY carrier 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
15
 AM review:
 Carrier is modulated by varying amplitude linearly
proportional to intelligence (baseband) signal amplitude.
 Block Diagram
x(t)
m
x
+
xAM(t)=Ac [1+mx(t)]cos
ct
Accosct
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AM: Time Domain
16
 AM in the Time Domain
Unmodulated
carrier
100% modulated
carrier
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AM: Frequency Domain
17
 AM in the Frequency Domain
carrier
lower
sideband
upper
sideband
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Double Sideband Modulation (DSB)
18
 Let’s just transmit the sidebands
x(t)
m
x
Accosct
+
xDSB(t) = Ac*m*x(t)*cosct
X
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DSB: Time Domain
19
 Double Sideband in the Time Domain
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DSB: Frequency Domain
20
 Double Sideband in the Frequency Domain
carrier was here
lower
sideban
d
upper
sideband
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Example of a DSB Signal
21
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DSB Spectrum
22
 Note: the upper and lower sidebands are the same
 Do we need both of them?
carrier was here
lower
sideband
upper
sideband
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SSB Signals
23
 A sideband signal is obtained by adding a sideband
filter to capture the upper or lower sideband.
Low Pass Filter
f
f
f
x(t)
x
Lower
Sideband
Filter
Accosct
f
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Example of a USB Signal
24
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Comparison of DSB and SSB
25
 Power: SSB requires half of the power of DSB
 Bandwidth: SSB requires half of the bandwidth of
DSB
 Complexity: SSB modulators/demodulators are
more complex
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SSB Example
26
 Start with arbitrary waveform in baseband:
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SSB Example
27
 Modulate as Upper Sideband Signal:
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SSB Example
AMP
LPF
ADC
I
LPF
ADC
Q
cos ωc t
sin ωc t
28
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SSB Example
29
AMP
LPF
ADC
I
LPF
AD
C
Q
cos ωc t
sin ωc t
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SSB Example
AMP
LPF
ADC
I
LPF
ADC
Q
cos ωc t
sin ωc t
30
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SSB Example
AMP
LPF
ADC
I
LPF
AD
C
Q
cos ωc t
sin ωc t
31
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SSB Example
AMP
LPF
ADC
I
LPF
ADC
Q
cos ωc t
sin ωc t
32
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SSB Example
cos ωf tn
I
Q
complex
multiply
n = sample
number
decimate
I
decimate
Q
To USB
and PC
sin ωf tn
33
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SSB Example
cos ωf tn
I
Q
complex
multiply
n = sample
number
decimate
I
decimate
Q
To USB
and PC
sin ωf tn
34
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SSB Example
cos ωf tn
I
Q
complex
multiply
n = sample
number
decimate
I
decimate
Q
To USB
and PC
sin ωf tn
35
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SSB Example
cos ωf tn
I
Q
complex
multiply
n = sample
number
decimate
I
decimate
Q
To USB
and PC
sin ωf tn
36
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Practical SSB Reception
37
 Example above assumed no other signals on the
band and perfectly synchronized oscillators
 Need to isolate (filter) the signal of interest and deal
with oscillators slightly out of sync
 GRC tutorial demonstrates Weaver’s Method of
demodulating SSB that solves these problems
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