I_andQ
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Transcript of I_andQ
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S H A R L E N E K A T Z
J A M E S F L Y N N
I and Q Components in Communications Signals
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OVERVIEW
Description of I and Q signal representation Obtaining I and Q components from the USRP I and Q components of a SSB signal Using I and Q to demodulate signals Planning for the Winter/Spring
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Standard Representation of Communications Signals
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 Quadrature components of a signal.
Complete description of a signal is:
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.
x(t) = I(t) + jQ(t)
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Overview of I and Q Representation
In Digital Signal Processing (DSP), reference is local sampling rate.
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.
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Overview of I and Q Representation
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 bandwidth is only 10 kHz. With I & Q, sampling requires only 20 kS/s.
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Overview of I and Q Representation
I and Q allows discerning of positive and negative frequencies. If :
Then:
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Overview of I and Q Representation
The traditional FM equation:
The analytic equation:
Modulation and Demodulation methods are different when I and Q representation is used
xFM (t) = cos( ct + k xm (t) dt)
xFM (t) = I(t)cos( ct) + jQ(t)sin( ct)
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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
complex multiply
sin f tn
cos f tn
decimate
decimate
n = sample number
I
Q
To USB and PC
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Complex Multiply
I
Q cos (f tn )
cos (f tn ) I
Q
(A + j B) * (C + j D) = AC BD + j (BC + AD)
I + j Q coswft +
sinwft
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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
complex multiply
sin f tn
cos f tn
decimate
decimate
n = sample number
I
Q
To USB and PC
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SSB Example
I
Q
complex multiply
sin f tn
cos f tn
decimate
decimate
n = sample number
I
Q
To USB and PC
-
SSB Example
I
Q
complex multiply
sin f tn
cos f tn
decimate
decimate
n = sample number
I
Q
To USB and PC
-
SSB Example
I
Q
complex multiply
sin f tn
cos f tn
decimate
decimate
n = sample number
I
Q
To USB and PC
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DEMODULATION
AM:
SSB:
FM:
PM:
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Planning for Winter/Spring
The remainder of the Fall semester Winter Break Spring Meeting Time Senior Project Overview