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

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

Standard Representation of Communications Signals

Modulation Time Domain Frequency Domain

AM

DSB

FM

XAM(f)

f -fc fc

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)

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.

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.

Overview of I and Q Representation

  I and Q allows discerning of positive and negative frequencies.   If :

  Then:

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(ω ct + k xm (t) dt)∫

xFM (t) = I(t)cos(ω ct) + jQ(t)sin(ω ct)

USRP DAUGHTER BOARD

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

FPGA

I

Q

complex multiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

Complex Multiply

I

Q cos (ωf tn )

cos (ωf tn ) I

Q

(A + j B) * (C + j D) = AC – BD + j (BC + AD)

I + j Q coswft +

sinwft

SSB Example

  Start with arbitrary waveform in baseband:

SSB Example

 Modulate as Upper Sideband Signal:

SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

complex multiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

SSB Example

I

Q

complex multiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

SSB Example

I

Q

complex multiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

SSB Example

I

Q

complex multiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

DEMODULATION

  AM:

  SSB:

  FM:

  PM:

Planning for Winter/Spring

  The remainder of the Fall semester  Winter Break   Spring Meeting Time   Senior Project Overview