I_andQ

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( ct + k xm (t) dt)

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

USRP DAUGHTER BOARD

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

FPGA

I

Q

complex multiply

sin f tn

cos f tn

decimate

decimate

n = sample number

I

Q

To USB and PC

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

SSB Example

Start with arbitrary waveform in baseband:

SSB Example

Modulate as Upper Sideband Signal:

SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

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

SSB Example

I

Q

complex multiply

sin f tn

cos f 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