Exercise 4

Topic: Hilbert-transform and complex demodulation.

This will be a normal lesson, approximately one hour.

Learning objectives: Basic definitions for complex representation of band-pass signals, and also implementing Hilbert transform, complex demodulation and reconstruction of band-pass signal.

Concepts: Band-pass signal, Hilbert transform, pre-envelope, in phase and quadrature component, carrier frequency.

Reading materials:
Haykin: Communication theory, p. 75 - 90, Papoulis: Signal analysis, p. 118-124. (will be handed out)
Oppenheim: Digital signal processing, ch. 7. J. Kirkhorn: IQdemodulation of RF data
You will find the books in the lunchroom, upper shelf.

Some headwords:

1. Hilbert transform. Definition, impulse and frequency response.

2. Complex demodulation by complex mixing and low-pass filter.

3. The relation between 1 and 2.

4. Reconstruction of RF signal from iq signal.

Matlab example: PulseEchoPlot.m  shows the received signal for an ultrasound pulse echo system with a reflector in a distance of z1.
Vary the distance over an appropriate area, for instance

for z1=(8:0.01:10)*1e-3;pulseEchoPlot(z1);end;

and observe how the signal, and its complex envelope (iq-signal), changes.
Plot the frequency specter for the signal, pre-envelope and complex envelope.
Vary the center frequency f0 and the pulse length.
How can the iq-signal be used to measure the motion of the reflector?