ECOMMS 10 - Lab 1 - Waveform Synthesis and Spectral Analysis

Laboratory Project 1 - Waveform Synthesis and Spectral Analysis

Objectives

Laboratory project 1 contains 4 parts. In Part 1, you will:

* Generate arbitrary waveforms with specified SNR's using software;
* Synthesize this waveform using an arbitrary waveform generator.

In Part 2, you will study the differences between the Continuous Fourier Transform (CFT) and the Discrete Fourier Transform (DFT) (this is homework!).

In Part 3, you will synthesize AM and FM bandpass signals and analyze their spectra.

In Part 4, you will capture and analyze the spectrum of an electrocardiogram (ECG/EKG) signal.

Equipment and Software

* HP 33120A Function/Arbitrary Waveform Generator
* Agilent Infinium Oscilloscope
* BNC "TEE" connector
* Powered speakers with 3.5mm stereo connector
* Wireless breadboard
* Convert-o-box (supplied with lab kit)
* Clinimark Pinstyle ECG Electrodes and leads
* Antiseptic prep pads
* Human with beating heart (or, if absent, a Lionheart 3 cardio-simulator)
* 9VDC battery
* 50ohm BNC Cable
* ECG module
* MATLAB (with Instrument Control Toolbox)
* MATLAB Connectivity Functions: >>writefunc(.), >>scopedat(.)

Click here for instrument connectivity guide and Matlab function downloads required

Instrument Connectivity

In this, and future labs, you will be required to send and gather data to various instruments at the station. To do this, you will need an active connection with the instruments by opening and refreshing the instruments in Agilent IO Libraries. Click Start>All Programs>Agilent IO Libraries Suite>Agilent Connection Expert. When the software is open, click the refresh button until the instrument icons are green. Obvioulsy the instruments will need to be powered on and past initialization before they are seen by Connection Expert.

You will also need the board index (the 'number' of the interface card), and the GPIB address of the instrument. To find the board index, open the tmtool link under Matlab>Start>Toolboxes>Instrument Control>Test and Measurement Tool (tmtool) OR type >>tmtool in the Matlab command window. Expand the Hardware and then the GPIB tab on the lefthand pane. The board index should be either 7 or 8. You will see that boards that have instruments connected to them will be expandable. The GPIB addresses are consistent across all instruments in the Mixed Signals Laboratory:

Oscilloscope: 7
HP8648A: 9
HP33120A (Upper): 10
HP33120A (Lower): 11
HP34970A: 12
Keithley 2000/2100: 16
HP/Agilent E3631A: 5

-> Please read the connectivity guide for full details

Part 1: Digital synthesis of arbitrary waveforms with specified SNR

Background

Procedure

* Synthesize a 1 second A-Sharp sinusoidal tone (466.16 Hz) sampled at 8 kHz.

* Plot this waveform; observe. Save this waveform to a .wav sound file, play and listen. (You can listen using the sound command in Matlab)

* Send the data to the HP33120 Arb. Function Generator using the >>writefunc(.) function in Matlab. NOTE: the HP33120A function generators and the >>writefunc(.) function can only handle <= 16,000 data points. You can check the length of your data vector by running the >>size(data) command. Please read help file: >>help writefunc. It must also be noted that the data, by default, is stored in the workspace. Any >>clear all or variable overwrite commands will remove the data! If you would like to save the data to the HDD, use Matlab's >>save(.) function. Also mind frequency scaling which can occur if improper considerations are made with regard to time vector length and signal generator frequency setting.

- Send one second of the sinusoid to the function generator and confirm via. data capture. In the >>writefunc(.) command, set FREQ to 1. This (coupled with the 1 second data length) will ensure that the sinusoid's specified frequency is maintained.

- If you wish to experiment: Note that for periodic waveforms, all that is required for perfect synthesis is one period of the signal. This means that ALL available memory (16k) can be 'stuffed' into the minimal amount of time required (i.e. one period), giving a much higher resolution signal. This method requires alternate consideration for obtaining the proper frequency, however! Experiment!

* Corrupt the signal (1 second of the A-sharp sinusoid) with a Gaussian noise source to get an SNR of 10 dB. Observe, listen and save waveform as before.

* Synthesize 1 second of the noisy waveform.

* Download the original and noisy signals to the HP33120A Arbitrary Function Generator using the MATLAB connectivity function: >>writefunc(.) . NOTE: Any amplitude sent to the function generator is normalized over a +/- 1 range. Real amplitude output voltage is controlled by the 'AMP' argument in the function. For noisy waveforms, outliers will appear at the extremes. A practical range should be specified so that the amplitude is correct. Any real amplitudes over 10Vpp cannot be realized on the HP33120A Function Generator.

* Vary the frequency and amplitude. Observe waveform using the oscilloscope.

* Repeat experiment with various SNRs.

* Experiment with other waveforms:

Example Matlab Code:

%ECOMMS Lab Project 1 Example Spring 10

%S. Mandayam, Rowan University
%This program generates a 1-second duration
%Asharp signal (466.16 Hz) with a specified SNR

%Specify SNR
snr=10;

%Generate Asharp signal
t=[0:1/8e3:1.0]';
s = 0.5*sin(2*pi*466.16*t);
sound(s);
wavwrite(s, 'asharp.wav');
save asharp.csv -ascii s;

%Compute signal variance
var_s = cov(s);

%Calculate required noise variance
var_noise=var_s/(10^(snr/10));

%Generate noise
n=sqrt(var_noise)*randn(length(s),1);
sound(n);

%Add signal to noise and generate message
m=s+n;
sound(m);
wavwrite(m,'asharp_noise.wav');
save asharp_noise.csv -ascii m;

Part 2: Comparison between CFT and DFT (FFT)
(Uses Matlab only - this is homework!)

Consider the signal shown in Figure 1:

Figure 1: Time-domain signal

* Model the signal as a continuous-time function and plot.

* Obtain, analytically, the CFT of the signal, and plot.

* Based on your observations of the frequency components of the signal, determine the maximum sampling period/minimum sampling frequency that will allow reconstruction of the continuous-time signal.

* Plot the DFT magnitude spectrum using Matlab's fft function.

* Attempt to reconstruct the original continuous-time function from its samples, either by: Convolving the time domain samples with appropriate Sinc function (difficult), or Windowing the Fourier transform and taking the inverse Fourier transform (easier).

* Comment on your results. What is the maximum sampling period/minimum sampling frequency that will allow reconstruction of the discrete-time signal from its DFT, that adequately represents the original continuous-time signal? Show plots of the discrete-time signals, the corresponding DFTs and reconstructions, for sampling intervals at, above and below this maximum allowed sampling period.

Part 3: Spectral Analysis of AM and FM Signals
(Uses Matlab, Oscilloscope, Function Generator and Spectrum Analyzer/FFT module)

* Synthesize a bandpass AM signal:

* Obtain and plot the spectral components of this signal using:

1. Matlab's fft function.
2. The spectrum analyzer/FFT module.

* Add noise to the RF signal, observe the signal in the time and spectral domains.

* Experiment with various fm's, fc's and SNRs.

* Synthesize a bandpass FM signal:

* Repeat earlier experiments.

Part 4: Spectral Analysis of ECG Signal
(Uses Matlab, Oscilloscope, ECG Electrodes and leads, Antiseptic Prep Pads, 9VDC battery, 50ohm BNC cable, ECG module, and Spectrum Analyzer/FFT Module)

NOTE: READ THIS FIRST!!!
This experiment must be conducted with the instructor present at all times when you are obtaining the ECG readings. The procedure that has been outlined below has been determined to be safe for this laboratory. You must use an isolated power supply (9VDC Battery) for powering the ECG module. This objective of this experiment is compute the amplitude-frequency spectrum of real data - this experiment does not represent a true medical study; reading an ECG effectively takes considerable medical training. Therefore, do not be alarmed if your data appears"different" from those of your partners. Also, if you observe any allergic reactions when you attach the electrodes (burning sensation, discomfort), remove them and rinse the area with water. Finally, if, for any reason, you do not want to participate in this experiment, obtain recorded ECG data from your instructor.

* Electrocardiagram (ECG or EKG) measurements are used to monitor the contraction of the cardiac muscles by measuring the propagation of electrical depolarization and repolarization in the atria and ventricles. The ECG is one of the many diagnostic tools for monitoring the normality of cardiac activity in a patient. The references provided below provide considerable additional information regarding the ECG. Figure 2 shows the components of a typical ECG signal.

Figure 2: Components of a typical ECG signal

* The schematic of the ECG module is shown in Figure 3.

Figure 3: Schematic of ECG module. Click to enlarge

* This module includes many features including:

- 2 (arms) or 3 lead (arms + leg) electrode tests. NOTE: for this lab, you will be doing a 2-lead experiment only (one electrode pad on each wrist). Be sure the "Guard" switch is in the OFF position and you use the correct electrode jack ("Arms").
- Adjustable gain (the "Gain" trimmer potentiometer located in the center of the PCB)
- 6th order Butterworth LPF with cutoff set at 50Hz (switchable on/off via the "LPF" switch)

* The PCB layout of the ECG module is shown in Figure 4.

Figure 4: PCB layout showing locations of important components. Click to enlarge

* The experimental set-up for taking ECG measurments with the supplied ECG module is shown in Figure 5.

Figure 5: Experimental set-up for taking ECG measurements. Click to enlarge

* Select one of your lab partners as the "patient" for obtaining the ECG. Use the antiseptic prep pads and thoroughly clean the wrist area where the electrodes will be attached. A thorough cleaning is required to ensure a good contact of the electrode with the skin - and a strong signal.

* Remove the electrodes from the release sheet and place each electrode on the inside wrist of each arm. (This method of electrode placement is known as Standard I Lead). Press firmly to ensure adequate contact.

* Attach the electrode lead wire pin into the hole on the top of the electrode. The other end of the lead wire is connected to the "Arms" jack on the ECG module. Be sure the "Guard" switch is in the "Off" position.

* Use a 50ohm BNC cable and connect the output terminal of the ECG module to the oscilloscope.

* With the instructor present, power on the ECG module by switching the POWER switch to the ON position. Observe the ECG signal on the oscilloscope. To obtain a strong signal, you may need help from your lab partner to press the electrodes firmly to your arm. Be as still and quiet as possible; any movement will induce noise and shift the ECG signal.

* Baseline scope settings should be 500ms/div to 1s/div. Most scopes display a small arrow pointing to where the signal is located, if it is off-screen. You may also wish to simply press the 'autoscale' button, then adjust the time scale accordingly (most likely, the autoscale will set the scope's focus on a much 'faster' part of the waveform).

* The "Gain" potentiometer on the ECG may be rotated clockwise with a trimmer screwdriver if additional amplification is needed.

* Capture the waveform using the >>scopedat(.) Matlab function, ensuring the 'patient' is as still as possible. Also be certain the FILTER switch is OFF. You may observe a strong 60 Hz ripple - you can eliminate this by filtering the signal using DSP techniques.

* Capture the ECG waveform again, but now with the LPF switch in the ON position. This will enable the on-board analog LPF and remove most of the 60Hz noise.

* Comment on the time and frequency components of the ECG signals.

Click here for required lab project report format.

Click here for suggestions for a good lab report.

References:

* HP 33120A Function Generator/Arbitrary Waveform Generator User's Guide
* Appendix B (p. 650) in textbook
* Zsolt Papay, Technical University of Budapest (TUB),"Experiments in Gaussian White-noise Generation," HP Test and Measurements Educator's Corner, http://www.home.agilent.com/upload/cmc_upload/All/Exp65.pdf
* Chapter 2 in the texbook.
* Class Demo: Sampling
* Class Demo: Discrete Fourier Transform
* Class Demo: Spectrum Analyzer
* L. A. Geddes and L. E. Baker, Principles of Applied Biomedical Instrumentation, 2nd Edition, Wiley, 1975.
* Frank G. Yanowitz, MD, University of Utah School of Medicine, The Alan E. Linday ECG Learning Center in Cyberspace, http://www-medlib.med.utah.edu/kw/ecg/ecg_outline/