Electrical Communications Systems 0909.331.01 Spring 2005

1. Electrical Communications Systems0909.331.01Spring 2005 Lab 1: Pre-lab InstructionJanuary 24, 2005 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring05/ecomms/

2. ECOMMS: Topics

3. Plan • Recall: • Deterministic and Stochastic Waveforms • Random Variables • PDF and CDF • Gaussian PDF • Noise model • Lab Project 1 • Part 1: Digital synthesis of arbitrary waveforms with specified SNR • Recall: • How to generate frequency axis in DFT • Lab Project 1 • Part 2: CFT, Sampling and DFT (Homework!!!) • Part 3: Spectral analysis of AM and FM signals • Part 4(a): Spectral analysis of an NTSC composite video signal • Part 4(b): Spectral analysis of an ECG signal

4. Waveforms Deterministic Stochastic Noise (undesired) Signal (desired) Recall • Probability Random Experiment outcome Random Event

5. Real Number, a Random Event, s Random Variable, X Random Variable • Definition: Let E be an experiment and S be the set of all possible outcomes associated with the experiment. A function, X, assigning to every element s S, a real number, a, is called a random variable. X(s) = a Real Number Random Variable Appendix B Prob & RV Random Event

6. Cumulative Distribution Function (CDF) of x Probability Density Function (PDF) of x f(x) x a b Parameters of an RV F(a) a

7. Why are we doing this? Transfer Characteristic h(x) • For many situations, we can “model” the pdf using standard functions • By studying the functional forms, we can predict the expected values of the random variable (mean, variance, etc.) • We can predict what happens when the r.v. passes through a system Input pdf fx(x) Output pdf fy(y)

8. f(x) x m PDF Model: The Gaussian Random Variable • The most important pdf model • Used to model signal, noise…….. • m: mean; s2: variance • Also called a Normal Distribution • Central limit theorem

9. f(x) N(m,s12) s22> s12 N(m,s22) x m Normal Distribution (contd.) f(x) N(m1,s2) N(m2,s2) m2> m1 x m1 m2

10. Generating Normally Distributed Random Variables • Most math software provides you functions to generate - • N(0,1): zero-mean, unit-variance, Gaussian RV • Theorem: • N(0,s2) = sN(0,1) • Use this for generating normally distributed r.v.’s of any variance • Matlab function: • randn • Variance Power (how?)

11. Lab Project 1:Waveform Synthesis and Spectral Analysis Part 1: Digital Waveform Synthesis http://engineering.rowan.edu/~shreek/spring05/ecomms/lab1.html

12. Continuous Fourier Transform (CFT) Frequency, [Hz] Phase Spectrum Amplitude Spectrum Inverse Fourier Transform (IFT) Recall: CFT

13. Equal time intervals Recall: DFT • Discrete Domains • Discrete Time: k = 0, 1, 2, 3, …………, N-1 • Discrete Frequency: n = 0, 1, 2, 3, …………, N-1 • Discrete Fourier Transform • Inverse DFT Equal frequency intervals n = 0, 1, 2,….., N-1 k = 0, 1, 2,….., N-1

14. n=0 1 2 3 4 n=N f=0 f = fs How to get the frequency axis in the DFT • The DFT operation just converts one set of number, x[k] into another set of numbers X[n] - there is no explicit definition of time or frequency • How can we relate the DFT to the CFT and obtain spectral amplitudes for discrete frequencies? (N-point FFT) Need to know fs

15. n=0 N/2 n=N f=0 fs/2 f = fs DFT Properties • DFT is periodic X[n] = X[n+N] = X[n+2N] = ……… • I-DFT is also periodic! x[k] = x[k+N] = x[k+2N] = ………. • Where are the “low” and “high” frequencies on the DFT spectrum?

16. w(t) 1V t in ms 0V 0.6 0.7 1.0 Part 2: CFT, DFT and Sampling • This is homework!!!

17. AM s(t) = Ac[1 + Amcos(2pfmt)]cos(2pfct) FM s(t) = Accos[2pfct + bf Amsin(2pfmt)] s(t) t s(t) t Part 3: AM and FM Spectra

18. Part 4(a): Composite NTSC Baseband Video Signal Color Television Black & White Analog Television

19. Part 4(b): ECG Signals • 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 for powering the instrumentation amplifier. • You must use a 10-X scope probe for recording the amplifier output on the oscilloscope. • 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. • If you observe any allergic reactions when you attach the electrodes (burning sensation, discomfort), remove them and rinse the area with water. • If, for any reason, you do not want to participate in this experiment, obtain recorded ECG data from your instructor.

20. R T wave P wave Q S ECG Signal Components of the Electrocardiogram P-Wave Depolarization of the atria P-R Interval Depolarization of the atria, and delay at AV junction QRS Complex Depolarization of the ventricles S-T Segment Period between ventricular depolarization and repolarization T-Wave Repolarization of the ventricles R-R Interval Time between two ventricular depolarizations A “Normal” ECG Heart Rate 60 - 90 bpm PR Interval 0.12 - 0.20 sec QRS Duration 0.06 - 0.10 sec QT Interval (QTc < 0.40 sec)

21. +9 V DC Battery/Isolated Power Supply - INA114 2 7 10-X Scope Probe 1 6 Oscilloscope RG 5 8 4 3 + -9 V DC Battery/Isolated Power Supply Right Arm Left Arm ECG: Experiment Drawing not to scale!

22. Lab Project 1:Waveform Synthesis and Spectral Analysis http://engineering.rowan.edu/~shreek/spring05/ecomms/lab1.html

23. Summary