2. How To Say What You Want Describing Signals

3. What have we learned? Any traveling sinusoidal wave may be described by y = y m sin(kx   t +  )  is the phase constant that determines where the wave starts;  = 2  f = 2  /T; k = 2  /  v = /T = f =  /k Light always reflects with an angle of reflection equal to the angle of incidence (angles are measured to the normal). When light travels into a denser medium from a rarer medium, it slows down and bends toward the normal. n 1 sin  1 = n 2 sin  2 sin  c = n 2 /n 1 NA = n 0 sin  m = (n 1 2 - n 2 2 ) 1/2.

4. What Else Have We Learned? Any periodic function of frequency f 0 can be expressed as a sum over frequency of sinusoidal waves having frequencies equal to nf 0, where n is an integer. The sum is called the Fourier series of the function, and a plot of amplitude (coefficient of each sin/cos term) vs. frequency is called the Fourier spectrum of the function. Any non-periodic function (so frequency f 0  0) can be expressed as an integral over frequency of sinusoidal waves having frequencies. The integral is called the Fourier transform of the function, and a plot of amplitude vs. frequency is called the Fourier spectrum of the function. The Fourier spectrum of a wider pulse will be narrower than that of a narrow pulse, so it has a smaller bandwidth.

5. What Exactly Is Bandwidth, and Why Do We Care? A range of frequencies Generally found by taking the frequencies with amplitudes more than half the maximum amplitude (e.g., on a Fourier spectrum) Bandwidth for a medium is the range of frequencies which can pass through that medium with a minimum of separation Sampling theory says that a signal transmitting N different amplitudes per second requires a bandwidth of at least N/2: B>N/2 Usually this ideal is not achieved, and the required bandwidth is larger –Grant says B approx N

6. Pulses and Data Can represent binary data with pulses in a variety of ways 10110 could look like... Non-return-to-zero (NRZ) Return-to-zero (RZ) Manchester Coding Bipolar Coding Notice that the NRZ takes half the time of the others for the same pulse widths

7. Do the Before You Start and the What Kind of Signal Is It? Parts of the Activity

8. Distortion No physical change is instantaneous If change is too slow, won’t have time to rise before needs to fall Results in data loss Sharp edges Since rise is generally exponential, we define “rise time” to be time from 10% of max value to 90% of max; “fall time” is time from 90% to 10% To be able to resolve data, the rise time and fall time must be less than 70% of the bit width Sizeable rise time Really Distorted

9. Do the Rest of the Activity

10. Why do we want to modulate signals? An antenna produces EM radiation from standing waves of current; the length of the antenna must be at least /4 For frequencies in the audio range, that antenna length must be hundreds of kilometers long! If you broadcast radio w/o modulation, only one signal could be sent at a time in any region; e.g, you’d only have one radio station, and its area couldn’t overlap any other radio station.

11. How do we modulate signals? Amplitude modulation: –A signal with a constant carrier frequency is sent –The original signal becomes the amplitude of the transmitted signal –Since the transmitted signal is not a simple sine wave, it has a bandwidth of Fourier components Frequency modulation: –A signal with a constant carrier frequency is sent –The original signal becomes the change in frequency of the transmitted signal –Since the transmitted signal is not a simple sine wave, it has a bandwidth of Fourier components –FM is easier to amplify, since only the frequency determines the signal.

12. How do we send these signals? Radio antenna (AM frequencies around 1000 kHz, FM frequencies around 100 MHz) TV antenna (VHF frequencies are around 100 MHz, on either side of FM frequencies, UHF frequencies around 500 MHz) These are public transmissions, and so the carrier frequencies are set and regulated Coaxial cable Optical waveguides ISDN These are private transmissions, and sent over range of frequencies

13. What exactly is a decibel? A ratio, often of power BUT, in logarithmic form: dB = 10 log (P 2 /P 1 ) e.g., if my received signal is 1/10 as big as my transmitted signal, my “gain” would be gain dB = 10 log (1/10) = -10 The minus sign denotes loss, or a second power less than the initial power

14. Why do I care about decibels? Signal-to-noise ratios are often given in decibels You want the signal to be larger than the noise, so the ratio (in dB) should be positive For digital data, we use bit error rate, not signal-to-noise Bit error rate is ratio of wrong bits to total bits - it should be small, whereas SNR should be large Bit error rate can be expressed as a plain number, or in decibels

15. Before the next class,... Re-Read Chapter 3-4 of Grant, focusing on discussion of modes and of different types of dispersion. Start Homework 3, due next Thursday (posted shortly) Do Activity 05 Evaluation by Midnight Thursday