How To Say What You Want

1
How To Say What You Want

• Describing Signals

2
What have we learned?

• Any traveling sinusoidal wave may be described by
• y ym sin(kx ? wt f)
• f is the phase constant that determines where
  the wave starts w 2pf 2p/T k 2p/l v
  l/T lf w/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.
• n1 sin q1 n2 sin q2
• sin qc n2/n1
• NA n0 sin qm (n12 - n22)1/2.

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What Else Have We Learned?

• Any periodic function of frequency f0 can be
  expressed as a sum over frequency of sinusoidal
  waves having frequencies equal to nf0, 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 f0 ?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.

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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 BgtN/2
• Usually this ideal is not achieved, and the
  required bandwidth is larger
• Grant says B approx N

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Pulses and Data

• Can represent binary data with pulses in a
  variety of ways
• 10110 could look like . . .

Notice that the NRZ takes half the time of the
others for the same pulse widths
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Do the Before You Start and the What Kind of
Signal Is It? Parts of the Activity
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Distortion

• No physical change is instantaneous
• If change is too slow, wont have time to rise
  before needs to fall
• Results in data loss

• 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

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Do the Rest of the Activity
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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 l/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, youd only have one radio station, and its
  area couldnt overlap any other radio station.

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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.

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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
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What exactly is a decibel?

• A ratio, often of power
• BUT, in logarithmic form
• dB 10 log (P2/P1)
• 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

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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

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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