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Signals

Signals. Signals are electric or electromagnetic encoding of data. Information, Data and Signals. Data - A representation of facts, concepts, or instructions in a formalized manner suitable for communication, interpretation, or processing by human beings or by automatic means

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Signals

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  1. Signals Signals are electric or electromagnetic encoding of data

  2. Information, Data and Signals • Data - A representation of facts, concepts, or instructions in a formalized manner suitable for communication, interpretation, or processing by human beings or by automatic means • Information - The meaning that is currently assigned to data by means of the conventions applied to those data

  3. Information, Data and Signals Information Data Signal 001011101

  4. Computers Use Signals for Communcation • Computers transmit data using digital signals, sequences of specified voltage levels. Graphically they are often represented as a square wave. • Computers sometimes communicate over telephone line using analog signals, which are formed by continuously varying voltage levels.

  5. Signal = Function of Time • The signal is a function of time. Horizontal axis represents time and the vertical axis represents the voltage level. • Signal represents data OR Data is encoded by means of a signal • Signal is what travels on a communication medium • An understanding of signals is required so that suitable signal may be chosen to represent data

  6. Continuous and Discrete Signal • Continuous or Analog signals take on all possible values of amplitude • Digital or Discrete Signals take on finite set of voltage levels

  7. Analog and Digital Signal • Continuous/Analog signals take on all possible values of amplitude • Digital or Discrete Signals take on finite set of voltage levels

  8. Analog and Digital Data • Analog data take on all possible values. Voice and video are continuously varying patterns of intensity • Digital data take on finite (countable) number of values. Example, ASCII characters, integers

  9. Periodic Signals • Some signals repeat themselves over fixed intervals of time. Such signals are said to be periodic • A signal s(t) is periodic if and only if: • s(t+T) = s(t) -< t < + • where the constant T is the periodic of the signal, otherwise a signal is aperiodic (or non- periodic).

  10. Periodic Signal Properties • Three important characteristics of a periodic signal are : • Amplitude (A): the instantaneous value of a signal at any time measured in volts. • Frequency (f): the number of repetitions of the period per second or the inverse of the period; it is expressed in cycles per second or Hertz (Hz). T=1/f • Phase (): a measure of the relative position in time within a single period of a signal, measured in degrees • Wavelength (): distance occupied by a signal in one period

  11. Spectrum and Bandwidth • Spectrum of a signal - the range of frequencies it contains • Absolute bandwidth - the width of the spectrum • Effective bandwidth or just bandwidth - the band of frequencies which contains most of the energy of the signal - half-power bandwidth

  12. Bandwidth and Data Rate • Width of the spectrum of frequencies that can be transmitted • if spectrum=300 to 3400Hz, bandwidth=3100Hz • Greater bandwidth leads to greater costs • Limited bandwidth leads to distortion • Analog measured in Hertz, digital measured in baud

  13. General Observations about Signals • For a signal with multiple frequencies, energy is in the first few frequency components • Increasing the bandwidth increases data rate • The transmission medium limits the bandwidth • Greater the bandwidth, the greater the cost • For a given data rate, limiting the bandwidth, increases distortion, and hence the error rate

  14. Transmission Impairments • Attenuation • Delay • Noise

  15. Attenuation • Loss of signal strength over distance • Use of amplifiers to boost analog signals; entire signal (including noise or distortion) is amplified • Use of repeaters for digital data; data recovered and then transmitted

  16. Attenuation Distortion • Analog signal is made up of several frequencies • Attenuation is different for different frequencies; Different losses at different frequencies • More of a problem for analog signals than digital

  17. Attenuation • Attenuation • – the strength of a signal falls off with distance • Attenuation Distortion • – attenuation varies as a function of frequency

  18. Attenuation is measured in deciBels - dB

  19. dB Calculation • Example • Input power is 1 Watt • Output power is 1 mW • dB Attenuation is • 10 * log (1 W/1 mW) = 10 * (3) • = 30 dB

  20. Use of Repeaters

  21. Delay Distortion • The velocity of propagation of a signal through a guided medium varies with frequency. • Different frequency components travel at different speeds therefore arrive at a destination at different times. • Particularly critical for digital data because bits may spill over causing Inter-Symbol Interference.

  22. Transmission Impairments Visually

  23. Noise • What is Noise? • Any unwanted signal • Types of Noise • Thermal • Intermodulation • Impulse • Crosstalk

  24. Thermal Noise • Thermal noise, white noise • Due to random motion of atoms • N = kTW • k = Boltzman Constant (1.381 X 10-23 J/K) • T = Absolute Temperature (Kelvin) • W = Bandwidth (Hz) • Why is it called White Noise?

  25. Inter-modulation Noise • Inter-modulation noise • when two signals at different frequencies are mixed in the same medium, sum or difference of original frequencies or multiples of those frequencies can be produced, which can interfere with the intended signal - occurs when there is some non-linearity in the system

  26. Noise • Crosstalk • when there is an unwanted coupling between signal paths. For example some times talking on the telephone you can hear another conversation. • Impulse noise • Due to lightning or some other random transient phenomenon

  27. Effect of Noise

  28. Transmission Impairments in Un-Guided Media • Free-Space loss • Signal disperses with distance • Atmospheric Absorption • Attenuation caused by water vapor and oxygen • Water vapor: High around 22 GHz, less around 15 GHz • Oxygen: High around 60 GHz, less below 30 GHz

  29. Transmission Impairments in Un-Guided Media • Multipath • Receive multiple signals reflected by many obstacles • Refraction • Radio waves get bent by change in speed with altitude • Thermal Noise • White noise. Important factor for satellite communications

  30. Channel Capacity • The rate at which digital data can be transmitted over a given communication channel • Two formulations • Shannon’s Formulation • Nyquist Formulation

  31. Shannon’s Law • Considers the noise (only white noise) • Key parameter is signal-to-noise ratio (S/N, or SNR), which is the ratio of the power in a signal to the power contained in the noise, typically measured at the receiver - often expressed in decibels • Maximum theoretical error-free capacity in bits per second C = W log2 (1+S/N)

  32. Signal to Noise Ratio - S/N • Signal to Noise ratio: power in signal to power contained in noise • Doubling the bandwidth doubles the data rate • At a given noise level, higher the data rate, the higher the error rate • Increasing signal strength increases intermodulation noise • Wider the bandwidth, the more noise is admitted. • As W increases, S/N decreases • Goal: Get highest data rate with lowest error rate at cheapest cost

  33. Example with S/N of 1000 for Telephone LIne • Example for voice-grade telephone line: • Using Shannon's formulation for channel capacity: • C = W * log2(1 + S/N) • Where log2 represent logarithm base 2 • 30 dB S/N = 1000 S/N • C = 3100 * log2(1 + 1000) • C = 30,894 bps • Hence the channel capacity is 30,894 bits per second.

  34. Nyquist Limit • Nyquist limit (in a noise-free environment) • C = 2 W log2M • Given a bandwidth of W, highest signal rate that can be carried is 2W with binary signaling (M=2) • For multilevel signaling C = 2W log2M • where M is the number of discrete signals or voltage levels

  35. Example with M-ary Signaling with 3100 Hz Bandwidth C = 2 W log2M

  36. BPS vs. Baud • BPS=bits per second • Baud= Number of signal changes per second • Each signal change can represent more than one bit, through variations on amplitude, frequency, and/or phase

  37. Why Study Analog? • Telephone system is primarily analog rather than digital (designed to carry voice signals) • Low-cost, ubiquitous transmission medium • If we can convert digital information (1s and 0s) to analog form (audible tone), it can be transmitted inexpensively • Media are inherently analog too, real world is analog

  38. Analog Transmission • Analog signal transmitted without regard to content • May be analog or digital data • Attenuated over distance • Use amplifiers to boost signal • Also amplifies noise

  39. Digital Transmission • Concerned with content • Integrity endangered by noise, attenuation etc. • Repeaters are used • Repeater receives signal • Extracts bit pattern • Retransmits • Attenuation is overcome • Noise is not amplified

  40. Use of Repeaters

  41. Which Signal/Data is Better Analog or Digital? • Digital is better • Even Analog data can be converted into digital data and transmitted as digital data • Digital data provide the following advantages: • Digital technology • Data integrity through EDC and ECC • Capacity utilization through TDM • Security and privacy through encryption • Integration of all forms of information

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