Communication Systems Chapter 8: Fourier Analysis
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Questions and Answers

Which type of cable allows transmission over long distances without amplification?

  • Fiber Optics
  • Magnetic Media
  • Coaxial Cable
  • Twisted Pair (correct)
  • What defines the number of twists per centimeter in twisted pair cables?

  • Category Type (correct)
  • Length of the wire
  • Type of shielding
  • Electrical resistance
  • What is the maximum theoretical data rate that fiber optics can achieve?

  • 10 Gbps
  • 50,000 Gbps (correct)
  • 1 Gbps
  • 20 Gbps
  • How does the twisting of wires in twisted pair cables affect signal quality?

    <p>Decreases crosstalk</p> Signup and view all the answers

    Which media has better shielding than twisted pair cables?

    <p>Coaxial Cable</p> Signup and view all the answers

    What is the bandwidth potential of coaxial cables?

    <p>1 GHz</p> Signup and view all the answers

    What characteristic of fiber optics contributes to a very low error rate?

    <p>Ultra-thin glass construction</p> Signup and view all the answers

    Which statement describes the category types of twisted pair cables?

    <p>More twists correspond to higher quality signals.</p> Signup and view all the answers

    What limitation is often observed in the practical performance of fiber optics?

    <p>Leaking signal transmission</p> Signup and view all the answers

    Which of the following characteristics is essential when selecting guided transmission media?

    <p>Band width, delay, cost, and ease of installation</p> Signup and view all the answers

    What mathematical technique is described as one of the most important for analyzing data transmission?

    <p>Fourier Analysis</p> Signup and view all the answers

    Which of the following statements about Fourier series is true?

    <p>It is a periodic function representation.</p> Signup and view all the answers

    Bandwidth of a signal is primarily dependent on which of the following factors?

    <p>Construction, thickness, and length of the medium</p> Signup and view all the answers

    Which of the following best describes a cutoff frequency (fc)?

    <p>Frequency beyond which the signal is attenuated</p> Signup and view all the answers

    What is the relationship between rms amplitude and power in bandwidth-limited signals?

    <p>Power is directly proportional to the square of rms amplitude</p> Signup and view all the answers

    Which of the following describes a root-mean-square (rms) amplitude?

    <p>The square root of the average of the squares of the amplitudes</p> Signup and view all the answers

    A periodic function can be represented using which of the following concepts?

    <p>An infinite series of harmonically-related sinusoids</p> Signup and view all the answers

    In the context of data communication, what does the Fourier coefficient represent?

    <p>Amplitude and phase of a sinusoid</p> Signup and view all the answers

    What role does the cutoff frequency play in bandwidth-limited signals?

    <p>It indicates the maximum frequency that can be transmitted without distortion.</p> Signup and view all the answers

    What kind of transmission media does the physical layer study cover?

    <p>Guided, wireless, and satellite media</p> Signup and view all the answers

    Study Notes

    Communication Systems and Computer Networks (1404703) - Part 8

    • The physical layer studies mechanical, physical, electrical, and timing properties of data transmission.
    • It analyzes different transmission media: guided, wireless, and satellite.
    • Data communication relies on functions (voltage or current) that can be mathematically analyzed.
    • Fourier analysis is a crucial technique for analyzing these functions.
    • Periodic functions can be represented by an infinite combination of sine and cosine waves.
    • Knowing the harmonics allows reconstructing the function.
    • Signal analysis helps determine proper sampling.

    Fourier Series

    • A Fourier series represents a function as a sum of harmonically-related sinusoids with varying amplitudes and phases.
    • The amplitudes and phases of these sinusoids are combined into Fourier coefficients (complex numbers).
    • Fourier series are only applicable to periodic functions.
    • For functions defined over a finite interval, the values outside that interval are irrelevant.
    • The Fourier series formula is given as a0/2 + Σ [an cos(nx) + bn sin(nx)] where the summation is from n = 1 to infinity

    Bandwidth-Limited Signals

    • Key factors include RMS (Root Mean Square) amplitude, bandwidth (related to construction, medium thickness and length), and cutoff frequency (fc).
    • Bandwidth-limited signals are crucial for data transmission.
    • Successive approximations to the signal using different harmonics provide a clearer illustration.
    • Increasing the number of harmonics closer approximates the original signal.

    Bandwidth-Limited Signals (2)

    • A binary signal and its Fourier amplitudes showcase how successive approximation improves the signal reconstruction.

    Bandwidth-Limited Signals (3)

    • A table illustrates the relationship between data rate (bps), time (msec), first harmonic (Hz), and the number of harmonics sent for different data rates.
    • This demonstrates how increasing data rates increase the number of harmonics required.

    Shannon's Maximum Data Rate of a Channel

    • Shannon's theorem states the maximum achievable data rate (bits per second) of a noisy channel.
    • This depends on the bandwidth (H, in Hz) of the channel and the signal-to-noise ratio (S/N).
    • The maximum data rate is given by the formula Max # of bits/sec = H log2(1 + S/N).

    Guided Transmission Media

    • Selection of transmission media depends on bandwidth, delay, cost, and ease of installation.
    • Magnetic media (skipped) are less relevant
    • Common types of guided media include twisted pair, coaxial cable, and fiber optics.

    Twisted Pair

    • Twisted pair consists of two insulated copper wires (1mm thick).
    • Twisting eliminates the antenna effect of parallel lines.
    • Twisted pairs are commonly used in telephones.
    • They can transmit data over several kilometers before requiring repeaters for extended distances.
    • Different categories (e.g., Category 3, 5 UTP) define the number of twists per centimeter affecting characteristics like crosstalk and bandwidth.

    Coaxial Cable

    • Coaxial cables offer better shielding compared to twisted pairs.
    • They are used for longer distances and faster data rates and also have higher bandwidth (sometimes up to 1 GHz).

    Fiber Optics

    • Fiber optics are ultra-thin glass fibers that transmit light signals converted to electrical signals.
    • Theoretical data rates are exceptionally high (50,000 Gbps) but the actual ability is only around 10 Gbps due to losses.
    • Light signals travel through the fiber in a process called total internal reflection.
    • Fiber optics are characterized by high bandwidth and low error rates, but are more expensive.

    Fiber Cables (2)

    • A comparison table for LEDs and semiconductor lasers as light sources in fiber optic systems.
    • The table highlights factors such as data rate, fiber type, distance range, lifetime, temperature sensitivity and cost.

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    Description

    This quiz covers key concepts from Chapter 8 of Communication Systems and Computer Networks, focusing on the physical layer and Fourier analysis. It examines data transmission properties, different transmission media, and the application of Fourier series in signal analysis. Test your understanding of these critical topics in communication technology.

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