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Digital Communications Overview
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Digital Communications Overview

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Questions and Answers

What is the condition for the sampling frequency to satisfy the Nyquist rate?

  • fs < 2B
  • fs >= B
  • fs > 2B (correct)
  • fs = 2B

    • Which of the following describes the Nyquist Interval?

  • Ts < 1/B
  • Ts = 1/2B
  • Ts < 1/2B (correct)
  • Ts > 1/2B

    • What does the output of the Low Pass Filter (LPF) represent during the recovery of an unsampled signal?

  • The weighted sum of all sample values (correct)
  • The average of all the samples
  • Only the original sample values
  • The ideal low frequency components

    • Which of the following describes a key advantage of digital communications over analog systems?

    <p>Ability to withstand channel noise and distortions</p> Signup and view all the answers

    Which filter is described as producing values between samples using linear approximation?

    <p>First Order Hold filter</p> Signup and view all the answers

    Interpolation yields values of g(t) between samples by considering which of the following aspects?

    <p>Weighted sum of all sample values</p> Signup and view all the answers

    What is the first step in transforming an analog waveform into a digital form?

    <p>Sampling</p> Signup and view all the answers

    According to the sampling theorem, how frequently must a signal be sampled to accurately reconstruct it?

    <p>At a rate greater than the maximum frequency in the signal</p> Signup and view all the answers

    What does quantization involve in the context of digital transmission of analog signals?

    <p>Converting the continuous amplitude values into discrete values</p> Signup and view all the answers

    Which of the following is NOT a step in the digital transmission process of analog signals?

    <p>Modulation</p> Signup and view all the answers

    What is a potential benefit of using regenerative repeaters in digital communications?

    <p>Increase in signal strength over long distances</p> Signup and view all the answers

    In a digital communication system, which aspect is superior compared to analog systems?

    <p>Flexibility in implementation</p> Signup and view all the answers

    Which of the following statements reflects a characteristic of an analog signal?

    <p>It can take on an infinite number of amplitude values.</p> Signup and view all the answers

    What is the purpose of companding in signal processing?

    <p>To compress and expand the signal for better transmission</p> Signup and view all the answers

    Which process takes place after the compression in the companding technique?

    <p>Expansion</p> Signup and view all the answers

    What is quantization noise?

    <p>Unwanted spectral components introduced during quantization</p> Signup and view all the answers

    What happens during quantizer saturation?

    <p>Signal amplitudes are clipped to extreme levels</p> Signup and view all the answers

    What is the impact of timing jitter in the sampling process?

    <p>Low-level additional spectral components and noise</p> Signup and view all the answers

    How are quantized sample values transmitted in Pulse Amplitude Modulation (PAM)?

    <p>With multiple levels of voltage values</p> Signup and view all the answers

    Which of the following is NOT a source of errors while quantizing?

    <p>Interference from external signals</p> Signup and view all the answers

    In Binary Pulse Code Modulation (PCM), what is done to each quantized sample?

    <p>It is digitally encoded into an n bit code word</p> Signup and view all the answers

    What is the minimum sampling frequency required for perfect reconstruction of a signal g(t)?

    <p>fs = 2B</p> Signup and view all the answers

    What condition must be met to avoid overlapping of the replicas in the frequency domain during signal sampling?

    <p>fs must be greater than or equal to 2B</p> Signup and view all the answers

    What process allows for the reconstruction of the continuous signal g(t) from its samples?

    <p>Interpolation</p> Signup and view all the answers

    In signal reconstruction, what type of filter is ideally used to recover the continuous time signal g(t)?

    <p>Ideal low pass filter</p> Signup and view all the answers

    What is the relationship between the sampling frequency fs and the bandwidth B for a signal that contains impulses?

    <p>fs must be greater than or equal to 2B</p> Signup and view all the answers

    What is the Nyquist interval in relation to sampling frequency?

    <p>1/(2B)</p> Signup and view all the answers

    If g(t) = sin(2Ï€Bt), what are the implications for the sampling frequency fs?

    <p>fs must be greater than B</p> Signup and view all the answers

    What characteristic of G(f) indicates the need for a higher sampling frequency?

    <p>Presence of an impulse at the highest frequency</p> Signup and view all the answers

    What is the primary purpose of passing a signal through an anti-aliasing filter before sampling?

    <p>To suppress frequency components above fs/2 Hz.</p> Signup and view all the answers

    Which of the following statements about the reconstructed signal spectrum is true?

    <p>The spectrum is Gaa(f) = G(f) for |f| &lt; fs/2.</p> Signup and view all the answers

    What occurs when a signal is undersampled?

    <p>The reconstructed signal will have aliased components.</p> Signup and view all the answers

    What is the critical sampling condition described to avoid aliasing?

    <p>Fs &gt; 2B</p> Signup and view all the answers

    What effect does the anti-aliasing filter have concerning noise components?

    <p>It suppresses noise components above fs/2.</p> Signup and view all the answers

    In the context of signal spectrum, what does it mean for a time-limited signal?

    <p>Its spectrum extends to infinity.</p> Signup and view all the answers

    How is a sampled signal represented within a pulse width modulation framework?

    <p>By changing the width of periodic pulse train.</p> Signup and view all the answers

    What is the sampling frequency Fs required, at a minimum, to avoid aliasing for a signal with maximum frequency fm?

    <p>Fs = 2fm</p> Signup and view all the answers

    Which sampling scenario correctly represents an oversampled signal?

    <p>Fs &gt; 2fm</p> Signup and view all the answers

    What does the notation G(f) signify when referring to signal spectra?

    <p>The spectrum of the original signal before sampling.</p> Signup and view all the answers

    Study Notes

    Digital Communications

    • Digital communication systems are more robust than analog systems due to their ability to withstand channel noise and distortions.
    • Digital communications systems offer flexibility due to the use of microprocessors and VLSI (Very Large Scale Integration) systems.
    • Error correction coding, multiplexing, storage, and reproduction of data are superior in digital communication systems.

    Digital Transmission of Analog Signals

    • Analog signals can take any value and are converted to digital signals for use in digital communication systems through the following steps:
    • Sampling
    • Quantization
    • Encoding
    • Baseband OR Passband Transmission

    Sampling Theorem

    • A band-limited signal can be perfectly reconstructed from its samples if the sampling frequency (fs) is at least twice the signal bandwidth (B).
    • The sampling rate must be greater than or equal to the Nyquist rate (fs >= 2B).
    • The minimum sampling frequency is called the Nyquist frequency, and the corresponding sampling interval is called the Nyquist interval.

    Sampling Process

    • The sampling process is performed by multiplying the signal with an impulse train.
    • The resulting sampled signal is a series of impulses, where the amplitude of each impulse represents the signal value at the corresponding sampling instant.

    Signal Reconstruction

    • The process of reconstructing the original signal from its sampled values is known as interpolation.
    • Interpolation can be performed using an ideal low-pass filter with a bandwidth equal to the signal bandwidth and a gain of Ts (sampling period).

    Practical Issues with Sampling

    • Realizability of Reconstruction Filter: An ideal filter is not physically realizable, so practical filters introduce distortions in the reconstructed signal.
    • Sampling Rate: In practice, the sampling rate must be significantly higher than the Nyquist rate to minimize aliasing artifacts.

    Under sampling & Aliasing

    • Under sampling occurs when the sampling rate (fs) is less than twice the signal bandwidth (B).
    • The result is the phenomenon called aliasing, resulting in a distorted reconstructed signal.
    • To avoid aliasing, an anti-aliasing filter is used prior to sampling, which removes frequency components above the signal bandwidth.

    Quantization

    • The process of converting a continuous-valued signal into a discrete set of values.
    • The number of quantization levels dictates the resolution of the quantized signal.
    • Quantization introduces quantization noise, a form of distortion that reduces the fidelity of the reconstructed signal.
    • Quantizer saturation occurs when the signal amplitude exceeds the maximum level of the quantizer, resulting in the amplitude being clamped to the maximum or minimum value.
    • Timing jitter occurs when the sampling instants are unstable, introduces noise and causes unpredictable timing errors in the reconstructed signal.

    Encoding

    • Encoding converts the quantized samples into a digital code representation.
    • Binary PCM (Pulse Code Modulation) encodes each quantized sample into an n-bit code word.

    Companding

    • Companding is a technique used to improve the dynamic range of the signal by using a non-linear mapping function to emphasize weaker signals and compress stronger signals.
    • Two common companding laws are:
      • μ-law: Used in North American standards.
      • A-law: Used in European standards.

    Sources of Errors while Quantizing

    • Quantization noise
    • Quantizer saturation
    • Timing jitter

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    Related Documents

    Comsys_Digital Representation of Analog Signals_L-14-18_16-26Sep24.pdf

    Description

    Explore the essentials of digital communication systems, focusing on their advantages over analog systems. Learn about the digital transmission of analog signals, including the crucial steps of sampling, quantization, and encoding. Understand the Sampling Theorem and its significance in accurately reconstructing signals.

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