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Questions and Answers
What is the condition for the sampling frequency to satisfy the Nyquist rate?
What is the condition for the sampling frequency to satisfy the Nyquist rate?
Which of the following describes the Nyquist Interval?
Which of the following describes the Nyquist Interval?
What does the output of the Low Pass Filter (LPF) represent during the recovery of an unsampled signal?
What does the output of the Low Pass Filter (LPF) represent during the recovery of an unsampled signal?
Which of the following describes a key advantage of digital communications over analog systems?
Which of the following describes a key advantage of digital communications over analog systems?
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Which filter is described as producing values between samples using linear approximation?
Which filter is described as producing values between samples using linear approximation?
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Interpolation yields values of g(t) between samples by considering which of the following aspects?
Interpolation yields values of g(t) between samples by considering which of the following aspects?
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What is the first step in transforming an analog waveform into a digital form?
What is the first step in transforming an analog waveform into a digital form?
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According to the sampling theorem, how frequently must a signal be sampled to accurately reconstruct it?
According to the sampling theorem, how frequently must a signal be sampled to accurately reconstruct it?
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What does quantization involve in the context of digital transmission of analog signals?
What does quantization involve in the context of digital transmission of analog signals?
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Which of the following is NOT a step in the digital transmission process of analog signals?
Which of the following is NOT a step in the digital transmission process of analog signals?
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What is a potential benefit of using regenerative repeaters in digital communications?
What is a potential benefit of using regenerative repeaters in digital communications?
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In a digital communication system, which aspect is superior compared to analog systems?
In a digital communication system, which aspect is superior compared to analog systems?
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Which of the following statements reflects a characteristic of an analog signal?
Which of the following statements reflects a characteristic of an analog signal?
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What is the purpose of companding in signal processing?
What is the purpose of companding in signal processing?
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Which process takes place after the compression in the companding technique?
Which process takes place after the compression in the companding technique?
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What is quantization noise?
What is quantization noise?
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What happens during quantizer saturation?
What happens during quantizer saturation?
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What is the impact of timing jitter in the sampling process?
What is the impact of timing jitter in the sampling process?
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How are quantized sample values transmitted in Pulse Amplitude Modulation (PAM)?
How are quantized sample values transmitted in Pulse Amplitude Modulation (PAM)?
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Which of the following is NOT a source of errors while quantizing?
Which of the following is NOT a source of errors while quantizing?
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In Binary Pulse Code Modulation (PCM), what is done to each quantized sample?
In Binary Pulse Code Modulation (PCM), what is done to each quantized sample?
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What is the minimum sampling frequency required for perfect reconstruction of a signal g(t)?
What is the minimum sampling frequency required for perfect reconstruction of a signal g(t)?
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What condition must be met to avoid overlapping of the replicas in the frequency domain during signal sampling?
What condition must be met to avoid overlapping of the replicas in the frequency domain during signal sampling?
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What process allows for the reconstruction of the continuous signal g(t) from its samples?
What process allows for the reconstruction of the continuous signal g(t) from its samples?
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In signal reconstruction, what type of filter is ideally used to recover the continuous time signal g(t)?
In signal reconstruction, what type of filter is ideally used to recover the continuous time signal g(t)?
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What is the relationship between the sampling frequency fs and the bandwidth B for a signal that contains impulses?
What is the relationship between the sampling frequency fs and the bandwidth B for a signal that contains impulses?
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What is the Nyquist interval in relation to sampling frequency?
What is the Nyquist interval in relation to sampling frequency?
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If g(t) = sin(2πBt), what are the implications for the sampling frequency fs?
If g(t) = sin(2πBt), what are the implications for the sampling frequency fs?
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What characteristic of G(f) indicates the need for a higher sampling frequency?
What characteristic of G(f) indicates the need for a higher sampling frequency?
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What is the primary purpose of passing a signal through an anti-aliasing filter before sampling?
What is the primary purpose of passing a signal through an anti-aliasing filter before sampling?
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Which of the following statements about the reconstructed signal spectrum is true?
Which of the following statements about the reconstructed signal spectrum is true?
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What occurs when a signal is undersampled?
What occurs when a signal is undersampled?
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What is the critical sampling condition described to avoid aliasing?
What is the critical sampling condition described to avoid aliasing?
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What effect does the anti-aliasing filter have concerning noise components?
What effect does the anti-aliasing filter have concerning noise components?
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In the context of signal spectrum, what does it mean for a time-limited signal?
In the context of signal spectrum, what does it mean for a time-limited signal?
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How is a sampled signal represented within a pulse width modulation framework?
How is a sampled signal represented within a pulse width modulation framework?
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What is the sampling frequency Fs required, at a minimum, to avoid aliasing for a signal with maximum frequency fm?
What is the sampling frequency Fs required, at a minimum, to avoid aliasing for a signal with maximum frequency fm?
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Which sampling scenario correctly represents an oversampled signal?
Which sampling scenario correctly represents an oversampled signal?
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What does the notation G(f) signify when referring to signal spectra?
What does the notation G(f) signify when referring to signal spectra?
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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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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.