Digital Communication Basics: Sampling, Quantization u0026 Encoding Quiz Quiz

Explore key concepts in digital communication including the principles of sampling, quantization, and encoding. This quiz helps reinforce important foundations for understanding how analog signals are converted and processed in digital systems.

1. Nyquist Theorem Application

   According to the Nyquist sampling theorem, what is the minimum sampling rate required to accurately digitize an analog signal with a maximum frequency of 10 kHz?

   1. 10 Hz
   2. 5 kHz
   3. 20 kHz
   4. 100 kHz

   Explanation: The Nyquist theorem states that the sampling rate must be at least twice the maximum frequency present in the signal, so for a 10 kHz signal, the minimum is 20 kHz. Sampling at 5 kHz or 10 Hz would violate the theorem and introduce aliasing. While 100 kHz would also work, it's not the minimum, making 20 kHz the correct answer.

2. Quantization Levels

   If a 3-bit analog-to-digital converter is used, how many distinct quantization levels are available for encoding the analog signal?

   1. 3
   2. 8
   3. 6
   4. 16

   Explanation: A 3-bit converter provides 2 raised to the power of 3, which means 8 quantization levels. 6 is incorrect because it's not a power of two; 16 would result from a 4-bit converter, and 3 reflects the number of bits, not the number of possible levels.

3. Quantization Error Concept

   What best describes quantization error in the context of analog-to-digital conversion?

   1. A type of noise added before sampling
   2. Error caused by sampling below the Nyquist rate
   3. The difference between the actual analog value and its nearest quantized value
   4. The loss of signal phase due to digital encoding

   Explanation: Quantization error occurs when a continuous range of values is mapped to discrete levels, resulting in a small difference between the actual analog value and its quantized representation. Noise added before sampling is not quantization error, and errors from low sampling rates or phase loss are related but different issues.

4. Binary Pulse Code Modulation

   Which of the following statements about binary Pulse Code Modulation (PCM) is correct?

   1. It avoids quantization and sampling altogether.
   2. It encodes signals using variable-length analog pulses.
   3. It only works for signals with frequencies below 1 kHz.
   4. It represents quantized values using a series of binary numbers.

   Explanation: PCM encodes sampled and quantized analog signals by converting them into binary numbers, making this the correct answer. It does not use variable-length analog pulses, is not limited to signals below 1 kHz, and quantization plus sampling are fundamental parts of PCM, so the other options are incorrect.

5. Encoding Bandwidth Impact

   How does increasing the number of bits used in encoding each sample of an analog signal affect the required bandwidth for digital transmission?

   1. It increases the required bandwidth, as more bits per sample must be transmitted.
   2. It leaves the required bandwidth unchanged regardless of bit depth.
   3. It decreases the required bandwidth because quantization error is lower.
   4. It provides no impact unless the sampling rate also increases.

   Explanation: Using more bits per sample means each sample carries more information, which increases the data rate and thus the bandwidth needed for transmission. A lower quantization error does not reduce required bandwidth. Bandwidth is directly affected by bit depth, not only by sampling rate. Therefore, only option one is correct.