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# Introduction to Digital Communications

Created by
@ReasonableNarwhal

### What does the Shannon-Hartley Theorem relate to?

Information capacity to bandwidth and signal strength

### According to Hartley's Law, information capacity is directly proportional to which two factors?

Bandwidth and transmission time

### What is the formula for information capacity in the context of Shannon's Limit for Information Capacity?

$C = 2B \log_2(M)$

### In Shannon's Limit for Information Capacity, what does 'M' represent in the formula $C = 2B \log_2(M)$?

<p>Number of levels transmitted</p> Signup and view all the answers

### How is the information capacity related to bandwidth and signal-to-noise ratio in terms of Shannon-Hartley Theorem?

<p>$I = B \log_2(1 + S/N)$</p> Signup and view all the answers

### What do the symbols 'B', 'T', and 'k' represent in Hartley's Law formula $I = kB^2T$?

<p>'B' as bandwidth, 'T' as transmission time, 'k' as a constant</p> Signup and view all the answers

### What is the relationship between the number of bits per sample (m) and the number of quantization levels (N) in PCM?

<p>N = 2^m</p> Signup and view all the answers

### If a PCM system uses 8 bits per sample, how many quantization levels are there?

<p>256</p> Signup and view all the answers

### What is the maximum possible quantization error in a PCM system?

<p>One-half of the voltage difference between adjacent quantization levels</p> Signup and view all the answers

### What is the dynamic range of a PCM system?

<p>The ratio of the maximum voltage level to the resolution</p> Signup and view all the answers

### How many bits are required for a PCM system with a dynamic range of 60 dB?

<p>12 bits</p> Signup and view all the answers

### In a PCM system, what is the effect of increasing the number of quantization levels?

<p>Both (b) and (c)</p> Signup and view all the answers

### According to the Shannon-Hartley theorem, what is the formula for the information capacity (I) of a communication channel?

<p>$I = B \log_2 (1 + S/N)$</p> Signup and view all the answers

### What does the 'S/N' term represent in the Shannon-Hartley theorem?

<p>The signal-to-noise ratio as a power ratio, not in decibels</p> Signup and view all the answers

### What is the relationship between the bandwidth (B) and the transmission time (T) of a communication channel?

<p>The bandwidth is inversely proportional to the transmission time</p> Signup and view all the answers

### What is the Nyquist sampling rate theorem?

<p>The sampling rate must be at least twice the highest frequency component of the signal to avoid aliasing</p> Signup and view all the answers

### What is the formula for calculating the frequency of the aliasing distortion ($f_a$) in a pulse modulation digital communications system?

<p>$f_a = f_s - f_m$</p> Signup and view all the answers

### What is the maximum theoretical data rate that can be transmitted over the telephone line described in the sample problem?

<p>The maximum theoretical data rate is 160 kbps</p> Signup and view all the answers

## Study Notes

### Pulse Code Modulation (PCM)

• Each sample is represented by the binary number representing the level closest to its amplitude, and is transmitted in serial form.
• In linear PCM, levels are separated by equal voltage gradations.
• The number of levels available depends on the number of bits used to express the value, given by N = 2^m, where N = number of levels, and m = number of bits per sample.
• Example: if the number of bits per sample is 8, N = 2^8 = 256 levels; if the number of bits per sample is 16, N = 2^16 = 65,536 levels.

### Quantizing Errors/Quantizing Noise

• The quantizing process produces errors called quantizing errors/quantizing noise, due to the original analog signal having an infinite number of signal levels.
• The largest possible error is one-half of the difference between levels (resolution).
• Increasing the number of levels decreases the quantizing errors, but also increases the number of bits that must be used per cycle.

### Dynamic Range

• The dynamic range is the ratio of the strongest possible signal that can be transmitted and the weakest discernable signal, given by DR = Vmax / Vmin.
• To determine the number of bits required for a PCM code, 2^n - 1 ≥ DR, where n = number of PCM bits, excluding sign bit.
• Example: a PCM system has a maximum analog input frequency at 4 kHz, a maximum decoded voltage at the receiver at ±2.55 V, and a minimum dynamic range of 46 dB.

### Shannon Limit

• The Shannon limit is a theoretical limit on the maximum rate of error-free transmission of information, given by I = B log2(1 + S/N).
• The Shannon limit is a fundamental limit on the maximum information capacity of a communication channel, and is dependent on the bandwidth and signal-to-noise ratio.

### Pulse Modulation

• Pulse modulation is used to transmit an analog signal by digital means, by sampling the signal at intervals and expressing the amplitude of each sample as a binary number.
• The samples can be reconstituted at the receiver to form a replica of the original signal.
• Natural sampling and flat-topped sampling (using a sample-and-hold circuit) are two types of pulse modulation.

### Nyquist Sampling Rate Theorem

• The Nyquist sampling rate theorem states that the sampling rate must be at least twice the bandwidth of the signal to be sampled, given by fsample ≥ 2 × fsignal.
• If the sampling rate is too low, aliasing or foldover distortion occurs, resulting in a penalty in the form of distortion.

### Aliasing/Foldover Distortion

• Aliasing or foldover distortion occurs when the sampling rate is too low, given by fa = fs - fm.
• Example: an attempt is made to transmit a baseband frequency of 30 kHz using a digital audio system with a sampling rate of 44.1 kHz.

### Digital Communications

• Digital communications systems have several advantages, including ease of processing, ease of multiplexing, and noise immunity.
• Digital communications involve the transmission, reception, and processing of information.
• Electronic communications systems involve the transmission, reception, and processing of information, and can be simplified with a block diagram of an information source, transmission medium, and information destination.

### Digital Transmission and Digital Radio

• Digital transmission involves the transmittal of digital pulses between two or more points in a communication system, requiring a physical facility between transmitter and receiver.
• Digital radio involves the transmittal of digitally modulated analog carriers between two or more points in a communication system, with the transmission medium being free space or earth’s atmosphere.

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## Description

Explore the fundamentals of digital communications, including analog modulation techniques (AM, FM, PM) and digital communication systems. Learn about the advantages of digital modulation systems such as ease of processing, multiplexing, and noise immunity. Dive into the world of electronics communications, covering transmission, reception, and information processing.

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