Shannon Hartley theorem by Shafiqa Memon (19ES30).pptx

this theorem provides the information about the maximum bit rate that can be transmitted over a communication channel and the maximum available bandwidth for a communication channel. this theorem provides a formula to calculate the capacity of the channel. There is a Shannon channel capacity calculator that can be used to calculate the capacity of any communication channel.

1. Advanced communication System Title: Shannon-Hartley theorem & TECHNOLOGY, NAWABSHAH QUAID-E-AWAM UNIVERSITY OF ENGINEERING, SCIENCE & TECHNOLOGY, NAWABSHAH Name: Shafiqa Memon Roll Number :19ES30 Assigned By: Dr. Nadeem Naeem Department of Electronic Engineering

2. Shannon Hartley theorem Introduction: The Shannon-Hartley theorem, also known as the Shannon capacity or the Shannon limit, is a fundamental result in information theory that establishes the maximum rate at which information can be transmitted over a noisy communication channel without error. It was formulated by Claude Shannon and later extended by Ralph Hartley.

3. Shannon Hartley theorem In reality, we cannot have a noiseless channel; the channel is always noisy. In 1944, Claude Shannon introduced a formula, called the Shannon capacity, to determine the theoretical highest data rate for a noisy channel. The theorem provides a mathematical formula to determine the maximum achievable data rate, known as the channel capacity (C), in bits per second (bps), for a given communication channel with a specific bandwidth and signal-to-noise ratio (SNR).

4. Shannon Hartley theorem Statement: The Shannon-Hartley theorem states that the channel capacity is proportional to the available bandwidth and to the signal-to-noise ratio. In simpler terms, the greater the bandwidth, the higher the capacity, and the higher the signal power relative to the noise power, the higher the capacity .

5. Shannon Hartley theorem The Shannon Hartley formula to find the channel capacity is given by: C =B× log2 (1 + SNR) Where: C is the channel capacity in bps B is the available bandwidth of the channel in hertz (Hz) SNR is the signal-to-noise ratio, expressed as a linear value (SNR = signal power / noise power)

6. Shannon Hartley theorem Example : Consider an extremely noisy channel in which the value of the signal-to-noise ratio is almost zero. In other words, the noise is so strong that the signal is faint. For this channel the capacity C is calculated as: C=B log2 (1 + SNR) C = B log2(1 + 0) C = B log2 (1) where log2(1)=0 C = B × 0 C = 0 This means that the capacity of this channel is zero regardless of the bandwidth. In other words, we cannot receive any data through this channel.

7. Shannon Hartley theorem Advantages and Applications: The Shannon-Hartley theorem has been influential in the development of digital communication systems and serves as a benchmark for evaluating the performance of various communication technologies, such as wireless networks, fiber optics, and satellite communications. It helps engineers and researchers understand the trade-offs between bandwidth, signal power, and noise in designing efficient and reliable communication systems.

8. Shannon Hartley Theorem Channel Capacity Calculator: This tool calculates the  channel capacity  according to the Shannon-Hartley theorem for a given bandwidth and SNR. The capacity is expressed in terms of bits per second .

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