Channel Capacity Bandwidth – In cycles per second of Hertz – Constrained by transmitter and medium Data rate – In bits per second – Rate at which data.

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Channel Capacity Bandwidth – In cycles per second of Hertz – Constrained by transmitter and medium Data rate – In bits per second – Rate at which data can be communicated

Data rate depends on three factors: The bandwidth available (The analog bandwidth of a medium is expressed in hertz; the digital bandwidth, in bits per second) The levels of signals we can use. The quality of the channel (the level of the noise) Data Rate

Bandwidth: bandwidth of the channel, L: number of signal levels used to represent the data. BitRate: in bits per second For a noiseless channel, the Nyquist bit rate formula defines the theoretical maximum bit rate: Noiseless Channel : Nyquist Bandwidth

Example 1: Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two signal levels. Calculate the maximum bit rate. Example 2: Consider the same noiseless channel with for signal levels. Calculate the maximum bit rate. Noiseless Channel : Nyquist Bandwidth

Noisy Channel :Shannon Capacity Formula Consider data rate,noise and error rate Faster data rate shortens each bit so burst of noise affects more bits – At given noise level, high data rate means higher error rate Signal to noise ration (in decibels) SNR db = 10 log 10 (signal/noise) Capacity C=B log 2 (1+SNR) B= Bandwidth This formula defines a characteristics of the channel not the method of transmission.

Signal to Noise Ratio A relative, not absolute measure. A high S/N means high quality signal reception. SNR dB = 10log 10 signal power/noise power An important parameter in determining the performance of a transmission system. Measured in decibel or dB to express ratio of two power, voltage or current levels.

High/Low SNR

Example:Calculate the theoretical highest bit rate of a regular telephone line. A telephone line normally has a bandwidth of 3000 Hz (300 Hz to 3300 Hz). The signal-to-noise ratio is usually Noisy Channel :Shannon Capacity Formula

The Shannon formula gives us 6 Mbps, the upper limit. For better performance we choose something lower, 4 Mbps, for example. Then we use the Nyquist formula to find the number of signal levels. Example (continued)

The Shannon capacity gives us the upper limit; the Nyquist formula tells us how many signal levels we need. Note