## The bandwidth and noise trade-off

#### Having briefly considered the question of 'how fast can we send data', it is immediately apparent that there are two fundamental factors affecting the information transfer rate on a channel, namely:
#### The maximum possible detectable rate of change of waveform or symbol state #### – The bandwidth of the channel (and any bandwidth limits imposed by the transmitting and receiving devices) will determine how quickly the signalling states on the channel can be changed.
#### The ability to resolve any number of discrete symbol states #### – The level of noise in the channel will impose an upper limit on the number of different unique symbol states that can be correctly resolved (decoded) at a receiver. – The degree of distortion introduced by the channel will also limit the number and rate of change of symbol states that can be accommodated with acceptable performance. #### So, if we had a channel with infinite bandwidth, or no noise and distortion, it would be possible to send the 1000000 bits of information 'instantaneously' – well, at the speed of light anyway.