Noise Limits Bandwidth

The amount of noise a digital signal is likely to pick up limits the number of bits that can be sent per second. Why?

We have seen that when a sound wave is digitised the

no. of bits per second    =    no. of samples per second    x    no. of bits per sample

The number of bits per sample, b, determines how many possible levels the each sample can have

no. of levels = 2^b

e.g. with 8 bits per sample then there are 2⁸ = 256 possible levels

Consider the diagram below showing a signal that has picked up noise.

There is no point having a difference between the sampling levels which is smaller than the amount of noise. Otherwise you would be sampling noise. So what is the maximum number of bits per sample we can have?

If the amplitude of the noise is equal to the difference between two sampling levels then the number of levels is given by

e.g. if the amplitude of the noise is 1% of the signal strength what is the maximum value for b?

Vs/Vn = 100  so                 if b = 6 then 2^b = 64            if b = 7 then 2^b = 128               the maximum b is therefore 6

The Shannon - Hartley Theorem states that

Nyquist rate

Hartley's law