# Designing a uniform quantiser

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1. Mar 15, 2017

### jendrix

1. The problem statement, all variables and given/known data

An analogue signal is uniformly distributed from -4,4. Design a uniform quantiser with minimum number of bits per sample, such that the signal to quantisation noise is at least 10dB.

How many bits are required per sample?
What is the mean square (quantisation) error for your quantiser?

2. Relevant equations

Mean square error

E{ε2} = Δ2/12

Signal to quantisation noise ratio

A2/(Δ2/12) =3*L2

3. The attempt at a solution

As SNRdB must be 10 minimum then 10=10log(snr) , solving for SNR

SNR must be at least 10.

SNR = 3*L2

⇒ number of levels 1.8 but as they must be an integer value we can say L=2

Δ=2A/L

Δ=4

We end up with a quantiser that requires 1 bit per sample.

The mean square(quantisation) error = Δ2/12

=16/12

=4/3

Thanks for looking.

Last edited by a moderator: Mar 15, 2017
2. Mar 20, 2017

### PF_Help_Bot

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