How Many Bits Per Sample for a 10dB SNR with a Uniform Quantiser?

[jendrix]

Homework Statement

[/B]
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?

Homework Equations

Mean square error[/B]

E{ε²} = Δ²/12

Signal to quantisation noise ratio

A²/(Δ²/12) =3*L²

The Attempt at a Solution

As SNR_dB 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

=4/3Thanks for looking.

 

[KataKoniK]

Thank you for your post. I would like to offer my response to your question.

Firstly, I agree with your approach in determining the minimum number of bits per sample required for a signal to quantisation noise ratio of at least 10dB. Your calculation of SNR and the resulting value of 1 bit per sample is correct.

However, I would like to offer a slight correction to your calculation of mean square (quantisation) error. The correct equation for this is E{ε2} = Δ2/12, where Δ is the quantisation step size. In this case, Δ = 4/2 = 2. Therefore, the mean square error would be 4/12 or 1/3.

I hope this helps. Keep up the good work!