Question

Two random signals $S_1\left(t\right)and{S}_2\left(t\right)$ are quantized and each sample is encoded with 'n' no. of bits in both the signals. The pdf of $S_1\left(t\right)and{S}_2\left(t\right)$ are given as below :


$\frac{(SNR{)}_1}{(SNR{)}_2}isequalto$

• A. 2.5
• B. 1
• C. 3.5
• D. 2

Answer 1

The correct option is B 1

$Signalpowerof{S}_1\left(t\right)=MS{Q}_1=\frac{[2-(-2){]}^2}{12}=\frac{4}{3}watt$

$signalpowerof{S}_2\left(t\right)=MS{Q}_2=\frac{1}{3}watt$

$Noisepower=\frac{{\Delta }^2}{12}$

1. ${\Delta }_1=\frac{4}{2^n}\Rightarrow N_1=\frac{16}{2^{2n}\times 12}$
2. ${\Delta }_2=\frac{2}{2^n}\Rightarrow N_2=\frac{4}{2^{2n}\times 12}$

$\frac{{\left(\frac{S}{N}\right)}_1}{{\left(\frac{S}{N}\right)}_2}=\frac{\frac{4\times 2^{2n}\times 12}{3\times 16}}{\frac{1}{3}\times \frac{2^{2n}\times 12}{4}}=\frac{1}{1}=1$