Question

1) Calculate the noise power and noise voltage generated by a 1M ohm resistor at 37 C over a 1Mhz bandwith?

2) Three messages A,B, C have probilities 0.4, 0.3 and 0.3 respectively of their occurence. If total 100 messages are sent out calculate the total information carried by them. Also calculate entropy of the signal?

Answer 1

1)

$$P=kTB\\P=(1.38\cdot10^{-23})(273+37)(10^6)\\P=4.28\cdot10^{-15}\ W$$

$$V=\sqrt{4kTBR}\\V=\sqrt{4(1.38\cdot10^{-23})(273+37)(10^6)(10^6)}\\V=1.31\cdot10^{-4}\ V$$

2) The entropy of the signal

$$H=0.4\log_2{\frac{1}{0.4}}+0.3\log_2{\frac{1}{0.3}}+0.3\log_2{\frac{1}{0.3}}\\H=1.57\frac{bits}{message}$$

The total information carried by them

$$R=1.57(100)=157\ bits$$