2. Suppose you yell in a canyon. You hear the echo of your voice 0.8 seconds later with an amplitude 5% as loud. But, that will echo back again from your side, so you will hear another echo 0.8 seconds later that is, in turn 5% as loud as the first echo. This repeats, with each subsequent echo getting software. Write a transfer equation for a filter that simulates this echo digitally.

Explanation:

If I is the intensity of first sound echo, then with each subsequent echo the sound gets softer by 5 %.

At t=0.8, s I=I0

At t=2*0.8 s=1.6 s, I=Io-I0*5/100

At t=3*0.8 s=2.4 s, I= (Io-I0*5/100)-(5/100)* (Io-I0*5/100)= (Io-I0*5/100)[1-0.05]

At t=4*0.8 s=3.2 s,I=(Io-I0*5/100)-(5/100)* (Io-I0*5/100)-(5/100) Io-I0*5/100)-(5/100)* (Io-I0*5/100)= (Io-I0*5/100)[1-0.05][1-0.05]= (Io-I0*5/100)[1-0.05]2

So,

I(n)=I0 for n=1

I(n)= (Io-I0*5/100)[1-0.05]n-2 for n=2 or n>2