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.

Question

Engineering

Frauline

3 June, 18:18

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.

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Anne Hanna · Answer 1

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