Question

a) In Audio editing software packages often contain effects to allow you to simulate different recording environments. An example could be to simulate the audio being produced in a concert hall, auditorium or pipe by adding echoes to the audio or to simulate a padded room by filtering the audio to dampen the sound.

A room contains a speaker in the top right-hand corner of the room which produces sound for the listener in the center of the room.
- Our listener experiences three versions of the audio;  
- The direct version coming straight from the speaker . There is no attenuation or delay with this audio (apart from the time it takes to get to the listener).
- A first echo bouncing from the right-hand wall which is delayed by Td1 seconds (relative to the direct path), the amplitude of this audio has also been attenuated by G1 of the direct audio’s amplitude and,
- A second echo bouncing from the left-hand wall which is delayed by Td2 seconds (relative to the direct path), the amplitude of this audio has also been attenuated by G2 of the direct audio’s amplitude.

Td1 = 0.2 Td2 = 0.6
G1 = 0.2 G2 = 0.1

Manually work out the number of samples your delays will correspond to and the weightings (ak) for each part of the filter.

ii. Manually work out the difference equation, impulse response and transfer function for this filter.
iii. Show the Direct Form I diagram for this filter (use a software package such as Microsoft Visio to show this neatly).

your first path will be delayed by 0.2 sec and attenuated to 20% of the original amplitude, your second path will be delayed by 0.6 sec and attenuated to 10% of the original amplitude.

Answer 1

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