Using all-pole filter to model the Room Impulse Response

Question

Why is all pole model pretty useful in modelling room acoustics?

Is it related to reverberation?

Answer 1

It's not because of reverberation.

When you want to model the Frequency Response of the room, it's common to simplify your approximation by using either all-pole or all-zero models. You don't want to use the full zero-pole model.

To get some intuition:

• zeros correspond to time delays and antiresonances
• poles correspond to resonances of your Room Response

In practice all-zero models are not being used due to various reasons, such as:

• required filter length is comparable to the IR length, and almost 40x the length of corresponding all-pole filter
• filter will be valid only for specific distances and positions between the source and receiver (remember: time-delays).

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That is why the all-pole model is used instead. As mentioned above, poles correspond to the resonances, i.e. standing waves, which are:

• independent of the source location (quite intuitive)
• independent of the receiver location (except of the nodes)

Additionally the required filter length is way less than in case of all-zero models. According to Mourjopoulos, for $RT_{60}\approx0.5 \mathrm{s}$, the required order is within the range of $50 < N < 500$. The same author, concludes that all-pole filters are easier to manipulate than all-zero filters, due to their filter length. Morevover, author mentioned that all-pole filters are sufficient approximation than using raw impulse response data.

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Here is some literature:

Mourjopoulos J. - On the Variation and Invertibility of Room Impulse Response Functions

Mourjopoulos J., Paraskevas M. A. - Pole and Zero Modelling of Room Transfer Functions