What is an "all pole source"?

Question

For background I am not an engineer, and reading about linear predictive coding, so this question may be very trivial.

I am trying to understand what a textbook means by referring to something as an "all pole source".

It says that speech (in the frequency domain) is not typically an all-pole source because there are zeros present in the spectrum due to glottal pulses and the physiology of the vocal tract.

As I have looked into this, it looks like "poles" are when an equation (transfer function?) blows up to infinity, and "zeros" are when it approaches zero. The textbook says that there are both poles and zeros present in a spectral representation of speech. Does that mean the energy present in the spectrogram? If this is so, there are no times when there is infinite energy, and no times when there is an absolute loss of energy, so I find this pretty confusing...

Given that context, my question is this: what does an "all pole source" mean in this context? And what does it mean to have poles and zeros in a spectral representation of human speech?

Answer 1

It simply refers to what a generic transfer function made up of poles and zeroes looks like:

$$H(s)=\prod_k{\frac{s-z_k}{s-p_k}}$$

where \$z_k\$ are the zeroes and \$p_k\$ are the poles, wth \$s=j\omega\$ being the complex operator. If you look, for example, on the Wikipedia page for the Butterworth filters, you'll see this comparison of the responses of various transfer functions. In the link, the two upper plots are all-pole, the two below are pole-zero. An all-zero transfer function is also possible, see FIRs.

I can't say how these affect the speech (I haven't gone that particular way), but you can see various filters in action on the Falstad page. Given your rather generic question, I thought this should cover it, but if you really want to get into gory details, I'd suggest you to ask this question in the dsp.ee, it's highly likely you'll get much more mathematically inclined answers there, provided you ask for the right details.

Answer 2

There are always some losses, some dampening, thus the "infinity" is never reached. Similarly, "zero" is not reached.