Nearfield measurements

[john k...]

John

Thats not true. A minimum phase filter that "flattens the response to DC" would always have two poles at zero Hz because the acoustic radiation always has two zero's at DC. Now if you are saying that because of errors in the data, truncation, noise, etc. the response is never zero at DC, then that is true, but that is because of the errors not because of the post processing.

Again, doing it make all the difference. I'm not saying that there are no poles at zero. Certainly the TF of the inverse of a HP filter has poles and infinite gain at DC. But in practice this is of no concern.

Suppose we sample a system with 100 Hz HP cut off at 48K and a sample length of 4096. The FFT of the measured impulse will extend to 11.72 Hz and will have 2048 frequency points. The discrete time transfer function can be expressed as T(fn) where fn are the discrete frequency points n x 11.72, n = 1, 2, 3, ...., 2048. We convolve the response with the inverse filter, 1/T(fn), in the frequency domain on a point by point basis. We only need information about the inverse filter to 11.72 Hz. That will flatten the response to 11.72 Hz. We need not worry about DC because by construction the DC value must be 1.0 as well. We do the IFFt of this convolution and we get a perfect sampled impulse, u(m) where u(1) = 1. and u(m>1) = 0. If we were to ignore the DC value in the convolution all that would happen is that the IFFT would be a perfect impulse with a DC offset, h(m) = u(m) - c. But when we FFt h(m) with said DC offset the only impact is on the DC value of the result, which we don't care about anyway.

Remember, this is being done in the discrete time domain as post processing of the impulse, not by using the matching filter to pre-emphasize the stimulus.

 

[dlr]

Remember, this is being done in the discrete time domain as post processing of the impulse, not by using the matching filter to pre-emphasize the stimulus.

I was trying to understand the differences of the two methods and the practicalities of each. Your example lined up the dots, so-to-speak. This last point connected the dots. Very interesting thread.

Dave

 

[gedlee]

But in practice this is of no concern.

I think this is the main point and one that I agreed with in my first response. As a practical matter the poles will not be right at DC because of the errors and they will be down from infinity.

 

[Helmuth]

Peter

That was it thanks. Good writup. When I went to save it I already had it. I must be lossing something.

At a certain age that is normal Earl