HOLMImpulse: Measuring Frequency- & Impulse-Response

[breez]

Originally Posted by askbojesen

Thanks, ARTA "2.3 Frequency Resolution of DFT and Octave-Band Analyzers"
if ARTA window = BLACKMANN3, then this corresponds to HOLMImpulse amplitude smoothing with N = 1, N = 3

The HOLMImpulse FR makes a calculation for all discrete frequencies, not only the ISO-standard-steps. I might implement an ISO-standard-step FR which will show bars and not a curve.

The discussion on windows, however, refers to the DFT resolution. The 1/N smoothing is discussed further down in that section with methods similar to Earl's (continuous smoothing).

[gedlee]

Originally Posted by askbojesen

1. When you sum the RF - is it then a complex sum? or do you sum the amplitudes?

2. When you use your weighting function - do you multiply with 1/f to compensate for your equidistant frequencies?

I sum the "magnitudes", and yes, you must do a 1/f compensation for the frequencies, but this is part of the "integration".

[askbojesen]

Originally Posted by breez

The discussion on windows, however, refers to the DFT resolution. The 1/N smoothing is discussed further down in that section with methods similar to Earl's (continuous smoothing).

Sorry, Yes I are right - he writes:
Power output of 6-pole Butterworth bandpass filter – First, the power spectrum is weighted with a squared magnitude of a bandpass filter response.

And not which bandpass filter he uses.

If I get the time and feel for it I can compare my amplitude smoothing with this

[askbojesen]

Originally Posted by gedlee

I sum the "magnitudes", and yes, you must do a 1/f compensation for the frequencies, but this is part of the "integration".

Then your post processing should equal my amplitude smoothing.

I suggest the following for a measurement:

1. Export unsmoothed FR or IR to your program
2. Your program -> Smoothed FR/IR -> HOLMImpulse
3. Compare

Perhaps you can email me an IR and your smoothed FR - then I can do the comparison?

[john k...]

Originally Posted by askbojesen

Still a problem?

Got it. I hade to update my Adobe reader.

[gedlee]

Originally Posted by askbojesen

Then your post processing should equal my amplitude smoothing.

I suggest the following for a measurement:

1. Export unsmoothed FR or IR to your program
2. Your program -> Smoothed FR/IR -> HOLMImpulse
3. Compare

Perhaps you can email me an IR and your smoothed FR - then I can do the comparison?

How can I import a FR curve? is there documentation of the proper format? After smoothing the FR curve is purely real there is no phase. Is this a problem?

If I smooth in Holm, can those curves be exported en-mass like the IRs?

[JohnPM]

Originally Posted by gedlee

I take the impulse response and find the FR, normal FFT. Then I go to a set of log spaced frequencies and at each of those find a weighting function that is 1/N wide - I use a gaussian type of shape. The magnitudes at each of the FFT data point is then weighted by this shape and integrated (summed). This procedure has trouble at LF when the frequency spacing of the data is comparable to the smoothing bandwidth, but works good otherwise.

Instead of using a gaussian window use a rectangular window but make 4 successive passes through the data. It is orders of magnitude more efficient (when correctly implemented) and is easily implemented as a sliding window (whose endpoints can vary logarithmically as you go for fractional octave filtering) for more accurate filtering.

[gedlee]

Originally Posted by JohnPM

Instead of using a gaussian window use a rectangular window but make 4 successive passes through the data. It is orders of magnitude more efficient (when correctly implemented) and is easily implemented as a sliding window (whose endpoints can vary logarithmically as you go for fractional octave filtering) for more accurate filtering.

Sounds interesting, could you ellaborate further. It would be way more efficient and I need that, but I am unclear on why multiple pass makes any difference, or exactly what you mean.

[JohnPM]

The second pass is equivalent to a triangular weighting function, successive passes approach ever closer to a gaussian function. See this link for details: Relatives of the Moving Average Filter. That is the method I use for the fractional octave filters in REW.

[john k...]

From a numerical analysis point of view smoothing always reduces to some form of integration:

A'(fc) = integral [W(f)A(f)]/ integral[W(f)] over some limits f1 to f2 where fc is between them. W(f) is a weighting function of choice, typically symmetric about fc. Obviously, in the digital domain the integrals are replaced with their representative summations.