One of the options in REW is for fractional octave filtering of the speaker response. Since the source code for REW is not available my question is does anyone know the formula or a link to the formula for fractional octave filtering of response data. I am trying to program it into code I am writing and cannot find an algorithm. For example is what is done is to apply a linear Gaussian filter using the log of the frequency data as an input? I can't think of any other way of defining a filter as a fraction of an octave. Also what is the most efficient way of implementing the Gaussian filter? I hope some of you have knowledge of these considerations.
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I implemented such a filter. The filter can be an arbitrary function. It must have the properties that energy is conserved and octaves (not bins) are weighted equally. These conditions are met by doing RMS summation with each bin weighted by frequency.
Ed
Ed
I weant and read the REW instructions and found out the following -
Apply a smoothing filter to the current channel. Repeating the action removes the smoothing. Variable smoothing applies 1/48 octave below 100 Hz, 1/3 octave above 10 kHz and varies between 1/48 and 1/3 octave from 100 Hz to 10 kHz, reaching 1/6 octave at 1 kHz. Variable smoothing is recommended for responses that are to be equalised. Psychoacoustic smoothing uses 1/3 octave below 100Hz, 1/6 octave above 1 kHz and varies from 1/3 octave to 1/6 octave between 100 Hz and 1 kHz. It also applies more weighting to peaks by using a cubic mean (cube root of the average of the cubed values) to produce a plot that more closely corresponds to the perceived frequency response. ERB smoothing uses a variable smoothing bandwidth that corresponds to the ear's Equivalent Rectangular Bandwidth, which is (107.77f + 24.673) Hz, where f is in kHz. At low frequencies this gives heavy smoothing, about 1 octave at 50Hz, 1/2 octave at 100 Hz, 1/3 octave at 200 Hz then levelling out to approximately 1/6 octave above 1 kHz.
REW's smoothing uses multiple forward and backward passes of first order IIR filters to implement a Gaussian smoothing kernel of the chosen fractional octave bandwidth. For log spaced data those are IIR approximations to a Gaussian filter after Alvarez-Mazorra. For linear spaced data the time constant of the first order filter is varied according to the sample index to reflect the equivalent fractional octave bandwidth desired at the frequency of the sample.
The question is which to use. I am torn between Psychoacoustic and ERB.
Apply a smoothing filter to the current channel. Repeating the action removes the smoothing. Variable smoothing applies 1/48 octave below 100 Hz, 1/3 octave above 10 kHz and varies between 1/48 and 1/3 octave from 100 Hz to 10 kHz, reaching 1/6 octave at 1 kHz. Variable smoothing is recommended for responses that are to be equalised. Psychoacoustic smoothing uses 1/3 octave below 100Hz, 1/6 octave above 1 kHz and varies from 1/3 octave to 1/6 octave between 100 Hz and 1 kHz. It also applies more weighting to peaks by using a cubic mean (cube root of the average of the cubed values) to produce a plot that more closely corresponds to the perceived frequency response. ERB smoothing uses a variable smoothing bandwidth that corresponds to the ear's Equivalent Rectangular Bandwidth, which is (107.77f + 24.673) Hz, where f is in kHz. At low frequencies this gives heavy smoothing, about 1 octave at 50Hz, 1/2 octave at 100 Hz, 1/3 octave at 200 Hz then levelling out to approximately 1/6 octave above 1 kHz.
REW's smoothing uses multiple forward and backward passes of first order IIR filters to implement a Gaussian smoothing kernel of the chosen fractional octave bandwidth. For log spaced data those are IIR approximations to a Gaussian filter after Alvarez-Mazorra. For linear spaced data the time constant of the first order filter is varied according to the sample index to reflect the equivalent fractional octave bandwidth desired at the frequency of the sample.
The question is which to use. I am torn between Psychoacoustic and ERB.
You have to tell us the intended use.
The algorithm I described in post #4 is intended for measurement.
The algorithms you described in post #5 are intended for perceived response.
Ed
The algorithm I described in post #4 is intended for measurement.
The algorithms you described in post #5 are intended for perceived response.
Ed
The following paper, published in 2017 by Tylka, Boren, and Choueiri, may be of help:
A Generalized Method for Fractional-Octave Smoothing of Transfer Functions that Preserves Log-Frequency Symmetry
Open Access JAES Paper
Which programming language are you using?