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FIR Filtering For Audio Practitioners

A basic introduction of FIR filter generation for audio systems.

Several FIR filter applications whose purpose is to create a conjugate of a measured data are as follows:

1. Creating a conjugate for a single measurement point.

For a one person listening spot (such as studio use), one measurement can be taken at the sweet spot position from each loudspeaker. An FIR filter can be developed to create a conjugate of the transfer function at that point.

This is useful to smooth out room effect and improve several loudspeaker non-linearities. The filter has many data points but it is for a unique position in space.

2. Flattening spatial averages or power response

By measuring the frequency response at different listener’s positions, one can average the frequency responses. This should be done per loudspeaker and good results can be achieved by averaging the frequency response at more than three locations. Averaging should not include phase response, only the magnitude.

The measurement can be taken simply by using an RTA. This is another useful way to compensate for the room’s modal behavior in a home theater environment, music listening room, or for sound system optimization for commercial/public places.

3. Loudspeaker correction

To properly create a loudspeaker correction, a controlled measurement environment is required. Control in this context means controlling the amount of reflected sound that is captured in the measurement.

The simplest and most effective way to do a good loudspeaker measurement is to do an outdoor ground plane measurement under supportive weather conditions or in a very large room. By placing the loudspeaker and mic on the reflective and smooth ground, one can get a good measurement data without a destructive interfering reflection from the floor.

When creating an FIR filter to linearize the phase response of a loudspeaker, its best to use measured data from a controlled measurement environment.

4. Combination

There are many possibilities to measure a loudspeaker and create FIR filters. One can create a loudspeaker correction using the outdoor ground plane method and create an FIR filter to linearize the loudspeaker’s direct field response. Then bring the loudspeaker inside the room and measure several spots in the room to create a power response/modeal compensation.

The two filters can then be convolved/combined. Just like combining IIR filters, several FIR filters with different functions can be combined too.

FIR filters are produced very differently than IIR filters. Both have pluses and minuses and the final result will depend on the intentions of the filter’s creator.

The authors would like to thank Pat Brown and John Loufik for their insights and for reviewing this article prior to publication.

You can find a PDF of this article here.

This article is provided by HX Audio Lab.

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