Tech Design.....

Recovery of low frequency response from in room
measurements using cepstral editing.
May 16, 2007

During the past couple of weeks Bohdan Raczynski (the developer of Sound Easy) and I have been
examining the possibility of removing room reflections from response measurement using cepstral
analysis and cepstral editing. The ideas behind cepstral editing are not new. Bauman, Lipshitz, Scott and
Vanderkooy reported on the approach at the 1984 AES Convention and in a companion paper by Bauman,
Lipshitz, and Vanderkooy presented at the 1985 AES convention. While the ideas are straight forward the
details of how the cepstrum is edited can affect the results significantly. Below are some preliminary result
obtained with the current implementation of the cepstral editing technique in SoundEasy which will be
released with Version 14.

The first two figures below shown the impulse response and corresponding frequency response of a
sealed box woofer system for a small 2-ways loudspeaker. The frequency response was obtained form
the impulse response using a 40 msec window. No smoothing was applied. The measurement was
made at approximately 1 meter. As can be seen, reflections from the room contaminate the impulse
response after about 5.6 msec leaving only a 2.3 msec reflection free window. This would allow  anechoic
response to be obtained to a lower frequency limit of about 370 Hz. The 40 msec window results in a very
irregular frequency response measurement result owing to the inclusion of the room reflections.
The frequency response is then "tailed" using a slope indicative of the woofer system type, sealed box,
ported, etc. In this case a 12 dB/octave tail was added, consistent with the sealed box system.
The minimum phase cepstrum is then computed from the from the tailed response as shown
below. This is essentially an inverse FFt operation on the natural log of the amplitude response.
The large peaks in the cepstrum are an indication of both room reflections and baffle diffractions.
The figure below shows that the room reflections begin somewheres around 2.3 msec.  Magnified
vertical and expanded horizontal scale.)
To edit the cepstrum the tail beyond the point of the first reflection must be modified. Currently
several options are provided in the developmental version of the procedure. These include point
wise and linear piece wise editing, moving averages and appending an analytical tail to the
cepstrum. Here I have chosen to append an analytical tail to the cepstrum, as shown below.
Once the room reflections have been edited from the cepstrum, a FFt operation is performed on
properly formated, edited cepstrum resulting is  the response shown in red below, overlaid with the
original response. As can be observed in the figure, the affects of the reflections have been
removed from the response.
Of course the question arises how good is this compared to other approachs to obtaining the low
frequency response of a system? At this juncture, with my limited experience in applying the
procedure I would say that cepstral editing is a blend of art and science. Experience and good
judgement are a requirement. However, to demonstrate the capability of the procedure I have made a
comparative measurement of the system using the
far field / near field approach.

To begin, a windowed, 1 meter,  far field SPL measurement is made. The impulse, window and
resulting frequency response is shown below. Since the window is short the frequency response
data is only good down to about 370 Hz.
Next the microphone is repositioned just off the dust cap of the woofer. The impulse and frequency
response are shown below. The window was 40 msec long yielding frequency response data down to
about 40 Hz. The obvious crossover compensation for the baffle step is apparent in the near filed
To correct the near filed response for the 2Pi to 4Pi transition which occurs in the far field a baffle
diffraction simulation of the speaker was performed.
The baffle diffraction correction is then applied to the near field frequency response and the resulting
corrected response is merged with the far field data at a suitable merging frequency. For the case
presented here, 330 Hz. The resulting merged response is shown directly below.
This last figure shows an overlay of frequency response obtained using the near field/far field approach
(red) with that obtained using cepstral editing (blue). Over all the result using cepstral editing is
reasonable close to the near field/far field result. Further development, refinement and automation are
expected to evolve over time. While these initial efforts appear promising it must be recognized that
cepstral editing is just another tool in the speaker design tool box and how well it works will depend on
the skills of the user. Additionally, like any tool, it will only perform well when used for the proper