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Loudspeaker Measurements Standard: On-Axis Frequency Response


On-axis frequency response is the starting place for measuring loudspeakers because it describes the initial sound that reaches a listener’s ear from a loudspeaker.  Although this response is the most revealing factor in determining how a loudspeaker sounds, it is only part of the complex auditory scene perceived by the listener.  Another part of the auditory scene is constructed from the interaction of a loudspeaker with the room that it is playing in.  Loudspeakers radiate sound into a room in various three-dimensional patterns that typically vary drastically as a function of frequency.  This causes a set of interactions only reproducible by, among other things, the combination of loudspeaker location, a specific listening environment and a precisely positioned listener.  The unique ear of the listener receives a barrage of acoustic information that is then converted into signals transmitted to the brain. The brain is a sophisticated signal processing system that more or less decides how the listener perceives the signals received.  Understanding how the brain processes sound is a topic of ongoing research and holds keys to advances in acoustics.

The frequency response of a loudspeaker can be obtained by first measuring the impulse response.  The impulse response, in theory, represents the output of the loudspeaker when presented with a pulse signal that lasts for an infinitely short amount of time.  Since there are some obvious issues with generating such a signal, it can be approximated using a maximum length sequence (MLS) consisting of pseudo-random pulses.  Circular cross-correlation of the MLS input with the loudspeaker output generates a good approximation of the system’s impulse response.  Assuming the loudspeaker is a linear time invariant (LTI) system, the time domain impulse response characterizes the loudspeaker frequency response through the properties of the Fourier transform.  Since this is all done using digital signals, the computationally efficient Fast Fourier Transform (FFT) algorithm is applied to obtain the Discrete Fourier Transform (DFT) of the impulse response.  For the interested reader, check out MIT’s cool tie wearing Alan Oppenheim’s course on discrete-time signal processing (MIT Open Course Ware - Discrete-time Signal Processing).


On-Axis Frequency Response Sample

The on-axis frequency response measurements are conducted with a 2.83VRMS excitation signal at a distance determined by proper summing of all drivers in the system.  This distance is determined by successively conducting the windowed measurement described below starting at 3 times the largest dimension of the source and decreasing the measurement distance in steps until one step before response deviations are apparent.  The SPL response for all measurements will be scaled to 1 meter mathematically.

Microsoft Anechoic Chamber

Anechoic Chamber - courtesy of Microsoft

Accurately measuring a loudspeaker’s impulse response is not a trivial task.  The difficulty lies in the fact that the measurements must be taken in a real space, and that space has some level of impact on the measurement.  One of the most useful places to conduct loudspeaker measurements is an anechoic chamber.  Anechoic chambers are large rooms with very thick sound absorption material on all surfaces and offer a good estimation of free-space measurements down to a cutoff frequency specific to the chamber.  Anechoic chambers can be calibrated to measure loudspeakers to frequencies below the cutoff frequency allowing full acoustic spectrum measurements. Unfortunately, they are very expensive to build.  Mere mortals are left measuring loudspeakers using quasi-anechoic techniques that are intended to approximate anechoic measurement techniques.

For measurements made in room, a signal processing technique called windowing is applied to only use the part of a measured impulse response that contains data before the first reflection of the sound from the nearest surface (usually the ceiling or ground). Calculating the length of the reflection free path and dividing by the speed of sound determines the reflection time. 

The reflection free path length is determined by the following equation:


As an example, a speaker 1.14 meters off of the ground with a microphone distance of 1 meter yields a reflection free path length of approximately 1.49 meters.  The amount of time before the first reflection arrives is simply calculated by dividing the reflection free path length by the speed of sound.  This means that, in this example, we can use 4.3ms worth of the impulse response or frequencies as low as 230Hz considering the speed of sound is 344 m/s.  A window with a length equal to the gate time is applied to the impulse response. This gated response means that the measurement taken at 1 meter is only valid from 230Hz on up to 20kHz+.  Analogous to Heisenberg’s uncertainty principle, more accuracy in the window time yields less accuracy in the frequency response.  This means that, in the case of a 4.3ms window time, the frequency resolution is 230Hz yielding a small number of data points for low frequencies.  Software interpolates the missing data points but the results can potentially miss important variance in the low frequency data.


Mic Distance Diagram

There are several techniques used to obtain the low frequency data.  The first technique discussed is ground plane measurement.  This measurement technique involves positioning the loudspeaker such that the primary acoustic axis of the loudspeaker is facing the microphone placed on the ground in a large open space (typically outdoors).  For a single bass driver, the loudspeaker can simply be tilted vertically to align with the measurement microphone on the ground.  In the case of a multiple bass driver loudspeaker, the line of drivers should be parallel to the ground plane with the cones tilted directly at the measurement microphone with the highest frequency driver being measured directly on-axis with the microphone. 

The degree of tilt is equated as follows:


The height of the speaker’s central axis is typically the height of the center of the cone from the ground.  The microphone distance is the distance along the ground from the microphone to the acoustic center of the baffle.

Since the measurement microphone is approximately coincident with the ground, the measurement uniformly includes the reflected signal from the ground called the virtual image. This measurement technique typically introduces increasing error with increasing frequency.  Ground plane measurements may be conducted to obtain low frequency data to confirm the following near-field technique or when other techniques are impractical.

The second method, which can be used to obtain low frequency data for most loudspeakers, is the near-field measurement technique.  This technique involves measuring each low frequency element with the tip of the microphone very close to the driver.  This includes measuring bass drivers, passive radiators, and ports.


Baffle Step Modeling

For near-field measurements, the system baffle is modeled and baffle step diffraction simulations are conducted to approximate the effects of baffle step diffraction.  The wavelength of sound is a function of frequency with higher frequencies having shorter wavelengths.  This means that high frequencies reflect off of the baffle while low frequencies have a tendency to radiate spherically well beyond the width of the baffle.  As the wavelength increases (frequency decreases) and reaches the baffle width, the edge diffraction effects of the loudspeaker cabinet become an important consideration.  If the transition from hemispherical (2*pi) to spherical (4*pi) radiation is significant below the window frequency, the modeled baffle step diffraction will be combined with the near-field response data.  The modeled baffle step diffraction accounts for various driver alignments, baffle shapes and edge profiles.


Baffle Step Diffraction Response

For near-field measurements, the same microphone gain settings are used for each measurement.  If a driver or port is located on the rear or side of the loudspeaker, the SPL is adjusted for the difference in distance from the reference plane.  The level matched near-field measurements and baffle step diffraction model are combined creating a single amplitude response including combined phase and accounting for diaphragm radiating areas.  The combined near-field response is then spliced with the gated response at approximately the window frequency.  The splicing technique requires level matching the low frequency data with the high frequency data before splicing together at a frequency below the crossover point of the driver’s measured near-field.  The technique requires finding a spot above the window frequency where the response contours and slopes match.  It is best to use the highest frequency possible to minimize the potential error due to the frequency resolution limit of the windowed response measurement.




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Recent Forum Posts:

Paul womble dung posts on September 13, 2016 17:45
i guess that some people don't understand why many of the technical technicalities can be very important to some other people.

not everyone only uses or needs good speakers at home to listen to music, or use a home theater/entertainment suite.

some people work with music, either in sound engineering, production, or are themselves musicians.
in which case they need speakers which are suited to them, and need to know WHY those particular speakers are suited to them, so they can recreate this wherever they are (obviously within the context of the average spaces they intend to do it in, even if they intend to use hired gear, it is wise to have even a basic understanding of all of this).

some musicians for example play acoustic instruments, and when they need amplified for some spaces, then generally certain set ups work much better for them.
other musicians may work purely electronically/digitally (like a techno music musician) so certain other set ups may suite them.

and you will find this will be similar for their home,perhaps, in that their domestic set up may reflect their work. although some of us like to leave work at work!

other folk need audio gear for research purposes and may be buying it on behalf of their university department so certain criteria may need to be fulfilled in various qualities.

i was quite impressed by how much detail the written stuff linked to from this page was, despite much of the language as yet being a bit over my head. but liked how it gave me a load of terms to look up and become familiar with.
although the algebra took a few reads through to grasp, it actually was not too difficult and was on a level with secondary education (middle school in U.S.?) and online calculators can help, or any basic calculator that has “scientific” settings on it.
my main interest at the moment is in deciding shapes and proportions with which to build cabinets for a slightly large sound system for mainly outdoor use, so i will need a little maths to work out the best proportions to get the best out of the materials used.

then that whole minefield of resistance, amps, etc etc etc, to get it all clean and efficient (with all of those taken into account and sorted, then even a 1500watt setup can rip the back-side off a much larger setup up, and save money, and weight.)

i think i will enjoy being a member of this forum!
DannyA posts on March 20, 2014 19:02
exlabdriver, post: 1024402

If your system sounds good to you then don't worry about it. Why care about what other's subjective opinions are? Yours is the only one that counts.

It's best just to enjoy…


Agreed. Sometime that curiosity bug gets the better of me though.
exlabdriver posts on March 20, 2014 18:34

If your system sounds good to you then don't worry about it. Why care about what other's subjective opinions are? Yours is the only one that counts.

It's best just to enjoy…

DannyA posts on March 20, 2014 16:26
At one point I was determined to know how my speakers stack up against other speakers in the same price/quality range. I eventually let the idea go. I like how my system sounds after all of the work I put in to placement and tuning. With that said, I've seen enough posts and comments about my speakers and their advertised specs to know that I would most likely be disappointed with the results. I could be wrong and I guess now I'm curious again but I don't want to ask “the question” if I can't live with the answer. What I don't know won't make my system sound any better or worse. But if I do know and the results stink, I'll be grinding my brain thinking about how to build a new system (that I can't afford right now).
Somehow I know my curiosity is going to get the best of me.
ira posts on March 20, 2014 13:10
Please keep in mind that if the multimeter you use is not a “true RMS” meter, it will have material errors in its RMS measurements. I could not tell the exact model number of the DMM you are using, so please make sure you look up its exact specs, and I recommend junking it if it's not a true RMS DMM - no need to include avoidable errors in your reviews.
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