Gating loudspeaker measurements

So you want to get a nice clean measurement to design a speaker or measure a speaker you already have and you don't have an anechoic chamber at your disposal. Kind of a conundrum. You need a pseudo-anechoic measurement, but how does one make a pseudo-anechoic measurement? Eazy Peazy, you have to gate out the room reflections. IOW, remove the reflections out of the visible frequency response measurement. Since sound has a time element to it--it is a temporal thing, we'll have to look in the time domain to separate it out. In order to do that you need to see what is speaker generated and what is boundary/room reflection generated. The frequency responses at your left were achieved by various levels of gating using either the impulse or the spectrogram to discover where the room reflections enter the response. You can essentially close the gate on the reflection trying to get into the graph. In the impulse you can see where the major, high amplitude reflections come into play just after 6 ms, but the spectrogram makes things a bit clearer if a bit less absolute. In the spectrogram you can see not only the timing and frequency of the reflections, but their amplitude as well. Gating not only removes room reflections, but also the amount of data points in the measurement. So the longer the gate, the more detailed your gated measurement. As you look at the frequency response graphs and how they are gated, you can see the impact of the time and amplitude of the reflections shown in the spectrogram at that gate setting. You can try the same thing for any speakers you would like, but there are other ways as well. Read on.........

For woofers and mid/woofers, gated measurements can be less easy to be exact and the resulting frequency response graph becomes less accurate in the low end d/t reduced resolution effects of less data points. Good thing that there typically aren't huge problems in this frequency band d/t the relative rigidity of the cone and our perception of this range is dominated by the room anyway (barring baffle step).

The triangle in the top picture is the key to the math though the above(impulse) method is more useful--Pythagoras is your friend.  'A' squared + 'B' squared = 'C' squared.  There are 2 right triangles in the pic above, just draw a straight from the midpoint to the floor and use it as 'A' or 'B'.   The time difference between the arrival of the direct sound and first reflection is how you set your gate (reflected time-direct time=gate length). Sound travels at about 1ft per ms or 1 meter per 3 ms.  Frequency Resolution of your gated frequency response = 1/Period(Gate). Let's say after you do your Pythagoras, a 6 ms gate is given(which would be excellent for in home).  This limits your lowest frequency measured and resolution to 166.67Hz. Call it 170Hz. At 3 milliseconds your resolution becomes 333Hz or roughly 350Hz. You'll be able to get a longer time period/cleaner measurement from higher directivity speakers as the reflections won't be as powerful. The closer your mic is to the speaker and the higher the speaker is off the ground, the longer the gate you can have. However, the big chiefs in the industry say you need to get the mic away from the speaker for appropriate wavefront formation in the low end so it can be far field.  

Them's the basics. Good luck.

Info on Distance

Forward Lobe

Another important aspect of speakers is their vertical polar response. Every typical two-way speaker will have lobes and nulls in the response formed by the non coincident sources playing the same frequencies. In the near field--before the reflections become a major player--these lobes/nulls are audible with fairly small head movements if the nulls are not spaced very far apart. So ideally a "near field" monitor would have a broad forward lobe. The forward lobe is dictated by the distance between the drivers, the crossover frequency and slope, phase, and driver directivity at the crossover frequency, but that can be a heavy topic. Essentially you want to forward lobe to point at your ears. Check this out for a great visual on lobing: Falstad's wave interference applet.

Let's have a look at the studio monitors we have on hand.

You can see in the top graph that there are 3 lines that are basically flat. Since the speaker is rotated in 11.25 degree steps toward the tweeter, that corresponds to a 22.5 degree forward lobe that is angled 11.25 degrees toward the tweeter. Behringer lists the crossover frequency at 2 kHz for the B2031P(the speaker graphed). Seems pretty darned accurate. This is pretty good performance for the near field, but not ideal. The graph toward the woofer is 5 dB down at 11.25 degrees off axis. I got to do a little more precise measurements in smaller increments on this at a friends house and it's actually a bit better performance than what this indicates and the lobe is centered at 10 degrees toward the tweeter. I didn't include the graph toward the woofer

The next is the Behringer 1030A--graphs 2 and 3. The 2nd is toward the tweeter and the 3rd is toward the woofer. Combining those 2 you can see four lines that are basically flat. That is impressive performance--33.75 degrees of good behavior. The wide directivity of the drivers (small mid/woofer and shallow waveguide--see horizontal polar pattern for evidence), low crossover frequency, and close driver spacing contribute to this.

Now let's check out the Mackie HR 624 mkII, the 4th and 5th graphs.

The Mackie looks to have a bit more narrow lobe than the B2031P and it seems almost perpendicular to the baffle but slightly toward the tweeter. Not necessarily a bad thing, but good to know info. Placement is critical with these speakers. To be sure, these are my favorites out of the bunch, but they are the most difficult to get right. In the near filed, small head movements can definitely alter the sound. The 1030A seems immune to them. I listen to these Mackie monitors from 6-9 ft away. That gives you a vertical window of a little over 2-3 ft respectively. Of course you are also into the reverberant field at 9 ft so you can all but totally ignore the lobe. At 6 ft in my room I can still hear it with pretty dramatic head movements unless placement of me and the monitors is just right. At 3 ft away and a 1 ft vertical window, head movements can be an issue if monitor placement is not precise.

OK, I did some more room tweaking with the Mackie monitors. I'm proud to say this is certainly among the best room responses I've ever seen and I did it with better placement rather than more treatment. Basically, that means I saved some dough. These are the averages across the room to make them simple. I threw the on axis vs. AVG response of the Mackie and the same with the center seat response and room average so the reader can make the correlation of how the polar response relates to what happens in the room above the modal region.