Nearfield/Farfield curve splicing

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It entirely depends on the room. Obviously in an anechoic chamber only the direct axis sound is important. In a very live room the power response is probably just as important as the axial response. Hence there is no single answer to your question. It all depends.

I like my rooms to be very lively as this kind of room sounds larger and more spacious. So to me power response is critical. If I designed my rooms to be dead then I would do things differently. But no room is so dead that the power response does not matter at all.

Have you ever listened to a speaker in an anechoic chamber? I have, its not appealing at all. Toole told me that he prefers his rooms on the lively side as well.
 
^
Your polar_map app doesn't work:

Code:
PLATFORM VERSION INFO
	Windows 			: 6.2.9200.0 (Win32NT)
	Common Language Runtime 	: 4.0.30319.34003
	System.Deployment.dll 		: 4.0.30319.33440 built by: FX45W81RTMREL
	clr.dll 			: 4.0.30319.34003 built by: FX45W81RTMGDR
	dfdll.dll 			: 4.0.30319.33440 built by: FX45W81RTMREL
	dfshim.dll 			: 6.3.9600.16384 (winblue_rtm.130821-1623)

SOURCES
	Deployment url			: http://gedlee.com/Polar_map.application
						Server		: Microsoft-IIS/6.0
						X-Powered-By	: ASP.NET

IDENTITIES
	Deployment Identity		: Polar_map.application, Version=2.2.0.6, Culture=neutral, PublicKeyToken=fa19fde47989b9bb, processorArchitecture=x86

APPLICATION SUMMARY
	* Online only application.
	* Trust url parameter is set.
ERROR SUMMARY
	Below is a summary of the errors, details of these errors are listed later in the log.
	* Activation of http://gedlee.com/Polar_map.application resulted in exception. Following failure messages were detected:
		+ Downloading http://gedlee.com/Application Files/Polar_map_2_2_0_6/Polar_map.exe.manifest did not succeed.
		+ The remote server returned an error: (404) Not Found.

COMPONENT STORE TRANSACTION FAILURE SUMMARY
	No transaction error was detected.

WARNINGS
	There were no warnings during this operation.

OPERATION PROGRESS STATUS
	* [13/02/2014 18:59:47] : Activation of http://gedlee.com/Polar_map.application has started.
	* [13/02/2014 18:59:47] : Processing of deployment manifest has successfully completed.
	* [13/02/2014 18:59:47] : Installation of the application has started.

ERROR DETAILS
	Following errors were detected during this operation.
	* [13/02/2014 18:59:47] System.Deployment.Application.DeploymentDownloadException (Unknown subtype)
		- Downloading http://gedlee.com/Application Files/Polar_map_2_2_0_6/Polar_map.exe.manifest did not succeed.
		- Source: System.Deployment
		- Stack trace:
			at System.Deployment.Application.SystemNetDownloader.DownloadSingleFile(DownloadQueueItem next)
			at System.Deployment.Application.SystemNetDownloader.DownloadAllFiles()
			at System.Deployment.Application.FileDownloader.Download(SubscriptionState subState)
			at System.Deployment.Application.DownloadManager.DownloadManifestAsRawFile(Uri& sourceUri, String targetPath, IDownloadNotification notification, DownloadOptions options, ServerInformation& serverInformation)
			at System.Deployment.Application.DownloadManager.DownloadApplicationManifest(AssemblyManifest deploymentManifest, String targetDir, Uri deploymentUri, IDownloadNotification notification, DownloadOptions options, Uri& appSourceUri, String& appManifestPath)
			at System.Deployment.Application.DownloadManager.DownloadApplicationManifest(AssemblyManifest deploymentManifest, String targetDir, Uri deploymentUri, Uri& appSourceUri, String& appManifestPath)
			at System.Deployment.Application.ApplicationActivator.DownloadApplication(SubscriptionState subState, ActivationDescription actDesc, Int64 transactionId, TempDirectory& downloadTemp)
			at System.Deployment.Application.ApplicationActivator.InstallApplication(SubscriptionState& subState, ActivationDescription actDesc)
			at System.Deployment.Application.ApplicationActivator.PerformDeploymentActivation(Uri activationUri, Boolean isShortcut, String textualSubId, String deploymentProviderUrlFromExtension, BrowserSettings browserSettings, String& errorPageUrl)
			at System.Deployment.Application.ApplicationActivator.ActivateDeploymentWorker(Object state)
		--- Inner Exception ---
		System.Net.WebException
		- The remote server returned an error: (404) Not Found.
		- Source: System
		- Stack trace:
			at System.Net.HttpWebRequest.GetResponse()
			at System.Deployment.Application.SystemNetDownloader.DownloadSingleFile(DownloadQueueItem next)

COMPONENT STORE TRANSACTION DETAILS
	No transaction information is available.
 
It entirely depends on the room. Obviously in an anechoic chamber only the direct axis sound is important. In a very live room the power response is probably just as important as the axial response. Hence there is no single answer to your question. It all depends.

I like my rooms to be very lively as this kind of room sounds larger and more spacious. So to me power response is critical. If I designed my rooms to be dead then I would do things differently. But no room is so dead that the power response does not matter at all.

I think we had already established the fact that power response has an audible effect. "It all depends" is not really a satisfying answer.

Have you ever listened to a speaker in an anechoic chamber? I have, its not appealing at all. Toole told me that he prefers his rooms on the lively side as well.

What's not appealing about it?
 
This helps me get a better idea of problem areas (holes or peaks) in the off-axis response. This information needs to be made available while you design the crossover (I think that is what you are showing above, not sure).

Another example how my LspCAD6Ext application creates e.g. horizontal off-axis responses below 390 Hz splicing frequency (red line). Time window function & excess group delay, short measuring distance & speaker dimensions etc. show about 2 dB extra directivity below 100 Hz, but the result is still much more realistic than with simple sharp splicing.

An externally hosted image should be here but it was not working when we last tested it.
 
Time window function & excess group delay, short measuring distance & speaker dimensions etc. show about 2 dB extra directivity below 100 Hz, but the result is still much more realistic than with simple sharp splicing.

Since we know that there can't be any directivity that low, this is likely due to a changing mic distance with rotation, i.e. not rotating about the acoustic center. Its hard to avoid.
 
Since we know that there can't be any directivity that low, this is likely due to a changing mic distance with rotation, i.e. not rotating about the acoustic center. Its hard to avoid.

When you take polars, do you try to rotate about the acoustic center* (presumably a bit behind the baffle plane) or about a the center of the baffle?

*which begs the question, acoustic center at what frequency?
 
What is the "right way" to sum up power response? Is there a general agreement of that? What about "weighted" measurements?

Usually when we refer to "power response" we are actually talking about some spherically integrated energy curve (proportional to pressure squared). It isn't power unless we calibrate to a PWL rather than an SPL. The proper way is to square pressure, do a conversion to power and then weight each measurement sample in proportion to area that each measurement represents. In the end we can ignore the conversion to true Watts if all we want is a spherically averaged SPL (squared, an RMS average, if you will) and this will allow us to compare axial pressure to "spherical pressure" (not a proper entity). The difference between those 2 curves will be the directivity index.

Power response can be equal but radiation pattern may be different - will these speakers sound different in a room with reflections?

This is something that I frequently point out: that power response or directivity index does not dictate a drivers polar paterns, "only the area under the curve". As such, having constant directivity is not a guarantee of good polar response or smooth frequency response away from the listening axis.

So if two speakers have the same axial response, same power response and very different polar curves then that opens the possiblitly that they have very different frequency response in any given direction. Will this be audible?

The Soren Bech studies are pretty good for this. He looked at the audibility of all the expected reflections in a typical listening room and found that outside of the floor bounce in front of a speaker and (rarely) the back wall and side wall first bounce that no later bounces were individually audible. Based on that it is safe to say that changing the level or frequency response of energy going in directions away from the listener are inconsequential as long as the level stays below those typical thresholds.

Lipshitz and Vanderkooy did a study of audibility of reflected energy and found similar results with the exception of strong side reflections in a smaller room adding some brightness to reproduction.

This brings us back to what we frequently debate, the audibility of power response, or the significance of speaker directivity. Everything I read points to power response (it's shape and it's level) being much less important than axial response or listening axis response. This is not to say that systems with very different power responses won't sound at all different, just that getting the listening axis response right first is imperative.

Certainly, plunking down and omni mic in a typical room and measuring the steady state response, then proclaiming "that is what it sounds like" ignores the ability of the ear to strongly key in on the early part of arriving energy (as well as ignoring binaural hearing).

David S.
 
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I think he's trying to explain that your simple question is a very complex answer and would be silly to even attempt. Would answer with a similar response. :) Have given very similar answers to various topics over the years. Even with internet friends wanting me to design them a circuit that would help them prove their misdirected theory/questioning. Ehhh, you want me to make something, possibly taking hundreds of hours, when I have already explained the reason why and then do it on my own dime? Oh Please ;)
 
When you take polars, do you try to rotate about the acoustic center* (presumably a bit behind the baffle plane) or about a the center of the baffle?

*which begs the question, acoustic center at what frequency?

I rotate about the center of the speaker box. Since my model is based on a piston in a sphere the center of the sphere, or the center of the box is the correct rotation point. It isn't critical however.
 
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