Click on hot link for info on "minimum phase" Long-winded "speech" follows: About 80-90% of bass energy under 80Hz. is reflected off one or more room surfaces on the way to your ears. Only 10-20% comes directly from the subwoofer to your ears. Under 80Hz. the frequency response at your listening position is greatly influenced by in-phase reflections between opposing room surfaces (aka standing waves, or room modes). After a small delay for standing waves to form (typically 15 to 45 milliseconds in a home listening room), the bass reflections will combine with the bass energy still coming from the subwoofer. The bass frequencies involved are determined by room dimensions. Standing waves do not require parallel walls to develop -- they just need opposing surfaces that reflect bass energy. The strongest standing waves are between two opposing surfaces (aka "axial"). There will be fixed (aka "standing") locations within a room where the bass reflections are out of phase (nulls) and other locations where the reflections are in-phase with bass energy still coming from the subwoofer. In actual rooms standing waves tend to be 3 to 10Hz. wide (measured using -3dB points) with 5Hz. wide being typical for plasterboard wall / plywood floor rooms. In a typical home listening room there will be about five axial standing waves under 80Hz. (sometimes six in large rooms). If a room happens to be square, some of the standing waves will be stacked at the same frequency. If the room is near-square, some of the standing waves will be at adjacent frequencies. If the room is well shaped, the standing wave frequencies will be at different frequencies not too close together ... or too far apart -- that allows our ears to apply their one-third octave smoothing effect. If we're lucky, no single standing wave will be noticeable. This is common in very large rooms where there are more than five or six axial standing waves under 80Hz. ... and in ordinary sized rooms above 100Hz. where standing waves are more dense than below 80Hz. In ordinary listening rooms, it's very likely a listener will be too close to one or more standing wave-related bass frequency peaks and nulls. The nulls tend to be very narrow, so just moving the listening position one foot or two in the right direction will move your ears away from the deepest portion of a null. But the peaks are much wider, so moving your seat is unlikely to get away from all of your room's "bass booms". Of course there are limitations to where you can move your listening seat, as you have to give top priority to the mid-range and treble frequencies to hear the proper stereo image. If you hear / measure one or more bass frequency peaks at your listening position, the peak SPL can be reduced using parametric EQ (typically 1/6 octave bandwidth). EQ applied to each of the three groups of axial room modes and the side effects on alternative seating positions: (A) For room modes between the front and back walls (a very common acoustics problem, and the only group of axial room modes not affected by using dipole speakers): - EQ that works for the listening position will also work well for people sitting to the left side or right side of the listening position (i.e.; people whose ears are located approximately the same distance from the front wall) . . (B)For room modes between the floor and ceiling: (a fairly common room acoustics problem, especially in rooms with cement floors and low ceilings): - EQ that works for the listening position will also work well for people sitting anywhere in the vicinity of the listening position whose ears are located approximately the same distance from the floor. . . (C) For room modes between the side walls: (Bass frequency peaks caused by these room modes are not a very common problem for two-channel stereo because the main listening position is usually half-way between the side walls, which is a null for many of these room modes ... and the left and right speakers are placed on different sides of the room, so they are out of polarity and can't excite many of these room modes) - EQ that works for the listening position will also work well for people sitting behind the main listening position whose ears are located approximately the same distance from side walls. Would also work well for someone sitting right in front of the main listening position ... but we can't allow that! . . . . From the Adire Audio website (click on "Paper that includes ... link): "The Hilbert transform is a method of deriving the acoustic phase from the acoustic magnitude (the typical frequency response curve shown in most all literature and design programs). There is one caveat: the Hilbert transform is valid ONLY for what is called a minimum phase system. What is a minimum phase system? The actual way to calculate one is also beyond the scope of this paper; however, for our purposes, a subwoofer driver operating in a box, in it's linear mode is a minimum phase system. Operate beyond the linear limits of the driver (where distortion, power compression, suspension compression, and other nonlinear issues come into play) and the system is no linger minimum phase, and hence cannot use the Hilbert transform." http://www.adireaudio.com/tech_papers/sub_gd.htm . . . . . From a Tom Nousaine post at the google.com link below: "The major problem at low frequencies is a relative lack of room modes. Standing waves (room modes) occur at all frequencies between any pair of opposing wall surfaces. If you play a 1000 Hz tone (wavelength of roughly a foot) you can hear the modal changes when you move your head a few inches. However because of the short wavelength you get the same effect anywhere in the room. At low frequencies with long wavelengths the main problem is that the pressure peaks and valleys occur in multiples of several feet. Therefore the energy in the room will be unevenly distributed. Remember that the modes are a function of the room dimensions. So the ONLY thing you can do is FAIL TO EXCITE a mode. Thus moving a subwoofer around in your room will simply fail to excite some modes. And the PROBLEM is a shortage of modes. For example below 100 Hz there will be only 3 axial and 3 2nd harmonics in an average 3000 ft3 room. If you fail to excite ANY of them you will worsen the distribution of energy in the room. Even if you find the optimal listening location you'll still fail to excite one or more of those 6 modes and worsen the situation if you choose ANY subwoofer location than a closed (a full wall and at least 5-feet of wall to either side) corner. Even using a corner won't give you even distribution of SPL at low frequencies BUT it will give you most uniform distribution you can get. The next job is to find the listening location that takes advantage of this. In several rooms that I've response mapped I've generally found that in a shoebox shaped room a spot centered on the short wall and about 1/4 of the length distance from the back wall is optimal." http://groups.google.com/groups?q=nousaine&start=350&hl=en&lr=&ie=UTF-8&scoring=d&selm=a6082001peo@enews1.newsguy.com&rnum=357
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