If one could listen to only the direct sound of a loudspeaker, the world would be a very different place! Unfortunately, free field listening, where you have no reflections, room modes or ambient noise, is hard to achieve in everyday life, so we listen to loudspeakers in real rooms.
The interaction of a loudspeaker system and a room can be very complex to understand, model or measure! One way to measure this interaction is to measure the impulse response of the loudspeaker/room system.
The impulse response of a typical sound system in a room contains lots of interesting information, including:
1) The delay between the loudspeaker and measurement microphone
2) The direct sound-to-reverberent level ratio
3) The time arrival, frequency content and level of reflections of sound
4) The early and late decay rates of the sound
5) The frequency response of the direct sound.
This last point is particularly interesting. The question is “What do we want to measure and why?”
One question that goes to the heart of “system” measurement and optimization issues is “If the impulse response contains the frequency response of the direct sound, can we separate the loudspeaker response from the room response?” Also “If we can, do we want to?”
Figure 1 shows an impulse response of a 1,250-seat multipurpose hall. displayed in the time domain. The x-axis is time (~0.75 sec) and the y-axis is magnitude in dB. Note the direct sound, reflections, the reverberant decay and the noise floor.
The “spike” that represents the direct sound actually contains the frequency and phase information about the loudspeaker. To see this information we must transform this portion of the impulse response into the frequency domain.
To achieve this isolation of the direct sound from the room response, we must select a time window that includes the direct sound but excludes the reflections and decay of the room.
Figure 2 displays such a time window. This measurement, in the same 1,250-seat hall, was made using a full-range loudspeaker system with the microphone approximately 60 feet from the loudspeaker. Pink noise was used as a reference signal and the impulse response was calculated using a 512K FFT (although only the first ~0.75 seconds are shown).
The vertical lines suggest a time window that ignores most of the effects of the room at frequencies whose periods are longer than the time window (i.e. low frequencies).
We can take the “time windowed” data and transform it into the frequency domain using FFT mathematics. This transformation yields a result that shows how much energy is present at each frequency, demonstrated in Figure 3, showing the frequency response of the direct sound portion of an impulse response in the 1,250-seat hall.
The response was calculated using a 512 point FFT (which equals a 512/48000 or ~11 msec). As you can see the frequency response shows a pronounced LF roll-off. You can also notice the lack of LF resolution in this figure. The lack of resolution at LF is offset by a excess of HF resolution.
This uneven resolution between LF and HF energy is the result of the FFT mathematics used to transform the data from the time domain to the frequency domain. Standard FFTs yield data that is distributed linearly in frequency (one data point every X Hertz). Unfortunately, humans perceive frequency logarithmically.
This lack of LF resolution in Figure 3 is a direct result of the use of a short time window in our transformation from the time domain to the frequency domain. It is interesting to note that this plot does not correlate with what we hear.
Simply listening to the full range loudspeaker system we were measuring made it clear that the system was reproducing LF energy down to at least 100 Hz!