Jul 1, 2000 12:00 PM, Sam Berkow
Time-domain measurements help provide a more complete picture of an audio installation's overall performance.
For sound contractors, consultants and live sound engineers, the most common type of acoustical measurement involves measuring the frequency response of a system. This frequency response may be estimated using a Real Time Analyzer (RTA), measured using a dedicated stimulus and response package, or generated by a real-time transfer function measurement. In any case, the results of the measurement are typically displayed with energy (in decibels) on the Y-axis and frequency on the X-axis. Charts of frequency domain data appear regularly in product specifications and have become extremely common in both technical and trade literature. Although frequency domain displays can be useful, analysis of time-domain measurements can provide a wealth of useful information not easily obtained from frequency-domain measurements.
The following example examines a time domain impulse response measurement. It is interesting to see how much information we can learn about our system from one time domain display. Figure 1 displays an impulse response measured in a real room, in this case a 1,200-seat theater. The measurement itself was made using the dual-channel FFT technique and represents the impulse response of the entire system under test; in this case the system includes both the sound system and the acoustical environment. In the Smaart software, the impulse response of the system is measured using the delay locator feature.
A real-world example
Whenever we look at a graph, it is best to begin by looking at the scales on each axis. The Y-axis in Figure 1 is in decibels. It is interesting to note that the Y-axis scale ranges from -15 dB to -75 dB, a range of 60 dB. Whenever decibels are used on a scale, it is important to note the reference value. In this case, the reference value is 0 dB equals full scale. The X-axis in Figure 1 displays time, ranging from 0 ms to approximately 840 ms, which is slightly more than three-quarters of a second.
An interesting thing about the impulse of a system is that the level of the peak energy, when compared with the noise floor, is often a good indicator of the quality of the impulse response data. Although this rule is certainly frequency dependent, we can see that our measurement has a peak value of approximately -20 dB, and the broadband noise floor is located at approximately -68 dB. Subtracting these two numbers yields the broadband S/N ratio of our measurement, -48 dB, which is a good value.
Having examined the axis scales of the plot, we can immediately note that the direct sound seems to have arrived at the measurement mic in 70 ms, which, using the speed of sound, is approximately 75.5 feet (23 m). It is critical to remember that this distance includes both the time required for sound to travel from the loudspeaker to the measurement mic and any delay through the sound system processing, such as A/D converters, delay lines or other devices with throughput delay.
We can compare the level of the direct sound to the level of the reverberance to obtain information about the intelligibility of the sound system room combination. The level of the reverberance is typically defined as the point in an impulse response at which the reverberant decay meets the direct sound. In our case, the level of reverberance is -40 dB, indicating that the direct sound is 20 dB higher than the level of reverberance. As a general rule of thumb, a difference between the broadband direct sound and the broadband level of reverberance of less than 10 dB indicates intelligibility problems. Values of 10 dB to 15 dB are considered fair. Values between 15 dB to 20 dB are good, and values above 20 dB are considered excellent.
This rule of thumb is certainly an easy value to measure, but is not foolproof. It is possible to have an excellent direct to reverberant level difference and poor intelligibility. This rule of thumb value should be used as one piece of the puzzle rather than an ironclad law of physics.
Another feature of the time-domain decay shown in Figure 1 is a prominent reflection located approximately 110 ms (123.5 feet or 37.6 m) after the direct sound. Although the effects of a strong reflection, such as comb filtering, can be seen in frequency-domain displays, time-domain analysis offers a direct way to see the position (in time) and magnitude of a reflection. In our example, the reflection is only 12 dB lower than the direct sound and seems to be rather discrete, meaning that there are no other such reflections. By looking at the geometry of the room and looking for paths of sound that start at the loudspeaker and end at the measurement mic, covering the same distance as our reflection, one can often determine the exact surface reflecting the sound energy. It is also possible to treat the suspect surface, even temporarily with a heavy blanket, and repeat the measurement to see if the reflection is reduced in amplitude.
A step further
Time-domain analysis offers a great deal of information about the character of the decay of a space. It is common for people to characterize the sound of a room by a single reverberation time number. The use of a single-value reverberation time number, however, is generally a poor indicator of the sound of a room.
By looking at the decay of a time-domain measurement over a wide range of frequencies, several common problems can be identified, quantified and evaluated. One of the most common acoustical problems in rooms ranging in size from small home listening rooms to major league sports arenas is the tonal imbalance caused by a lack of low-frequency absorption in the room. This tonal imbalance is often the result of a facility using acoustical materials that are absorptive in the mid- and high-frequency ranges but have only marginal effectiveness at low frequencies. To measure this phenomenon, we can filter the impulse response data, and look at the decay of energy in several octave bands.
Within Smaart, these decay curves are displayed in a plot that calls them "Time Slices." Figure 2 shows the 4 kHz, 1 kHz and 125 Hz octave-band Time Slices calculated from the impulse response shown in Figure 1. It is immediately obvious from Figure 2 that the decay rates at 1 kHz and 4 kHz are almost identical. The decay at 125 Hz, however, seems to be longer and more erratic than the higher frequency decays.
Another useful rule of thumb is that in a tonally balanced room, the low-frequency decay rate, expressed in RT subscript 60 values, should not be more than 50% larger than the mid-high frequency. In our room, the decay at 1 kHz and 4 kHz is about 64 dB/second, an RT subscript 60 value of about 0.9 seconds. The 125 Hz octave band decay seems to decay at about 31 dB/second, an equivalent RT subscript 60 of 1.9 seconds. The ratio between the two values is more than 2 (1.9/0.9 = 2.1). Such a high ratio suggests a room that is, at least at the measurement location, boomy and tonally unbalanced.
Figure 2 also shows how the decay of sound within the room not only decays erratically, but also actually builds up over the first 100 ms. This build-up of low-frequency energy is common in smaller rooms or in under-balcony spaces where energy can be effectively trapped and can build-up, reducing both intelligibility and tonal balance. This situation is a common one, and the time-domain measurement can help to determine when acoustical treatment, rather than an electronic solution, is required.
Lastly, time-domain measurements are the basis for the speech transmission index (STI), the rapid speech transmission index (RSTI) and the percent articulation loss of consonants (%Al subscript cons), widely used for measurement and calculation of intelligibility metrics. In Figure 3, the level of the direct sound (L subscript d), the level of the reverberance (L subscript r) and the level of the broad-band noise floor (L subscript n) are all marked and used in the calculation of several intelligibility metrics. The blue line showing the decay rate in Figure 3 is slightly different from the Time Slices in Figure 2. This decay curve is called the Schroeder integration curve and is another way to display the change in energy over time of a decay.
As I hope the examples above demonstrate, taking a few moments to understand time-domain analysis can be informative and rewarding, helping people to understand sound systems, rooms and their interactions better.