TDS (time delay spectrometry) in Sound Measurements (Jan. 1978)

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The only licensee of time delay spectrometry (TDS) in the audio industry to date is Cecil Cable, an audio consultant from Edmonton, Alberta, who has spent the last five years applying the basic ideas of TDS to professional sound system applications. The first detailed explanation of a sound system's early room-reflection interactions in the determination of bandwidth of the filter required to suppress feedback modes resulted from this research on TDS in large arenas (AES Convention, May 1977). Before we go into some of the practical sound system applications of such devices, let's look at the basic theory behind this fascinating tool.

TDS Basics

Sound travels through air at a finite speed (typically around 1130 ft/sec at 70°F), thus it is possible to speak of the distance sound travels in either feet or milliseconds. If we divide one second into 1000 mS, we then find that the sound has traveled 1.13 feet in one mS or it takes 0.885 mS to go one foot.

Therefore, if we placed a microphone 10 feet in front of a loudspeaker and switched on a 1 kHz tone to the loudspeaker, the microphone would not receive the tone until 0.885 mS x 10 ft = 8.85 mS after the loudspeaker first sent it.

At the instant the loudspeaker emitted the tone, if the generator driving the loudspeaker were to begin a sweep upwards in frequency at the rate of 10,000 Hz/sec or 10 Hz/mS, by the time 1000 Hz reached the microphone, the loudspeaker would be sending at the very same instant in time 1000 + (10 Hz/mS x 8.85 mS) = 1088.5 Hz.

If the microphone is connected to a narrow (10 Hz) filter capable of sweeping at the same rate (10 Hz/mS) as the generator but synchronized to start its sweep at the exact instant the signal arrives at the microphone (8.85 mS after the generator sends it or 88.5 Hz behind the generator, then the readout device (meter, oscilloscope, wave analyzer, etc.) will see only the frequency arriving at the microphone, and by means of the filter's selectivity, discriminate against all other frequencies (see Fig. 1). Thus, room reflections caused by lower frequencies can't get past the filter and only the direct sound of that frequency from the loudspeaker itself is present at the microphone during the time the filter is tuned to that frequency.

Figure 2 illustrates graphically these interlocked relationships, and Fig. 3 shows Cecil Cable's modified H.P. 8552B/8556A analyzer with the accompanying digital frequency counter that allows the monitoring of the frequency between the generator and the receiving filter.

The arrangement discussed thus far allows rapid, accurate plots of the direct sound from the loudspeaker without any influence from the room.

This is a truly anechoic response plot.


-----Above: Audio consultant Cecil Cable is shown at work with his modified Hewlett Packard 8552818556A analyzer with the digital frequency counter.

Early Reflections Spectra

It can be seen that by "tuning further out" in space (or time), that is, by delaying the receiving filters' sweep until after the direct sound has passed the microphone, that it becomes possible to discriminate against the direct sound as well and see, for example, only the spectrum of a reflection off a nearby wall, ceiling, or floor (see Fig. 4). If, for example, the microphone were 10 feet from the loudspeaker and the reflective surface was another 10 feet from the loudspeaker beyond the microphone, the frequency offset (FO) required between the generator and the filter, if the sweep rate were 10,000 Hz/Sec, would be: 10,000 s\ 1130 = 265.49 Hz (*Note: the sound travels 20 ft from the loudspeaker to the reflective surface and then 10 feet more returning to the microphone.)

Practical Uses of TDS

The ability to directly compare the difference in level between the direct sound spectrum and the chosen reflected sound spectrum makes absorption vs. frequency immediately visible, and the focusing of reflective surfaces is easily identified.

One of the fundamental measurements undertaken by Cecil Cable was the identification of time align anomalies that interact with the normal modes in a room to create acoustic feedback as system gain is increased (see Fig. 5). Cable has shown that the feedback modes that occur when a sound system is used in an enclosed space are due to the room modes riding on the "comb filter" response of the time align anomalies generated by the early reflections spectrum. This coincidence of the early reflection spectrum and the room modes have, at long last, demonstrated why it seemed as if the room modes joined into clusters of modes, rather than operating as individual, very narrow areas.

By being able to place the total spectrum of both the direct sound and the total reflected sound on the same analyzer screen, it becomes practical to study how loudspeaker Q, the critical distance, and the ratio of direct-to-reverberant sound behaves at differing locations of source, listener, and boundary surfaces relative to frequency.


Fig. 1--Relation between sweep rate, time, and offset. The frequency offset in Hz = 0 Hz sweep rate ( Distance l Velocity of sound 1


Fig. 2--The relation between the generator and the receiver during the sweep.


Fig. 3--Basic time delay spectrometry equipment.


Fig. 4--Measuring the spectrum of a reflective surface.

"Dead" Rear Wall Wrong?

A "dead" rear wall with a hard front wall in a control room is fundamentally questionable. Presuming that the loudspeakers are properly flush mounted, then the early reflection spectrum will look like a comb filter with very broad (one octave or wider) humps which are quite audible. If, however, the loudspeakers are properly flush mounted (an art in itself), the adjacent surrounding area is made very absorptive, and the rear wall is made hard and diffuse, then the early reflection spectrum will look like a comb filter with a large number of very narrow humps, which individually are not significant, but as a group enhance the sound level. Obviously, the larger the control room the better, with up to 40 feet in depth offering good acoustic possibilities.

Time delay spectrometry (TDS) allows us to look at the spectrum of the early reflections and objectively analyze them. Time align(TM) monitors have eliminated many of the subtle masking effects.

TDS Instrumentation

The present instrumentation format is not considered ideal, but is the result of adapting as economically as possible an available precision spectrum analyzer. One "flaw" in the present system is that the display on the screen is linear along the frequency base (1000 Hz per division), while a logarithmic display would be preferable.

In order to achieve such a display, it might be necessary to exchange frequency offset between the tracking generator and the filter for a continuously variable time delay and "trigger."


Fig. 5--Acoustic feedback's parameters. The lower trace shows the frequency response of early sound with the loudspeaker 2.26 feet in front of hard wall. Upper trace shows the room mode pattern through a two-second window, while the dotted lower trace is shown with loop gain.

The baseline markers indicate order in which oscillatory feedback appeared.

Summary

TDS has demonstrated its fundamental usefulness to those of us privileged to use it thus far (a small but select group at this writing. However, it has been shown and demonstrated by Cecil Cable at each of the Syn-AudCon sound engineering seminars since May, 1977). It is obvious, at present, that it only awaits publication of its benefits, along with the educational assistance of those who would respond to its enormous promise, in order to become the first logical extension beyond the acquisition of real time spectrum analysis.

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(Source: Audio magazine, Jan. 1978; Don Davis [Synergetic Audio Concepts, Tustin, Calif.] )

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