Log-Squared Response

Let’s take a walk across the log-squared response of the room/sound system. Starting at time zero, the first major spike will be the first pressure wave arrival from the loudspeaker. It is normally followed closely by successive spikes which are usually delayed energy arrivals from within or around loudspeaker. This may be due to sound reflecting internally in the enclosure, sound reflecting between the walls of a horn, or sound diffracting off of the face of the loudspeaker cabinet. Loudspeaker de signers pay much attention to these early arrivals, as they smear the time response of the loudspeaker, with consequent degradation of the frequency response of the loud speaker.

The time span of the display can be shortened to provide a better view of these early sound arrivals. Within a few milliseconds of the first arrival, there is usually a point where the first arrival and very early reflections (from within the loudspeaker) decay to the noise floor of the display. This marks the separation of the “direct field” from the loudspeaker from the reflections from the room. Placing a dividing cursor at this point and integrating (summing) the data points on both sides of the divider yields the ED/ER (direct-to-reflected) energy ratio at this microphone position. This is also where we would place a divider if we wished to examine the response of the loud speaker while ignoring the later energy arrivals from the room. The same dividing cursor can be moved to various time intervals after the first arrival to yield the clarity ratios (C7, C35, C80) at this microphone position. Acousticians use this information to evaluate the clarity of speech and music. The higher the number (in dB) the stronger the early energy (left of divider) dominates the late energy (right of divider), and the higher the clarity of the sound. C7 and C35 are used to evaluate speech clarity, and C80 is used to evaluate music clarity.

Schroeder Integration

Manfred Schroeder proposed a method of reverse-integrating the data, beginning at the right side of the display and summing the individual samples toward the left of the display. This yields the envelope of the room decay, and is useful for placing markers to evaluate the rate of decay for various parts of the data. Of interest to system designers is the early decay rate of the sound system and room, as well as the late decay rate (usually referred to as the reverberation time for 60 dB of decay, or RT To find the early decay time, (EDT) we would place a marker on the first energy arrival and another 10 dB down on the integration curve. A fast early decay time means that the first reflections are low in level with respect to the direct sound arrival. This is what we would expect if a directional loudspeaker were used to minimize the energy striking the room surfaces. A slow EDT indicates the presence of strong early reflections. This usually results from low directivity loudspeakers that place high energy levels on the walls and ceiling.

In general, the highest sound clarity (and articulation) is achieved with fast EDTs. In a acoustically “dead” environment, the presence of early reflections do not hinder intelligibility, and in some cases can actually enhance it. In acoustically “live” environments, the strong early reflections cause a higher reverberant field level, and can impair the clarity of the system by causing excess reverberation in the room. A skilled system designer can judge when to maximize early reflections and when to minimize them. A fast EDT can provide good speech clarity, even when the overall room decay time is very long.

In rooms that have long decay times (>1.5 seconds) the integration curve becomes a straight sloped line (we are still using a log vertical axis). Using the cursors to section off the straight portion of this line yields the classical RT for the room, the parameter which Wallace Sabine originally measured with a stopwatch. This is more a parameter of the room rather than the sound system, while the EDT is more a parameter of the sound system and room. While the RT is a useful number for describing the overall energy decay characteristics of the room, the EDT is of greater interest to the sound system engineer, as maximizing it can allow for clear sound reproduction in reverberant environments.

One the energy ratios and decay times are known at a microphone position, several algorithms exist to process the information to indicate the intelligibility of speech. One such method is the Percentage Articulation Loss of Consonants of Speech (%Alcons). Developed by V.M.A. Peutz, this algorithm uses the LD (direct field level), LR (reverberant field level) and EDT to yield an intelligibility score that compares favorably with live listener intelligibility tests performed in the space. As one might expect, the lower the EDT and higher the direct field level, the better the %Alcons score.

The impulse response can also be processed to yield the Speech Transmission Index (STI). This is another method of rating the speech communication properties of the room/system, based on evaluation of the reduction of speech modulation by noise and reverberation. A complete description of how to compute the STI can be found in Syn-Aud-Con Tech Topic, A Do-it-Yourselfer’s Guide to Computing the Speech Transmission Index.

At this point, we have shown how the impulse response of a room / sound system can be processed to yield important information about polarity, clarity and intelligibility. Our next part of the series will describe how we can take this time domain information and view it from an other perspective, the domain of inverse-time, or frequency. c