Think about what might be an important specification for a loudspeaker, loudness for example. Typical of audio measurements, a concept like loudness is not easy to express. For example, it is generally easier for us to hear middle frequencies (speech related stuff: "Grok! Run! Saber tooth tiger! Waga waga!") than low frequencies. To date there has not been any strong evolutionary pressure to hear the lows of a really bitchin' bass groove, though I personally recommend you get some speakers the size of refrigerators and . . . Anyway, you may be familiar with the equal loudness contours of human hearing (often called Fletcher-Munson or Robinson-Dadson curves). These equal loudness contours describe how our perception of loudness is different depending on the frequency and amplitude of the sound we are listening to. For example, perhaps you have been enjoying Prince's latest, letting it shake the walls while you check out the great sound of the album. Your neighbor calls (you could barely hear the phone ring) and asks you (edited for family reading) to “Turn it down, please.” If and when you turn it down to a neighborly level, your ability to hear bass is lowered more than the amount you turned the level down, because at low volumes we humans can't hear much bass. When you punch the loudness button it will boost the bass so it is perceived at a level closer to the perceived level of the rest of the spectrum.

Given the above, it should be clear that something as seemingly straightforward as loudness is difficult to measure. "Loudness" as a subjective value changes in an observable way when the frequency is changed, when the amplitude is changed, when the humidity is changed, etc. And this is but one of the many subjective audio parameters we try to glean from the countless specifications accompanying audio electronics.

One tool I use to help make sense of the peculiarities of audio perception in humans is the Audio Window (see "Spectral Management" in the July issue of H&SR).

Figure 1: The Audio Window

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The window views audio in three dimensions or axes:

1. Loud to Soft
2. High to Low
3. Fast to Slow

The Loud-to-Soft dimension has already been considered in our discussion above but let's look more closely. There is a single specification often seen that essentially measures the range of this axis, called Dynamic Range. A device's capability to produce a range of amplitudes is reported as its Dynamic Range, which is simply expressed as the difference in decibels between the level at which the sound distorts and the level of residual hiss and/or hum in the system. The dynamic range reported for a given product determines how much of the range along this axis of the Audio Window that the product can use. Keep in mind that our ears have their dynamic range specification too. Some sounds are too quiet for detection by humans. At the other extreme, sounds can reach a level where they become painful and even unhealthy. Our physiology limits our hearing to a dynamic range of about 120 dB (a power ratio of one trillion to one!), which means there is a natural limit to the dynamic range we require from audio equipment. It is also important to note that dynamic range tells us nothing about the quality of the sound at any level. We need other specifications for that.

The next axis on the Audio Window, High-to-Low, is quite obviously critical for audio. Interestingly, though, it is important not to focus too much on the outer limits obtainable by the piece of equipment (how high and how low can it go?). It is true that we can hear frequencies as low as about 20 Hz. and up to frequencies approximately 1,000 times as high as that -- 20,000 Hz., but having electronics that can produce frequencies across that range is standard practice for most gear these days. What is really important is the ability of the audio product to perform consistently along this axis of the Audio Window. This is still an engineering problem for electromechanical and electromagnetic devices (such as transducers, which include loudspeakers, microphones, tape heads, etc.) Consider the loudspeaker. Clearly it is desirable for the loudspeaker to be just as loud at 10 kHz as it is at 1 kHz when being driven by 'equal amounts' of power at each frequency. See the sidebar on Pink Noise. Without consistent performance across the spectrum, the speaker would emphasize some frequencies and suppress others, coloring the sound. The test we call Frequency Response is a measurement of the product’s amplitude at each frequency, revealing which frequencies are boosted and which are attenuated and by how much.

Figure 2

	Figure 2. Typical loudspeaker frequency response plot

Graphically, the plot of such a test contains a lot of information, but is comparatively expensive to print, and overwhelming to look at and consider in the profusion of products in a catalog. If you doubt this, try perusing a catalog of tweeters and woofers and see how long it takes for your eyes to glaze over! So, more typically, manufacturers replace the plot with two sets of numbers derived from it:

1. Frequency Range: the range of frequencies over which the product performs. This is generally limited by the frequencies below or above which the product suffers a clearly audible drop in level, such as a 3 dB drop (which is also, just so you know, a drop to half the power). A typical specification might be: “Frequency range: 30 - 17,000 Hertz.” This would mean that all frequencies within that range would be handled by the device with no more than 3 dB loss.
2. Amplitude Range: describes (in decibels) the variation above and/or below an average level reproduced by the system. A typical specification might be: “+/- 2 dB.” This means that within the stated range there will be no variations greater than 2 dB from the nominal stated level of the signal passing through the device.

Be wary of the often quoted but fundamentally meaningless: "This beauty has a frequency response of 20 to 20k!" By telling you nothing about amplitude they have told you nothing about frequency response; look for values on both the frequency and amplitude axes.A stated frequency response of 40 to 18 kHz, +/- 2 dB suggests that the performance of the product falls off significantly below 40 Hz and above 18 kHz and that between those limits it favors some frequencies by a maximum of 2 dB (That's the plus 2 dB part of the specification) and discriminates against others by up to 2 dB (That's the minus 2 dB part of the specification).

While helpful, frequency response described only by these numbers is incomplete. Figure 3 below shows two frequency response plots that would both be described by the same "40 to 18 kHz, +/- 2 dB" specification.

Figure 3

	Plots of two devices (see next image) with a stated frequency range of 60 to 18 kHz, +/- 2 dB

	Plots of two devices (see previous image) with a stated frequency range of 60 to 18 kHz, +/- 2 dB

As you can see, the frequency response numbers do not tell you where in the spectrum the various regions of emphasis and de-emphasis are. You are not given any sense of the product's general consistency. Is it reproducing all frequencies with almost uniform consistency with the exception of a single peak above the general level and a single dip below? Is it wildly inconsistent producing frequencies at levels throughout the stated +/- 2 dB all across the spectrum? Look for a more complete description of frequency response.

One final thing to worry about here is that when the sales guys get hold of the response plots from engineering, the first thing they do is compare them with the plots published by the competition. Then they run back to the engineering team and ask, “Is there any way you can redo these to make them better than Brand X, here.” The engineering group (and I am not making this up; I have watched it happen) says, “Well, X obviously made their measurements in such and such a way -- if we change our data acquisition speed and smooth the curves here and here, which takes out all the grunge in the plot that you can’t hear anyway, then it should look great! There! How’s that?” The plots a manufacturer publishes are usually a whole lot different from the ones that engineering got when they measured the device in the privacy of their lab. Beware. It’s not that the manufacturer is cheating, exactly, but there is a difference in goals here. The engineering team needs to find out the worst about their product, so that they can improve it, while the sales team needs to show the product in its best possible light!

The third axis of the Audio Window, Fast-to-Slow, merits its own separate discussion. Interesting but somewhat obscure characteristics such as phase shift, slew rate and flutter are measured along this axis. Compared to issues of amplitude and frequency, these qualities have less dramatic audible impact. Also, the nature and quality of our perception changes as a function of how long an event is, and events of different lengths are processed in different parts of the auditory system and brain. Differing time relationships (as I’ve tried to suggest in my articles on early delays, comb filtering and the phantom image) are used by the auditory system to give different values and information to the conscious mind. The time axis represents most of the really fascinating psychoacoustic phenomena of stereophony, localization and reverberance.