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Jon M. Risch, Peavey Electronics Corp., Meridian, MS. USA            Copyright 1998

Presented at the 105th Convention of the Audio Engineering Society
1998 September 26-29th, San Francisco, California as preprint #4803


An in-band multitone test signal designed to maximize detection of harmonic, intermodulation, aharmonic and cross-modulation products, despite the presence of multiple frequencies in the test signal, is presented.  Measurements of electroacoustic systems are presented and contrasted against traditional harmonic distortion and intermodulation measurements.  Measurements of other audio components, such as electronics, is also explored.

0  Introduction

One of the stimuli for this project was a search for a test signal to better correlate with perceived listening clarity.  Examination of a device using only harmonic distortion measurements does not provide a straightforward and consistent relationship between the measurements and listening results, especially once the measured harmonic distortion falls below a certain level.  Traditionally used intermodulation test signals were considered, but these typically tend to provide only a few intermodulation or crossmodulation products within the audio band.  Multitone signals looked to be the most promising type of measurement, as these would provide a complex stimulus for the DUT, and generate a larger number of intermodulation and crossmodulation products.       

1.0  Limitations of Existing Signals

    1.1 Harmonic Distortion
It can be confusing to try and correlate harmonic distortion measurements with what is heard.  Once harmonic distortion levels are below several percent in the midband, it is a tossup as to which device will sound better or clearer.  Up to a certain point, a given level of even order harmonics are more benign sonically than a given level of odd order harmonics, while higher orders are generally more irritating than the lower order harmonics.  A significant amount of second harmonic distortion may actually sound preferable to much lower amounts of third or fifth harmonics.   A certain amount of second harmonic distortion may even be preferred to a system that has little or no second harmonic distortion.  With all these confusing factors, harmonic distortion is not a clear cut way to evaluate a system or device once the levels have reached typical values for a modern high performance audio device.

    1.2 Intermodulation Distortion

Intermodulation distortion measurements typically use just two tones, such as SMPTE, DIN, or CCIF, with a limited number of intermodulation and crossmodulation products within the audio band.  There are a few three tone intermodulation tests that were proposed, but they have not become popular or mainstream tests. (1)  The classic two-tone tests are severely limited in how much distortion across the audio band they will expose.  Even performing tests using all the variations of the mainstream standards will still leave large gaps in the characterization of the DUT’s intermodulation distortion performance, and consume a fair amount of time.

    1.3 Spectral Contamination

Spectral Contamination testing has been proposed by Sokolich and Jensen (2).   This looks more promising, but one of the proposed test signals covered in the paper is completely outside of the audio band, with signal stimulus extending from 150 kHz to 300 kHz, and it uses equal frequency spacing; in the example used in the paper, 9.36 kHz.  The other proposed test signal spectrum extends from 10 kHz to 25 kHz, and has 120 Hz signal spacing.  Equal frequency spacing means that many of the various intermodulation products and even some of the crossmodulation products will have the same resultant frequency.  In the out of band version, this does generate a range of signals spaced 9.36 kHz apart in the audio band. For the 10 kHz to 25 kHz stimulus with 120 Hz spacing, the audio band distortion products tend to be at 120 Hz spacing, with a lot of the products at 120 Hz.

Placing the stimulus frequencies all outside of the audio band means that the device or system under test must possess greatly extended bandwidth and a concurrent extension of linearity, which may or may not relate to use within the audio band.  It also means that the signal is ineffective for use with inherently bandwidth-limited systems  such as loudspeakers, and most current digital audio systems.   Additionally, the distortion products must all be of two kinds: crossmodulation products that divide down into the audio band and intermodulation products that subtract down into the audio band.
No harmonics will be present within the audio band.

The version with the stimulus band from 10 kHz to 25 kHz still limits the use to wide band electronics, and precludes most digital and acoustic systems from being measured with this signal.  It has similar restrictions as to what distortion products are displayed.

A third test signal is suggested, one which has signal components within the audio band, and a space or gap left in the middle of the band.  This is designated as an "in-band" measurement.  No frequencies or other details are suggested, and no measurements were performed using this signal in the Sokolich and Jensen paper.

    1.4  SYSid Version of Spectral Contamination

Spectral contamination as performed by the SYSid measurement system has an in-band form of spectral contamination measurement.  This signal has already found some use in correlating perceived clarity with the measurement (3).  However, the usefulness is not as complete as it could be.   In the default setup file, the frequencies either have equal spacing, or arbitrary spacing between the multiple frequencies.  A total of 15 tones are used, with default frequencies of:  80, 100, 120, 160, 200, 240, 300, 400, 500, 700, 900, 1200, 1500, 2000 and 3000 Hz, which is spacing of: 20, 40, 60, 100, 200, 300, 500, 1000 Hz, this yields frequency to next frequency ratio's (or multiplier's) of 1.2, 1.25, 1.33, 1.4 and 1.5, not necessarily in any given order.

A formula is given in the owner's manual to achieve equal log spacing within a specified band, but this results in tone spacing that are a product of a given chosen bandwidth and number of tones, and has no other purpose other than to provide the equal spacing.   The results from this formula are virtually random with respect to frequency spacing ratio's.  A utility is provided called GENFN, which allows custom selection of the test frequencies for the SYSid spectral contamination test.  The test frequencies selected and entered are placed into the closest FFT bin.  This is done to maximize the ability of the FFT to examine the frequencies between these filled bins, but may make the spacing turn out to be less than optimum.

There is an admonition in the owner’s manual to avoid making the test frequencies an integer multiple of one another, but this does not prevent the frequency spacing from generating intermodulation or crossmodulation products that can be covered up by a primary tone.   For instance, intermodulation products that fall at 100 Hz or 200 Hz are completely masked by the primary tones at these frequency's.  These frequency spacing allow the harmonics of the lower frequency test signals to be covered up as well, so even simple harmonic distortion products are hidden for some of the test signal tones.

The sheer number of tones can also present a problem in some cases, as the level of individual tones within the multitone signal must be at least 23.53 dB down from nominal in order to avoid clipping and other gross errors due to phase shifts in the system under test.   This effectively limits the available measurement dynamic range with a 16 bit testing system to about 72 dB or less.  The author is not aware of any capability within SYSid to set the relative phase of the various test tones.

Also, the number of tones within that frequency range makes it difficult to ascertain exactly where the distortion products are coming from, due to limitations in spectrum analyzer resolution.  The density of the primary tones makes it hard to clearly ascertain the origin of the distortion products that are not already covered up by primary tones.  This forces the use of the highest spectral resolution that the system is capable of, and still limits how accurately some of the distortion products can be ascertained.

Another concern with the SYSid default setup frequencies is that lower order harmonics are only present up to a certain point.  The last primary frequency in the test signal is 3 kHz, and stopping the test signal content at this frequency limits the ability to determine both the level of harmonics for the rest of the audio band above 3 kHz, and the ability to detect intermodulation and crossmodulation products at higher frequencies.  The limited band that the signal covers essentially limits it's use to the upper bass and midrange.  Two or three way speaker systems would have virtually no excitation of the tweeter with this test signal.

The sequence starts out fairly low at 80 Hz, or even lower if a default file with a start frequency of 60 Hz is used, which is beyond the full capability of some smaller speaker systems and some other bandlimited systems.  In my opinion, a widely acceptable test signal should be useful on almost any audio device, even a bandlimited one.   A low frequency of 100 Hz is more appropriate for a test signal to have a more universal application.

To the credit of the designers, the flexibility of the SYSid test system allows the user to generate a user defined set of spectral contamination test tones.  This will enable the SYSid system to take advantage of the newly designed test signals presented herein.

    1.5  Audio Precision Multitone Signals

The Audio Precision System One DSP and System Two both have a multitone in-band test signal capability, with the default setup having frequencies spaced according to 1/3 octave ISO centers, which is a multiplier ratio of 1.25.  With this spacing, every third frequency is spaced an octave apart, and the resultant frequencies often end up at even spacing amounts.  A total of 31 separate tones are used, which reduces the dynamic range available.  Individual tones must be at -29.83 dB from nominal, unless phase manipulation is used to reduce the crest factor.   As noted earlier, this may not be a good idea if the system or device under test is known to have amplitude roll-off in the audio band, excess phase shifts or time delays built into the system.

Audio Precision does adjust the frequencies to correspond to an FFT analyzer bin center frequency, in order to maximize the ability to use the empty analyzer bins to best advantage.  These 31 frequencies are: 16.15, 21.53, 26.92, 43.07, 53.83, 64.60, 80.75, 102.28, 123.82, 156.12, 199.18, 253.02, 317.61, 398.36, 500.65, 635.23, 802.11, 1001.3, 1248.9, 1598.8, 1997.2, 2503.2, 3154.6, 3999.8, 4995.7, 6352.3, 7999.6, 10002, 12500, 16005, and 19999 Hz.  Note that none deviate from the standard ISO centers by more than about 5 Hz.

This does offset the exact regularity that would tend to occur with such ISO-center frequency spacing, but since the analyzer bins are limiting the ability to resolve the distortion products to any better accuracy, these minor offsets are not very effective in avoiding intermodulation and crossmodulation product cover up, or harmonic cover up by the primary tones.  Even with the slight offset in the stacking up of harmonics, intermodulation and crossmodulation products will not be able to be resolved due to the inherent width of the FFT bins.

The Audio Precision systems can be programmed or set to generate and test using any frequencies chosen by the user, but they do not offer a means or advice on avoiding the generation of multiple distortion products at the same resultant frequency, and at the same frequencies as some of the primary tones.

There is an AP codec test signal (5), which has two bands of 8 frequencies (16 total) separated by a two octave gap.  These are not all at ISO centers, +/- the FFT bin center, but they still exhibit some stacking of distortion products.  This test signal is similar to the one proposed by Sokolich and Jensen.

The frequencies are: 53.83, 123.82, 209.95. 312.23, 446.81, 608.31, 807.50, 1060.5, 3999.8, 5022.6, 6287.7, 7859.6, 9808.4, 12230, 15234, and 18965 Hz.

The frequency spacing for the various tones is not according to any pattern or design that is readily apparent.  Information about this particular AP test signal was not received until the basic research for this paper had been completed.

2.0  New Spectral Contamination Signal
After discovering that harmonic, intermodulation, and crossmodulation products were being masked to one extent or another by the present implementations of spectral contamination tests, I sought a series of frequencies which would avoid this problem.  A number of options were explored, and while frequencies could be picked at random, or arbitrarily, it was felt that some sort of defining function or multiplier would be more useful and consistent.  It was found that a multiplier based on the Golden Ratio, or the final ratio of the mathematical Fibonacci sequence, of 0.618034 worked very well.  By using a multiplier of 1.618 or 2.618, a sequence of tones is generated that avoids any of the harmonics, and almost all of the intermodulation and cross-modulation products from being covered up spectrally by any of the other tones or products.

    2.1  Working Criteria

It was desired that the tone sequence start and stay within the audio band, so that bandlimited systems would be fully excited by the test stimulus.  Accordingly, 100 Hz was arbitrarily chosen as a start frequency that was well within the range of even small multimedia loudspeakers. This results in a series of 6 tones using the 2.618 multiplier at frequencies of: 100, 261.8, 685.4, 1794.4, 4697.9, and 12299 Hz for the test signal I call the Phi6 spectral signal.  Figure 1 graphically depicts the FFT spectrum of the signal as output from a CD player, through a mixer for level control.

In an effort to limit the loss of dynamic range, it was decided that there should be a practical limit to how many tones were used.  Starting from 100 Hz, and using the 1.618 multiplier, 12 tones within the audio band result, and this was felt to be a good upper limit.
Using a much lower frequency only results in a few more tones within the audio band, and these frequencies are all fairly low.

The 12 tone signal using the 1.618 multiplier results in the former frequencies plus: 161.8 Hz, 423.6 Hz, 1109.0 Hz, 2903.4 Hz, 7601.3 Hz, 19900 Hz, and is called a Phi12 spectral signal.  Figure 2 graphically depicts the FFT spectrum of the signal from the CD player, and through the mixer.

Further refinements and variations on the test signals suggested themselves after working with the proposed test signals to actually measure a system.  These variations are covered in the experimental results section, as they were developed as a result of the experimentation.    


Link to 2nd web page on this paper

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