TONE COMPONENT ADJUST SUBMENUS:

• Tone Components - Introduction
• On/Off
• Freq Hz
• Phase degrees
• Start
• Rise duration
  • Experiment: Rise/Fall vs. Spectrum Width
  • Practical Example
• Sustain duration
• Fall duration
• Level %
  • Attenuation vs. Level
  • Combining Tone Components
  • Intermodulation Distortion

TONE COMPONENTS - INTRODUCTION:

There are 4 separate tone component submenu pages, which you can move among with the CTRL-Pg keys.

On / Off:

For any active DAC output, you must always have at least one active page or you will get an alert and warning:

    'Must have at least one active page per output.'

Freq Hz:

The frequency should be less than half the sample rate, or you will get "aliasing" down to frequencies lower than you intend. Ideally, you want to use low tone frequencies and high sample rates so there will be many output samples per cycle of tone for a good approximation of a sine wave. Theoretically, a sine generated with K samples per cycle will have no distortion products below the Kth harmonic.

If you can't arrange to sample at a high enough rate (possibly by use of Sample Factor oversampling) for the tone frequency you need to generate, consider using an external low-pass reconstruction filter to reduce the worst of the harmonics.

Also, consider if you really need to worry about these harmonics. If you will be presenting tones to a human subject, for instance, you don't generally need to worry about harmonics above 20 kHz. So if you want to use tones up to 16 kHz, and your sample rate is over 40 kHz or so, you probably don't have anything to worry about. Your subject surely won't hear even the second harmonic of your 16 kHz tone (at 32 kHz), much less any higher ones. Just be sure any power amplifiers, etc, that must handle the stimulus will not behave poorly in the presence of these upper harmonics. This is not usually a problem with modern equipment, but if it is you can often cure things with a very simple low-pass filter made from a single resistor and capacitor.

Phase degrees:

This is the phase when the wave actually starts at the beginning of the Rise samples, which may be delayed by Start samples. With a large (slow) Rise, the initial output samples will be too small to discern the phase at that point, but you can see its effect upon later samples.

Start delay:

Rise duration:

By making the rise longer, or the exponent smaller, you reduce the amount of "spectral splatter" or audible click associated with the onset of the tone. In a detection experiment, the click might be audible where the tone itself is not, giving a misleading result.

But if you are determining the subject's detection threshold by recording neural responses, you must also take care not to make the rise too long, either, as explained below in the Rise/Fall Practical Example.

EXPERIMENT: RISE/FALL vs. SPECTRAL WIDTH:

Set Start to zero and Sustain to about 128 samples. With a sample rate of 20 kHz, set Freq to 2000. Set Rise and Fall to 128 samples each. In Sequential mode, you should see a single tone burst which takes up the first 384 samples of the waveform trace. Flip to the power spectrum display with the F-key and Y-key. Note the width of the spectrum spread on either side of 2000 Hz as you cut Rise and Fall in half to 64 samples each. Keep cutting these in half and watch the spectrum widen further.

RISE/FALL PRACTICAL EXAMPLE:

As you lengthen the rise time, however, the response gets progressively smaller. This is because an evoked response is the summation of many neurons firing at once. Since the individual firing rates and threshold sensitivities of these neurons are not all alike, to get them to fire at the same time you must give a stimulus that quickly goes from below all neuron thresholds to above many neuron thresholds.

Each neuron will thus start its pulse train at the same time, so all the initial pulses will be superimposed to form the evoked response peak. But subsequent neural pulses will not be in synchrony, so the response rapidly falls. With a slow rise time, the different neural thresholds are reached at differing times, so the number of pulses superimposing to form the evoked response is reduced.

Sustain duration:

Fall duration:

Level %:

On the other hand, a separate attenuator that acts on the analog output of the DAC could preserve the 16-bit approximation and the corresponding low distortion. This could be an internal or external digitally-controlled analog attenuator, or a manual knob-type unit, or even a simple potentiomenter "volume control".

Although you wouldn't want to use Level as the only attenuator in your system, you can use it to "trim" an attenuator that has only coarse steps. For example, if your attenuator has steps of 6 dB each and you need 1 dB resolution, you can use Level alone to set any effective attenuation from 0 dB (100.0%) down to 5 dB (56.2%), then set the attenuator to 6 dB and set Level to back 100% or 0 dB for steps from 6 to 11 dB. You can continue this process to get any desired amount of attenuation while never setting Level below 50%, an equivalent of losing only 1 bit of resolution.

ATTENUATION VERSUS LEVEL:

 dB  Level %   dB  Level %   dB  Level %   dB  Level %
 0.0 100.0     2.0  79.4     4.0  63.1     6.0  50.1
 0.1  98.9     2.1  78.5     4.1  62.4     6.1  49.5
 0.2  97.7     2.2  77.6     4.2  61.7     6.2  49.0
 0.3  96.6     2.3  76.7     4.3  61.0     6.3  48.4
 0.4  95.5     2.4  75.9     4.4  60.3     6.4  47.9
 0.5  94.4     2.5  75.0     4.5  59.6     6.5  47.3
 0.6  93.3     2.6  74.1     4.6  58.9     6.6  46.8
 0.7  92.3     2.7  73.3     4.7  58.2     6.7  46.2
 0.8  91.2     2.8  72.4     4.8  57.5     6.8  45.7
 0.9  90.2     2.9  71.6     4.9  56.9     6.9  45.2

 1.0  89.1     3.0  70.8     5.0  56.2     7.0  44.7
 1.1  88.1     3.1  70.0     5.1  55.6     7.1  44.2
 1.2  87.1     3.2  69.2     5.2  55.0     7.2  43.7
 1.3  86.1     3.3  68.4     5.3  54.3     7.3  43.2
 1.4  85.1     3.4  67.6     5.4  53.7     7.4  42.7
 1.5  84.1     3.5  66.8     5.5  53.1     7.5  42.2
 1.6  83.2     3.6  66.1     5.6  52.5     7.6  41.7
 1.7  82.2     3.7  65.3     5.7  51.9     7.7  41.2
 1.8  81.3     3.8  64.6     5.8  51.3     7.8  40.7
 1.9  80.4     3.9  63.8     5.9  50.7     7.9  40.3

NOTE:
If you set Level to 0.00%, that tone component page goes Off and is simply omitted from the output. However, you must always have at least one active component for any active DAC output, so if you try to set 0.00% on the only active page, you will get an alert and warning message:

   'Must have at least one active page per output.'

COMBINING TONE COMPONENTS:

The stimulus waveform display will show the possible overlap areas, but since it is small you should not rely on it to insure there is no distortion... compute the sum of Levels if there is any doubt.

If possible, consider putting one component on each output channel and sum the DAC outputs externally with a mixer.

INTERMODULATION DISTORTION:

One approach is to generate the tones from separate DAC channels and use them to drive separate amplifiers and speakers, with the sound mixed together acoustically. Since air is much more linear than any driver, the intermodulation will be greatly reduced. Some small amount may remain, particularly if the sound must be mixed in a closed system, due to sound pressure from one source moving the other. Note that this technique does nothing to reduce HARMONIC distortion, which is generated separately from each source.

Using the Step N mode to generate the two tones will insure that they fall exactly on spectral lines, along with all harmonic and inharmonic distortion products, to allow simple measurements without "skirts".

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