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Noise Band Rise and Fall Edge Frequencies

Controls: Gen Dlg >> Stream >> Wave >> Band >> Rise/Fall
Macros: BandRise, BandFall

To create a band of noise between two frequencies, set Rise Fc to the lower frequency and Fall Fc to the upper frequency.

To create low-pass noise, set Rise Fc to 0.

To create high-pass noise, set Fall Fc to the Nyquist frequency (half the sample rate).

To create a wideband noise with a gap between two frequencies, set Fall Fc to the lower frequency and Rise Fc to the upper.

Like all other frequency controls in Daqarta, these respond to the various Frequency entry modes. You can set the current (global) mode via the dialog open button below the Rise Fc control.

See Ratios and Octaves if you want to set the band limits such that they define an octave or fractional octave about a specified center frequency, such as "1/3 octave centered at 10 kHz".

Although the Rise and Fall controls set the "frequency" of a noise band, this is not a value that can be modulated directly. Just like the other Noise sources, when Band is active, the modulator options are reduced to Burst and AM only... no FM, Phase, or Sweep. However, it is indeed possible to create a swept or modulated Band center frequency in many cases.

This technique works best for narrow to moderate width noise bands. Set Rise to 0 and Fall to half the desired bandwidth, giving a low-pass noise. Now go to a higher stream and set up a sine wave whose frequency will be the center of the noise band. Set the AM Source on that stream to the stream with the low-pass noise, and set AM Depth to 200%. (That changes the AM to straight multiplication.) Turn on AM and you will see the low-pass noise band mirrored about the selected center frequency.

To understand what's happening here, consider that when two frequencies are multiplied together, the product contains only the sum and difference of the original frequencies. (Check out the AM Depth section for the formula.) That applies to the individual low-pass noise frequencies as well, so each instantaneous frequency in the original noise becomes two frequencies in the product, one above and one below the center frequency.

(Note that you could have just as well used the sine wave as the AM modulator on the noise stream. Since only lower-numbered streams can modulate higher, you'd need to reverse the stream order so that the noise was on a higher stream than the sine.)

Now all you need to do is apply a Frequency Sweep or FM to the center frequency, and it becomes applied to the noise band instead. Note that if you use too wide a band, or sweep too far, you can run the noise above the Nyquist frequency or below zero. In those cases the band folds back on itself, raising the level of the wrapped region by 3 dB.

Note also that this technique does not allow swept or FM equalization via the use of Curves with Noise Band Shape - Taps. The Curve equalization would be applied only to the low-pass noise that is being multiplied by the frequency-changing sine, not to the overall frequency range of the product. The instantaneous band would have the original equalized low-pass shape mirrored about the band center, and that mirrored shape would then be swept.

Astute observers might object that a noise band created via this mirror technique is not really the same as the equivalent band created in the normal way. The fact that the noise components always come in matched pairs means it is not totally random. But unless the band is extremely narrow, such that there are not a lot of other components, this fact will not be detected via listening tests. This technique was used for years with real electronic filters, oscillators, and analog multipliers to create adjustable narrow noise bands for psychoacoustics tests, long before the digital era.

You can create low-pass noise with a variable cutoff frequency by allowing the noise band to fold back on itself, if you can accept the resulting low-frequency level boost. Set Rise to 0 and Fall to half of the maximum desired cutoff frequency. When the modulating sine frequency is also at half the cutoff, the mirrored noise extends from 0 to the cutoff. When the modulating sine moves lower, the noise wraps at 0 and there is a 3 dB boost at the wrapped frequencies.

The same idea can be used to create high-pass noise, if you can accept the resulting 3 dB boost from wrapping at the high-frequency end.

You can use these concepts to create moving gaps, but the same wrapping problems will be present at both ends of the spectrum. The most general approach uses separate moving low-pass and high-pass streams, whose separate modulating sine waves have the same frequency deviation. This approach uses all 4 streams of one channel, but allows the widest range of useful gap frequencies, and even allows a variable-width gap by proper selection of the modulating sine frequencies and deviations.

A more limited approach uses only a single band of noise (instead of low-pass) mirrored about the gap center. The basic idea is that when you multiply this band by the center frequency, you will have two bands flanking the center. The distance from the center frequency to each band will be equal to the Rise frequency. (Remember, the lower band has been mirrored; it starts from the center frequency and runs downward.)

Now the trick is to adjust the Fall frequency, which controls the outer band edges, so that there are no extra gaps at the extreme high and low frequencies. If the gap were to be at a fixed frequency in the center of the range, this would clearly be no problem; you'd just set Fall to half the total Nyquist range and the outer edges would fall neatly at the ends.

But if Fall is larger than half, the outer edges will wrap back into the main range, raising the level of the wrapped region by 3 dB.

Next you have to determine how far you will need to move your noise gap from the center of the range. The farther down you move it, the more wrap you get at the bottom and the more chance for another gap to slip in from the top. You need to make Fall large enough so that when the gap has moved to its lowest extreme, there will still be no gap at the high end. But if you make it too large, the wrapped portion will fall into the desired gap from the bottom. The exact same consideration applies when moving the gap up instead of down.

This method is thus best limited to modest gaps with modest motion near the center of the range. It's cumbersome to set up, but uses only 2 of the 4 Generator streams.

Macro Notes:

L.1.BandRise=1k sets Left Stream 1 Rise to 1000 Hz. L.1.BandFall=4k sets Fall to 4000 Hz. The actual values may be quantized depending upon the setting of the Frequency Entry Step Mode

To increment or decrement the current Rise value, use BandRise=>1 or BandRise=>-1, respectively. The increment size is set via the Frequency Entry Step Mode. Only +/-1 step is accepted.

See also Band-Limited Noise, Noise Waves, Wave Dialog.


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