Noise Band Taps

Controls: Gen Dlg >> Stream >> Wave >> Band >> Taps
Macro: BandTaps

Taps can be set from 8 to 512 in powers of 2. The higher the Taps setting, the steeper the edges of the selected band. However, a higher value uses more memory and more CPU time.

The noise band (or gap) is generated by filtering a wideband white noise source, using what is known as a Finite Impulse Response (FIR) filter. Conceptually, this consists of a delay line that the input noise passes through; each stage of delay is one sample period in duration, and after each there is a "tap" to tap off the noise at that stage. That doesn't affect the noise at all, just peeks at it on its way through.

The output of each of these taps is still white noise, just delayed differently from the other tap outputs. To see how this might be used to make a filter, consider what happens if we add two tap outputs together: For some frequency of the input (which is white noise containing all frequencies), the delay between the two taps will be exactly the duration of one whole cycle at that particular frequency. At that frequency (and multiples thereof, as it turns out), the two outputs will be "in phase" and the amplitude of that component will be doubled. But at some other particular frequency (and multiples thereof), the delay will be only a half cycle, such that it will be added with a sign change; the output will be cancelled at those frequencies.

The net effect of adding two taps is called "comb-filtered" noise, with alternating peaks and dips whose spacing is determined by the relative delay. (See Comb Filtering and "Flanger" Effects for further discussion.) To get a more useful filter, additional taps can be added, and each tap output can also be multiplied by some weighting constant before being added into the final output.

Imagine starting with the multiple peaks and dips of the simple 2-tap comb filter, then selecting additional taps and constants such that some peaks are boosted further, and some are cancelled. The more taps you have to work with, the more peaks can be boosted or cancelled. By proper selection of tap constants, an arbitrary filter shape can be created. Using still more taps will always allow a better filter.

Since each tap requires a multiplication by its constant, and all the taps must be added to get each output sample, this process can be quite slow. To avoid multiplying, Daqarta uses a trick: To understand this, first note that binary noise is still white noise; you can verify this by looking at the spectrum of the White source and changing the Timing Quant value from 0 (no quantization) to 1 (binary). There is a slight increase in level because the output spends more time at the full-scale limits, but the spectrum remains flat. (Alternatively, you could leave Timing Quant at 0 and set Generator Bits from 16 down to 1. In that case, the two output states are 0 and -100% so the sound is softer, but otherwise the same.) In listening tests, the binary and ordinary White noise sound absolutely identical except for the overall level difference.

Now consider that binary noise is nothing but a string of 1s and 0s (or +1s and -1s). Multiplication by a constant thus turns out to be merely adding or subtracting, depending on the data value; this is much faster than a true multiplication. Daqarta further improves on this concept by building look-up tables containing the summed output for strings of bits, so the final output can be found very quickly via a few table look-ups. (Whenever you change any Band parameter, a whole new set of look-up tables is built.)

So, how does all this affect actual use of the Band source? For the vast majority of applications it has no effect at all. Use of binary noise only affects the amplitude distribution of the values, not the spectrum. Since our ears don't hear amplitude distributions, this has no effect on listening tests. (See GausWhit.GEN Setup File - Comparing Noise Distributions in the Applications section for a demonstration that compares Gauss and White. You can use this same approach to compare any two distributions that have the same spectrum.)

What's more, even with binary noise as the input, the output of the FIR filter is not in general binary... after all, each output value is the sum of many taps, each of which has been scaled by a different constant to some non-binary value. So in most respects the final output, including its waveform and amplitude distribution, is indistinguishable from a noise band produced by any other method.

However, since the Band source is fully adjustable, it is possible to set it to have very little filtering action. Clearly, if you set Rise Fc to 0 and Fall Fc to maximum, the essentially unfiltered noise will show a binary appearance in its waveform. As you reduce Fall this appearance is less and less apparent, and is essentially gone by the time Fall is half of maximum (ie. half of Nyquist). This binary appearance happens with low-pass noise; if you set Rise much above 0 so you get a band of noise, even with Fall set very high to give a really broad band, you won't see it.

You may also see the binary appearance with gap noise, when you set a narrow gap near the top of the range.

Since this binary appearance is inaudible, the main issue is whether there is some other effect it might have. If you are using the Band output to modulate some other source via the Stream Modulation option, for example, then the distribution of the values might make a difference. You might want to add a small amount of Smoothing to reduce this, although it will cause the spectrum to tilt downward.

(Note that in general you should not use Slow or Step Timing with the Band source. If you do, you will get a series of decreasing "images" in the spectrum: Copies of the desired band that appear due to aliasing, since you have effectively reduced the sample rate.)

Macro Notes:

L.1.BandTaps=128 sets the Left Stream 1 Band Taps to 128. Valid settings are 8, 16, 32, 64, 128, 256, and 512. Other values will be rounded to the nearest valid setting.

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