This document provides a very short overview of the near-field effect (NFE). A variety of simple HOA example implementations follow.
We'll by briefly reviewing the near-field effect (NFE) in the context of FOA and HOA.
The near-field effect (NFE) has been formally included within the Ambisonic framework since its initial design. In the classic days of Ambisonic hardware, users usually only directly interfaced this aspect of Ambisonics through the use of:
The ATK's FOA toolset includes NFE radial filters in their classic Ambisonic form. In the FOA context a travelling wave encoded with all real, aka basic, coefficients represents a planewave. The ATK also names this travelling wave as a basic wave, because of the use of basic, real coefficient encoding. SuperCollider's PanB is a basic, planewave encoder.
An Ambisonic system's reference radius is the radius at which a basic wave is encoded. So the reference radius locates the radius at which the system's encoding uses real numbers only.
For FOA, the reference radius is infinity. A wave arriving from infinity is a planewave, which is why FOA's basic wave is a planewave.
The FOA near-field compensation filter returns the inverse of the FOA proximity filter, and given the same radial argument undoes the curvature to the wavefront that had been applied. In the context of loudspeaker decoding, the near-field compensation filter is intended to remove the wavefront add by the nearness of the loudspeakers. I.e., near-field compensation filter removes the curve added by the physical nearness of real monitors in the real world.
Parameters theta and phi supply the look direction. The angle argument continuously transforms the image between:
The term radial beamforming is used to describe this soundfield operation. With radial beamforming the soundfield can be decomposed and recomposed as spherical waves, at whatever radius we choose.
It could be argued that the greatest innovation in Daniel's reframing of Ambisonics in a higher order context is the translation of the basic wave to a radius other than infinity.
If we'd like to think in a real world way, this is equivalent to pre-filtering a soundfield with the near-field compensation filter in anticipation of decoding to loudspeakers located at a pre-determined radius. This radius is the reference radius. We can view this as the anticipated loudspeakers finishing off the synthesis of the curve of the encoded waves by physically adding the remaining curve.
This is all good, but the true genius is the inclusion of a the near-field effect control filter, which combines the near-field compensation and proximity filter into a single block. The arrangement is as illustrated above, but without the inclusion of focus. Also, instead of having a single distance argument, there are two, one for each filter. Doing so makes it very easy to translate the reference radius. In other words, we can move where basic waves are encoded, which easily facilitates radial beamforming.
If we prefer thinking in terms of virtual loudspeakers, changing the reference radius corresponds to moving the virtual loudspeakers. This then corresponds to moving the soundfield sampling radius when it comes to decomposition and recomposition.
As part of the ATK's HOA toolset we have three principal filters tasked with the near-field effect.
Each of these has a distinct role:
Signal: *hoaDist is the associated FIR kernel designer.
Note, an associated FIR kernel designer is not provided.3
Signal: *hoaCtrl is the associated FIR kernel designer.
E.g., a planewave in NFC-HOA is not a basic wave. Conversly, complex coefficients are required to encode and synthesize a planewave.
Unlike their FOA equivalents, HoaNFDist and HoaNFProx do not have an exposed distance argument. By default, the distance argument is set internally to the ATK's reference radius for HOA, 1.5 meters.5 Doing so enforces the ATK's NFE encoding convention.
HoaNFCtrl has two arguments, encoding radius and decoding radius, which allows comprehensive control of the near-field effect in HOA.
We'll review some examples, below.
Two examples intended to offer insight into what encoded spherical waves look like with respect to signal phase and gain.
For this first example we'll encode a travelling wave. The three example radii all return spherical waves. One of these, encoded at 1.5 meters, is a basic wave.
Observe this in the scope.
By sampling a soundfield at the radius a spherical wave was originally encoded, we can recover the original source.
This is called radial soundfield sampling. We look into the soundfield at a specific radius.
The look direction of the beamformer, HoaDecodeDirection, is slowly moving back and forth. This movement is what is responsible for the varing gain of the returned beam.
Beaming and nulling transforms are spatial bandpass and bandreject filters. Instead of operating in the frequency domain, we're operating in the spatial domain.
Given the same beamshape, the beam summed with a corresponding null will return the original soundfield.
Used in this way, these two transforms allow us to easily process different parts of the soundfield in different ways. E.g., the null could be lowpass filtered and then remixed with the beam.
Encode six sinusoids on the axes, then sample the soundfield with a single beam.
The beam is reencoded, so we're auditioning a virtual speaker at the beam sampling radius, which can be varied. We'll need a decoder to audition.
This is like spatially bandpass filtering the soundfield.
Similar to Beamform with HoaBeam, but this time beaming with a static matrix.
To beam at another radius, we'd have to use the technique illustrated below.
Same test as above, but we form a null, instead. We are spatially rejecting part of the soundfield.
The Near-Field Effect Control filter (NFE-C), HoaNFCtrl has a wide number of uses in HOA. Here are a few important examples.
Radial encoding followed by decoding with loudspeaker near-field compensation.
When the real loudspeaker radius doesn't match the reference radius, we need to use HoaNFCtrl to reset the radial encoding.
We can view this as HoaNFCtrl finishing the radial part of the panning law, to match our actual loudspeaker array.
Here we synthesize a soundfield that is diffuse at a specified encoding radius.6
Translate from source radius to target radius. A very useful trick!
The use of two HoaNFCtrl transformers offers the possibility of modulation at a given radius.
The soundfield is decomposed into a collection of samples at a certain radius. These are then modulated. The soundfield is re-encoded, and samples are returned to their original radius.
If we wish to granulate at a radius other than the reference radius, for instance, this example illustrates how to do so.
If you haven't already, do review Ambisonic Format Exchange.