# Spat 6.0 7 Full Versionl

A collection of functions to create spatial weights matrix objects from polygon 'contiguities', from point patterns by distance and tessellations, for summarizing these objects, and for permitting their use in spatial data analysis, including regional aggregation by minimum spanning tree; a collection of tests for spatial 'autocorrelation', including global 'Morans I' and 'Gearys C' proposed by 'Cliff' and 'Ord' (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), 'Hubert/Mantel' general cross product statistic, Empirical Bayes estimates and 'Assunção/Reis' (1999) Index, 'Getis/Ord' G ('Getis' and 'Ord' 1992) and multicoloured join count statistics, 'APLE' ('Li 'et al.' ) , local 'Moran's I', 'Gearys C' ('Anselin' 1995) and 'Getis/Ord' G ('Ord' and 'Getis' 1995) , 'saddlepoint' approximations ('Tiefelsdorf' 2002) and exact tests for global and local 'Moran's I' ('Bivand et al.' 2009) and 'LOSH' local indicators of spatial heteroscedasticity ('Ord' and 'Getis') . The implementation of most of the measures is described in 'Bivand' and 'Wong' (2018) , with further extensions in 'Bivand' (2022) . From 'spdep' and 'spatialreg' versions >= 1.2-1, the model fitting functions previously present in this package are defunct in 'spdep' and may be found in 'spatialreg'.

## Spat 6.0 7 Full Versionl

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This attribute exposes a Python view of the root node in the cKDTreeobject. A full Python view of the kd-tree is created dynamicallyon the first access. This attribute allows you to create your ownquery functions in Python.

sparta_ambiBIN - A binaural ambisonic decoder (up to 7th order) with a built-in SOFA loader and head-tracking support via OSC messages. Includes: Least-Squares (LS), spatial re-sampling (SPR), time-alignment (TA), and magnitude least-squares (Mag-LS) decoding options.

sparta_array2sh - A microphone array spatial encoder (up to 7th order), with presets for several commercially available A-format and higher-order microphone arrays. The plug-in can also present objective evaluation metrics for the currently selected configuration.

sparta_dirass - A sound-field visualiser based on re-assigning the energy of beamformers. This re-assigment is based on DoA estimates extracted from "spatially-constrained" regions, which are centred around each beamformer look-direction.

sparta_sldoa - A frequency-dependent sound-field visualiser (up to 7th order), based on depicting the direction-of-arrival (DoA) estimates derived from spatially localised active-intensity vectors. The low frequency estimates are shown with blue icons, mid-frequencies with green, and high-frequencies with red.

The plug-in employs a dual decoding approach, whereby different decoder settings may be selected for the low and high frequencies; the cross-over frequency may be dictated by the user. Several ambisonic decoders have been integrated, including more perceptually motivated methods such as the All-Round Ambisonic Decoder (AllRAD) [1] and Energy-Preserving Ambisonic Decoder (EPAD) [2]. The max-rE weighting [1] may also be enabled for either decoder. Furthermore, in the case of non-ideal Ambisonic signals as input (i.e. those derived from physical/simulated microphone arrays), the decoding order may be specified for the appropriate frequency ranges; energy-preserving (EP) or amplitude-preserving (AP) normalisation is then used to maintain consistent loudness between different decoding orders. However, this feature may also be used creatively. For example, one can reduce the decoding order only for a certain frequency-range, thereby making the reproduction more spatially spread at these specific frequencies (due to the inherently lower spatial resolution when using lower-order Ambisonic signals for decoding).

A frequency-dependent Ambisonic dynamic range compressor (DRC). The gain factors are derived by analysing the omnidirectional component for each frequency band, which are then applied also to the higher-order components. The spatial properties of the original signals remains unchanged; although, your perception of them after decoding may change. The implementation also keeps track of the frequency-dependent gain factors for the omnidirectional component over time, which is then plotted on the user interface for visual feedback.

A bare-bones Ambisonic encoder which takes input signals (up to 64 channels) and encodes them into Ambisonic signals at specified directions. Essentially, these Ambisonic signals describe a synthetic sound-field, where the spatial resolution of this encoding is determined by the transform order. Several presets have been included for convenience (which allow for 22.x etc. audio to be encoded into 1-7th order Ambisonics, for example). The panning window is also fully mouse driven, and uses an equirectangular respresentation of the sphere to depict the azimuth and elevation angles of each source.

'Array2SH' spatially encodes spherical/cylindrical array signals into spherical harmonic signals (aka: Ambisonic or B-Format signals). The plug-in utilises analytical descriptors, which ascertain the frequency and order-dependent influence that the physical properties of the array have on the plane-waves arriving at its surface. The plug-in allows the user to specify: the array type (spherical or cylindrical), whether the array has an open or rigid enclosure, the radius of the array, the radius of the sensors (in cases where they protrude out from the array), the sensor coordinates (up to 64 channels), sensor directivity (omni-dipole-cardioid), the speed of sound, and the acoustical admittance of the array material (in the case of rigid arrays). The plug-in then determines the order-dependent equalisation curves that need to be imposed onto the initial spherical harmonic signals estimate, in order to remove the influence of the array itself. However, especially for higher-orders, this generally results in a large amplification of the low frequencies (including the sensor noise at these frequencies that accompanies it); therefore, four different regularisation approaches have been integrated into the plug-in, which allow the user to make a compromise between noise amplification and transform accuracy. These target and regularised equalisation curves are depicted on the user interface to provide visual feedback.

The plug-in also allows the user to 'Analyse' the spatial encoding performance using objective measures described in [8,10], namely: the spatial correlation and the level difference. Here, the encoding matrices are applied to a simulated array, which is described by multichannel transfer functions of plane waves for 812 points on the surface of the spherical/cylindrical array. The resulting encoded array responses should ideally resemble spherical harmonic functions at the grid points. The spatial correlation is then derived by comparing the patterns of these responses with the patterns of ideal spherical harmonics, where '1' means they are perfect, and '0' completely uncorrelated; the spatial aliasing frequency can therefore be observed for each order, as the point where the spatial correlation tends towards 0. The level difference is then the mean level difference over all directions (diffuse level difference) between the ideal and simulated components. One can observe that higher permitted amplification limits [Max Gain (dB)] will result in noisier signals; however, this will also result in a wider frequency range of useful spherical harmonic components at each order. This analysis is primarily based on code written for publication [10], which compared the performance of various regularisation approaches of encoding filters, based on both theoretical and measured array responses.

Note that this ability to balance the noise amplification with the accuracy of the spatial encoding (to better suit a given application) is very important, for example: the perceived fidelity of Ambisonic decoded audio can be rather poor if the noise amplification is set too high; therefore, typically a much lower amplification regularisation limit is used in Ambisonics reproduction when compared to sound-field visualisation algorithms, or beamformers that employ appropriate post-filtering.

A spatially localised direction-of-arrival (DoA) estimator. The plug-in first uses VBAP beam patterns (for directions that are uniformly distributed on the surface of a shere) to obtain spatially-biased zeroth and first-order signals, which are subsequently used for the active-intensity vector estimation; therefore, allowing for DoA estimation in several spatially-constrained sectors for each sub-band. The low frequency estimates are then depicted with blue icons, mid-frequencies with green, and high-frequencies with red. The size of the icon and its opacity correspond to the energy of the sector, which are normalised and scaled in ascending order for each frequency band. The plug-in employs two times as many sectors as the analysis order, with the exception of the first-order analysis, which uses the traditional active-intensity approach. The analysis order per frequency band is user definable, as is the frequency range at which to analyse. This approach to sound-field visualisation/DoA estimation represents a much more computationally efficient option, when compared to the algorithms that are integrated into the 'Powermap' plug-in, for instance. The plug-in also allows the user to place real-time video footage behind the activity-map, in order to create a make-shift acoustic camera. 350c69d7ab