SOFA specifications

Specifications

• SOFA 1.0 is reflected by the AES69-2015 standard. It mostly corresponds to SOFA 0.6, which specs can be downloaded here. A document with SOFA 1.0 specs is under preparation.

Older specs:

• Version 0.5: Download specifications
• Version 0.4: Discussion on the specifications (closed)
• Version 0.3: Download specifications
• Version 0.2: Specifications
• Version 0.1: Specifications as presented at the AES Convention 2013 in Rom

Coordinate system

Data Types

FIR (SOFA 1.0)

For storing impulse responses.

Note: Delay is mandatory (set to 0 if not used).

Name	Default	Flags	Dimensions	Type	Comment
GLOBAL:DataType	FIR	rm		attribute
Data.IR	0	m	mRn	double	Impulse responses
Data.SamplingRate	48000	m	I	double	Sampling rate of the samples in Data.IR
Data.SamplingRate:Units	hertz	m		attribute	Unit of the sampling rate
Data.Delay	0	m	IR, MR	double	Additional delay of each IR (always in samples, i.e. units of N)

TF (SOFA 1.0)

Useful to describe a transfer function by a sparse number of frequencies. The guys from BEM simulations like it.

Note: the dimensional variable N is mandatory, it must be of dimension N, and must provide the frequency values.

Name	Default	Flags	Dimensions	Type	Comment
GLOBAL:DataType	TF	rm		attribute
Data.Real	0	m	mRn	double	The real part of the complex spectrum
Data.Imag	0	m	MRN	double	The imaginary part of the complex spectrum
N	0	m	N	double	Frequency values
N_LongName	frequency			attribute
N_Units	hertz	m		attribute	Unit of the values given in N

FIRE (proposed)

FIRE is based on FIR and is intended for storing impulse responses which depend on the emitter (E).

Note: Delay is mandatory (set to 0 if not used).

Name	Default	Flags	Dimensions	Type	Comment
GLOBAL:DataType	FIRE	rm		attribute
Data.IR	0	m	mREn	double	Impulse responses
Data.SamplingRate	48000	m	I	double	Sampling rate of the samples in Data.IR
Data.SamplingRate:Units	hertz	m		attribute	Unit of the sampling rate
Data.Delay	0	m	IRE, MRE	double	Additional delay of each IR (always in samples, i.e. units of N)

SOS (proposed)

This DataType stores a filter as a broadband delay and an arbitrary number of second order sections (SOSs).

The transfer function H(z) of a filter can be described as:

[math]\displaystyle{ H(z) = \frac{B_1(z)}{A_1(z)} \cdot \frac{B_2(z)}{A_2(z)} \cdot ... \cdot \frac{B_p(z)}{A_p(z)} }[/math]

where [math]\displaystyle{ p }[/math] is the number of second order sections, [math]\displaystyle{ A(z) }[/math] is denominator representing the poles of a filter, and [math]\displaystyle{ B(z) }[/math] is numerator representing the zeros of a filter. Then, each SOS can be described as:

[math]\displaystyle{ B_i(z) = b_{i,0} + b_{i,1} z^{-1} + b_{i,2} z^{-2} }[/math]

[math]\displaystyle{ A_i(z) = a_{i,0} + a_{i,1} z^{-1} + a_{i,2} z^{-2} }[/math]

Note that usually, [math]\displaystyle{ A_i(z) }[/math] is normalized such that [math]\displaystyle{ a_{i,0} = 1 }[/math].

Thus, in the DataType SOS, a filter is represented by three mandatory variables:

• Data.SamplingRate: sampling rate used to describe the filter.
• Data.Delay: broadband delay (in samples resulting from SamplingRate). Note: Use Delay of zero when not used.used).
• Data.SOS: list of coefficients of all SOSs.
  • Size: Data.SOS has the size of [ M R N ] with N as the total number of coefficients, thus an integer multiple of 6 corresponding to [math]\displaystyle{ 6p }[/math].
  • Format of the list: Along the dimension N, the list goes like: [math]\displaystyle{ [ b_{1,0}\ b_{1,1}\ b_{1,2}\ a_{1,0}\ a_{1,1}\ a_{1,2}\ b_{2,0}\ b_{2,1}\ b_{2,2}\ a_{2,0}\ a_{2,1}\ a_{2,2}\ ... b_{p,0}\ b_{p,1}\ b_{p,2}\ a_{p,0}\ a{p,1}\ a_{p,2} ] }[/math] which corresponds to [math]\displaystyle{ [ B_1(z)\ A_1(z)\ B_2(z)\ A_2(z)\ ... B_p(z)\ A_p(z) ] }[/math]

Name	Default	Flags	Dimensions	Type	Comment
Data.SOS	permute([0 0 0 1 0 0],[3 1 2])	m	mRn	double	Filter coefficients as SOS coefficients.
Data.SamplingRate	48000	m	I	double	Sampling rate of the coefficients in Data.SOS and the delay in Data.Delay
Data.SamplingRate:Units	hertz	m		attribute	Unit of the sampling rate
Data.Delay	0	m	MR	double	Broadband delay (in samples resulting from SamplingRate)