Editing Head-related transfer function (section)

=== HRTF magnitude synthesis ===
We solve the above minimization problem using [[least absolute shrinkage and selection operator]]. We assume that the HRTFs are represented by the same relation as the anthropometric features.<ref name="Bilinski"/> Therefore, once we learn the sparse vector β from the anthropometric features, we directly apply it to the HRTF tensor data and the subject's HRTF values H{{sup|'}} given by:

: <math> H'_{d,k} = \sum_{n=1}^N \beta_n H_{n,d,k} </math>

where The HRTFs for each subject are described by a tensor of size ''D''&nbsp;×&nbsp;''K'', where ''D'' is the number of HRTF directions and ''K'' is the number of frequency bins. All ''H''{{sub|''n'',''d'',''k''}} corresponds to all the HRTFs of the training set are stacked in a new tensor ''H'' ∈ '''''R'''''{{sup|''N''×''D''×''K''}}, so the value H{{sub|n,d,k}} corresponds to the ''k''-th frequency bin for ''d''-th HRTF direction of the ''n''-th person. Also ''H''{{sup|'}}{{sub|''d'',''k''}} corresponds to ''k''-th frequency for every d-th HRTF direction of the synthesized HRTF.