{"id":165801,"date":"2013-10-01T00:00:00","date_gmt":"2013-10-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/efficient-implementation-of-the-spectral-division-method-for-arbitrary-virtual-sound-fields\/"},"modified":"2020-06-04T18:09:03","modified_gmt":"2020-06-05T01:09:03","slug":"efficient-implementation-of-the-spectral-division-method-for-arbitrary-virtual-sound-fields","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/efficient-implementation-of-the-spectral-division-method-for-arbitrary-virtual-sound-fields\/","title":{"rendered":"Efficient Implementation of the Spectral Division Method for Arbitrary Virtual Sound Fields"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The Spectral Division Method is an analytic approach for sound field synthesis that determines the loudspeaker driving function in the wavenumber domain. Compact expressions for the driving function in time-frequency domain or in time domain can only be determined for a low number of special cases. Generally, the involved spatial Fourier transforms have to be evaluated numerically. We present a detailed description of the computational procedure and minimize the number of required computations by exploiting the following two aspects: 1) The interval for the spatial sampling of the virtual sound field can be selected for each time-frequency bin, whereby low time-frequency bins can be sampled more coarsely, and 2) the driving function only needs to be evaluated at the locations of the loudspeakers of a given array. The inverse spatial Fourier transform is therefore not required to be evaluated at all initial spatial sampling points but only at those locations that coincide with loudspeakers.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Spectral Division Method is an analytic approach for sound field synthesis that determines the loudspeaker driving function in the wavenumber domain. Compact expressions for the driving function in time-frequency domain or in time domain can only be determined for a low number of special cases. Generally, the involved spatial Fourier transforms have to be [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Proc. 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