Multichannel recordings are usually performed by means of microphone arrays. In many cases "sparse" and discrete microphone arrays are used, where each microphone is employed for capturing one of the channels, which in turn is routed to one loudspeaker. However, also the usage of "dense" microphone arrays has a long history, dating back to the first MS-matrixed microphones setups and passing through the whole Ambisonics saga. A dense microphone array is employed differently from a sparse array: each channel is obtained by a combination of the signals coming from all the capsules, by means of different matrixing and filtering approaches. And similarly, each loudspeaker feed results from a re-matrixing of all the transmitted channels. This paper is the third of a series: in the previous two [1,2] a numerical method for computing a matrix of FIR filter was employed for processing the microphone signals (encoding, [1]) and for computing the speaker feeds (decoding, [2]). In this third paper, the same numerical approach is extended to intermediate processing (rotation, zooming, stretching, spatial equalization, etc.): hence we have now a general meta-theory, providing a unique framework capable of processing the signals for any kind of dense microphone array, providing any kind of intermediate manipulation, and finally projecting the signal to every kind of loudspeaker arrays. The same framework can operate according to different standards and formats, including A-format (raw signals), B-format (High Order Ambisonics signals), G-format (speaker feeds) and P-format (Spatial PCM Sampling signals), and can be used for converting freely among them. Experimental results are presented, including "traditional" tetrahedral probes, a commercial spherical microphone array, and two newly-developed massive microphone arrays developed by the authors, a cylindrical and a planar array, both incorporating 32 high-quality condenser microphones and a panoramic video camera.
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