On Sun, Sep 26, 2010 at 4:12 AM, <fons@xxxxxxxxxxxxxxx> wrote: > The reason is that step (5), multiplication in the > frequency domain, is equivalent to convolution in the > time domain. And the convolution of two signals of N > samples (T1 and T2) has lenght 2*N-1. This means that > this result is wrapped around in step (6) since the > inverse FFT produces only N samples. Doesn't this also apply to basic digital "mixing" of audio signals -- and appears to be the fundamental difference in both sound and algorithm between "analog summing bus", where each digital output in the mix is sent to an independent DAC, getting full 24 bit resolution per and full samplerate per signal, and then summing that in the analog domain. This effectively multiplies the bitrates of all the sources and is the equivalent to the "convolution of C-number of signals of N samples (T1 and T2) has length C*N-1" And yet, traditional digital mixing, would mix C-number of signals of N samples each into N samples. Which is a vastly different quantity of information than would be conveyed via an analog summing bus which would be C*N samples. When is it valid, and not valid, for so much information to disappear in the process of performing an analog-domain task in the digital realm? In fact, both sampling and mixing are both "multiplication in time" operations, -- per http://www.analog.com/static/imported-files/application_notes/5847948184484445938457260443675626756108420567021238941550065879349464383423509029308534504114752208671024345AN_756_0.pdf ///// ///// ///// ///// ///// ///// "As stated previously, the sampling process is a multi- plication process in time and, therefore, a convolution process in the frequency domain. While it is clear that a mixer multiplies two analog signals in the time domain with the results being the convolution of these two in the frequency domain, it may be less clear that the sampling process is also a multiplication in time process." ///// ///// ///// ///// ///// ///// There's also no reason why a digital equivalent of an analog summing bus -- which preserves or allows direct control over, and optimization of both bit-depth preservation, and also sample-rate multiplication, on a per-source basis. This would allow the sound engineer to design-in the desired tradeoffs in resulting sound, sample-rate, bit depth, etc -- on a per-signal basis. Since it doesn't make sense to give the exact same treatment to synthesized atmosperics layered on top of multi-miked results (where you might want to put a premium on the phase-relationships between microphones, while preserving bit depths would just pickup noise with higher fidelity). Perhaps, products like the following appear to be heading in that direction: http://www.slatedigital.com/vcc.php ... and of course this is a long contentious topic ( http://emusician.com/mag/emusic_sum_tracks/ ), which IMHO is clarified by considering a convolution and information-theoretic-perspective to the problem of mixing signals in a digital system .... -- Niels http://nielsmayer.com _______________________________________________ Linux-audio-user mailing list Linux-audio-user@xxxxxxxxxxxxxxxxxxxx http://lists.linuxaudio.org/listinfo/linux-audio-user
