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Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics. |
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Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics. |
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In Reply to: RE: Long-term DBT example posted by morricab on April 29, 2008 at 04:13:50:
"For myself, using Keith Howard's software was enlightening in that by adding quite low levels of harmonic distortion (obviously I could not add noise and other aspects of the amplifiers I was "modeling") I could hear differences and formed preferences. If you could make the model frequency dependent it would be even more interesting."
Unfortunately, when frequency dependence is combined with nonlinearity, a formal mathematical treatment is pretty darned intractable. In the case of Keith's software, he's modeling a "memoryless" system. For such a system, the output at time, say, t0 is dependent only on the nonlinear transfer characteristic and the value of the input at time t0. But for systems with frequency-dependent behavior, the output at time t0 depends not only on the input at time t0, but also the history of the input prior to time t0.
Mathematically, combining nonlinearity with frequency dependence involves the dreaded Volterra series expansion. In that formula, the first term in the summation is a single integral, the second a double integral, the third a triple integral, and so on. So if you wish to model, say, 9th order distortion with frequency dependence, this involves the computation of a 9-dimensional integral. But before you evaluate that integral, it's necessary to determine the function you must integrate - the so-called Volterra kernel (of 9th order in this case). I have never done this, but it involves fitting this 9-dimensional function to the data of the device you're trying to model. Of course, one must also determine the 8th-order, 7th-order, etc. kernels and their corresponding integrals (down to order 1) to finish it all up.
The Volterra series ends up being of mostly theoretical interest. So a purely numerical approach is probably called for. I think Rick mentioned below that some SPICE simulators allow specifying the circuit input as a WAV file. I have messed around with this a bit in LTspice and found the simulations to take a very long time even with quite simple circuits. The other thing that concerns me is Rick's statement that the simulator does linear interpolation between data points of the WAV file to determine the equivalent analog signal to be applied. If that is so, the frequency domain equivalent of that is a rather poor low-pass filter that may have audible rolloff at the high end of the audio band. However, all non-oversampling DACs have this problem and many people swear by them, so maybe it's a non-problem subjectively.
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Follow Ups
- RE: Long-term DBT example - andy_c 07:44:10 04/30/08 (0)
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