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First choice : Convert the Laplace transform of your process to the Z-domain using the ZOH method as it models your DAC. In your case, your DAC is a PWM. Second choice : Work in the Laplace domain but take in account the delay due to your PWM, which should be T/2 where T is your PWM period. To model the delay, you can use the Padé approximation. I ...


I don't know why but I couldn't get the equations to output any audio when using the Euler method given. Maybe I screwed it up somehow or this is not the best place for that type of approximation. When I substituted $s=(2(z^{-1}−1))/(T(z^{-1}+1))$ it works perfectly. So problem solved either way. Thanks.


First of all, it's important to understand that there is no single best way to transform a continuous-time system to a discrete-time system. The method you're using is called backward Euler method, and it is defined by the mapping $$s\leftarrow\frac{1-z^{-1}}{T}\tag{1}$$ Note that in $(1)$ you scale by $1/T$, where $T$ is the sampling interval (i.e., $1/T$ ...


I don't understand much of this myself. Probably less than you. :) But I think something you're looking for is this: It provides basic substitution functions (if I am understanding correctly) for converting between the time, z, and laplace domains.


$z$ is interpreted as the time advance operator. $z^{-1}$ is the time delay operator. So for a difference equation like $$ y[n]=a x[n]+b x[n-1] $$ in the $z$ domain $$ Y(z)=(a+ b z^{-1}) X(z)$$


$z = e^{j\omega}$ is a convenient substitution for a complex valued function.


The answer was there is no need to incorporate sample rate at all. Since I am using the simple case where Hb(s) is a constant, I just had to multiply that against the summed samples and subtract the result from both delay lines. It works irrespective of sample rate. I tried it with sampling at 11 kHz and 96 kHz and it sounds the same. I don't really ...


I believe, mike, that the answer to your question is likely the Bilinear Transform. Make sure you identify the significant frequency (likely the resonant frequency of the LPF1 and LPF2 or $H_b(s)$ and apply prewarping to that frequency, so that the digital filter hits at the same place that the analog filter. Remember the transfer functions of the two ...

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