New answers tagged

2

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 ...


0

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.


5

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., $1/T$ ...


0

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


6

$z$ 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 $$ Y(z)=(a+ b z^{-1}) X(z)$$


-1

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


0

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 ...


0

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 ...


Top 50 recent answers are included