Hi Sven,

I assume there is a sampling operation between the ct integrator and dt differentiator. I suspect you also have a zero-order-hold somewhere in the path. The zero-order-hold will give you a sinc frequency response. As for ct integrator and dt differentiator, I come back to the sampler between the two. The sampler will convert the ct integrator into a dt version, with a z-domain transfer function of 1/(1-z^-1). As I see it, that transfer function cancels with the dt differentiation transfer function, which is why I suspect you have a ZOH somehere in the path since your simulations exhibit a sinc response.

In summary, I think you can combine dt and ct transfer functions but you must use the samplers that follow the ct blocks to convert the ct transfer functions to dt transfer functions. If you have dt blocks preceding ct blocks, you usually use a ZOH to convert dt blocks to ct blocks.

-Jess

-Jess

Hi Sven,

Do you actually have a sampler between the ct and dt blocks? If so, I don't think the bilinear transformation would be appropriate. The bilinear transformation is used when you want to build a dt equivalent of a ct filter. There are a few different transformations you can use to design the dt filter. However, when you sample the output of an analog filter, you do not have a choice. The sampling operation involves multiplication by a train of Dirac delta functions. To compute the dt transform of the sampled signal, you must convolve the analog Laplace transform with the Laplace transform of the delta sequence. You end up with a contour integral that can be closed to the left or the right. Closing to the right gives you an expression that explains aliasing. Closing to the left gives you another expression for the dt transform. For a ct integrator, the transform is 1/(1-Z^-1).

How are you simulating the system? If you are using an analog simulator, your output will be a staircase waveform, meaning that there is an implicit ZOH. When you apply an FFT that samples more than once between steps, you will see the filtering effects of the implicit ZOH.

-Jess