Why is the result of the step signal convoluted with the impulse response of a lowpass filter not equal to the stepresponse of the lowpass filter?

[Star Strider]

The Laplace transform of an impulse (delta function) is 1, not 1/s.

[timling]

Hi, Thanks for the quick answer

I thought modeling the impulsresponse of (1/s) is another way to get the step function in the time domain

And if you convolute the Stepfunction with the impulse response of the lowpass filter you would get the stepresponse of the lowpass filter

But it seems i got it to work like you said (replace the step with constant) and additionally i had to get rid of the impulse (also replace with constant):

[Star Strider]

My pleasure.

I’m glad you got it sorted.

Answer 1

[Honglei Chen]

You are mixing continuous and discrete in your model. For example, your impulse is discrete, your convolution is discrete, but your integrator is continuous. The following example used all discrete version and you can see the results match.

HTH

[timling]

Yes, but that is not the step response of a lowpass filter which it should be because you are convolving the impulse response of a lowpass filter with a step signal.

[Honglei Chen]

I just meant to show how can you match the two results.

[timling]

Yes, I did mix discrete and continous Systems. Thanks for pointing that out. For sure that is the reason why both examples i showed in the beginning don't match. But I still don't understand why the result in every cas is the step Response of a highpass filter.