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R

Is a "z" missing in the numerator of Equation (5)?

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M

The initial -90° is due to the pole at zero not the zero.

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Should the limit for the first example be -2 not infinity? If you cancel the two s terms first one gets -2, also L'Hopital says the limit is -2. However, if one takes the limit from the positive direction it is infinity.

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In the article titled RELATIONSHIP BETWEEN S/Z PLANES AND TIME DOMAIN, there is a false claim that a real negative z-plane pole cannot be represented by a single s-plane pole. It's actually a matter of the interpolation method used when converting from Discrete to Continuous (z to s). This claim arose from the output of MATLab's d2c() using its default interpolation method ZOH, as shown slightly above section #7 in the article. If the Tustin (Bilinear Transform) is used, then the order of the system will be unchanged. All of this is detailed on Mathwork's documentation https://www.mathworks.com/h...

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S

An "s" is missing in the denominators of Y(s)=...

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Hi I have the same question as someone had here. the final result dont quiet match. You wanted to have y[k] = a y[k-1] + x[k]*[1-a]; however you get y[k] = a y[k-1] + x[k-1]*[1-a]. In other words you have x[k] in the first equation, but have x[k-1] in the final equation. why is that? can you please explain? Maybe I am missing something.

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M

Hi, I was also really bothered by the same issue - happy that I discovered this page, to see I'm not the only one. One thing I do want to mention though, is that despite the difference in the delay between the correct form and the form presented by the author, the magnitudes of both forms are similar (the difference is only in the phase). So what he states about the magnitude and corner frequency of the presented form equally applies to the original form of the filter.

Nevertheless, I did expect at least a note from the author or something, and not just ignoring this difference.

And now to the main question, if the presented continuous function, when transformed to discrete doesn't result in the desired discrete function, what should be the correct form of continuous function that represents this filter? Is there even one?

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S

Thanks for the article which is helpful - quite hard to find material on s to z plane mapping. suggestions: (1) add description of primary strip where you state "There are many values of "s" for each "z"," (2) not sure what you mean by "The dominant feature of the plane is the unit circle" ... you mean the stable region? (3) "Frequency is expressed as the distance from the origin in the s-plane." ... no - s-plane frequency is the imaginary component - think you mean natural frequency (4) " the maximum frequency is limited and defined as two signal samples per sampling period" - this is a key point - it would be good if you could if you could elaborate i.e. Nyquist says a MINIMUM of 2 samples so not sure that Nyquist alone explains this point (5) not a fan of using stairs() to plot discrete data - think you should only plot the discrete-time points

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N

Hi. shouldn't it be x[k] at the final result and not x[k-1], to match with y[k]? this is what i've seen pretty much everywhere online

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I had the same question. I understood everything except the part where he ends up with x[k-1] when it should be x[k] to match original question. Did you figure it out?

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Thank you. The article is being very helpful to me.

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M

Very very poor explanations... you tell that you will show the relationship between a and w0 and ... nothing ! which value is a ? which is the relation ?

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T

Hi Mel, thank for your comment - the article has been updated. The relationship between the discrete-time and continuous-time domains should be clearer now.

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Hi Tomas Sadilek, can you please answer my question above of why you ended up with x[k-1] in the last equation but the first equation you have x[k]. Can you explain why you have an extra delay. the equations dont match.

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