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I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles?

Secondly, the theory says that a system is stable when poles are in left s-plane and, thus, decay in time. But, wait. Does'n "pole" mean the infinite response -- the growth in time?

Finally, is it right question in DSP? IMO, D stands for digital whereas s-domain is analog. I do not find s-plane or Laplace transform tags to label my post.

update Thanks for the answers. It seems that I have got it except the one minor but fundamental thing -- the relationship of poles (and zeroes) with frequency. Basically, why are eigenvalues (or, how do you call the $s$ operator/variable) related with frequency? It should be somehow related with exponential growth and Laplace transform. I quite understand that poles happen to be eigenvalues (especially for discrete recurrences). But, how is this related with frequency?

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles?

Secondly, the theory says that a system is stable when poles are in left s-plane and, thus, decay in time. But, wait. Does'n "pole" mean the infinite response -- the growth in time?

Finally, is it right question in DSP? IMO, D stands for digital whereas s-domain is analog. I do not find s-plane or Laplace transform tags to label my post.

update Thanks for the answers. It seems that I have got it except the one minor but fundamental thing -- the relationship of poles (and zeroes) with frequency. Basically, why are eigenvalues (or, how do you call the $s$ operator/variable) related with frequency? It should be somehow related with exponential growth and Laplace transform. I quite understand that poles happen to be eigenvalues (especially for discrete recurrences). But, how is this related with frequency?

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles?

Secondly, the theory says that a system is stable when poles are in left s-plane and, thus, decay in time. But, wait. Does'n "pole" mean the infinite response -- the growth in time?

Finally, is it right question in DSP? IMO, D stands for digital whereas s-domain is analog. I do not find s-plane or Laplace transform tags to label my post.

update Thanks for the answers. It seems that I have got it except the one minor but fundamental thing -- the relationship of poles (and zeroes) with frequency. Basically, why are eigenvalues (or, how do you call the $s$ operator/variable) related with frequency? It should be somehow related with exponential growth and Laplace transform.

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles?

Secondly, the theory says that a system is stable when poles are in left s-plane and, thus, decay in time. But, wait. Does'n "pole" mean the infinite response -- the growth in time?

Finally, is it right question in DSP? IMO, D stands for digital whereas s-domain is analog. I do not find s-plane or Laplace transform tags to label my post.

update Thanks for the answers. It seems that I have got it except the one minor but fundamental thing -- the relationship of poles (and zeroes) with frequency. Basically, why are eigenvalues (or, how do you call the $s$ operator/variable) related with frequency? It should be somehow related with exponential growth and Laplace transform. I quite understand that poles happen to be eigenvalues (especially for discrete recurrences). But, how is this related with frequency?