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Olin Lathrop
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You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than solely looking at zeros. For one thing, a zero can be used to offset the affects of a pole, or the other way around.

Each has the opposite affect on the response to frequency and phase shift.

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I see there is some discussion about the concept of poles can be used to offset the effects of zeros. As Willpower points out, zeros don't directly cancel poles, and I fixed my statement above to not say so. However, some combinations of poles and zeros can, over some range, offset the affects of other poles and zeros.

Consider the transfer function of old vinyl records. The information in the grooves was deliberately high-pass filtered, then the inverse of this filter applied in the playback circuit to ideally get a flat frequency response from original signal to final reproduced signal. There were various poles and zeros in the system along the way, some unavoidable due to the process, others deliberately introduce, and other poles and zeros applied to offset them. In this case, the ideal net result was a flat transfer function over the audio range. For more information on this, look up something called the RIAA equalization curve.

You would get a very wrong idea of the overall system by looking only at the poles and not the zeros, or just the poles and zeros in just the playback amp, for example.

You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than solely looking at zeros. For one thing, a zero can be used to offset the affects of a pole, or the other way around.

Each has the opposite affect on the response to frequency and phase shift.

You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than solely looking at zeros. For one thing, a zero can be used to offset the affects of a pole, or the other way around.

Each has the opposite affect on the response to frequency and phase shift.

Added

I see there is some discussion about the concept of poles can be used to offset the effects of zeros. As Willpower points out, zeros don't directly cancel poles, and I fixed my statement above to not say so. However, some combinations of poles and zeros can, over some range, offset the affects of other poles and zeros.

Consider the transfer function of old vinyl records. The information in the grooves was deliberately high-pass filtered, then the inverse of this filter applied in the playback circuit to ideally get a flat frequency response from original signal to final reproduced signal. There were various poles and zeros in the system along the way, some unavoidable due to the process, others deliberately introduce, and other poles and zeros applied to offset them. In this case, the ideal net result was a flat transfer function over the audio range. For more information on this, look up something called the RIAA equalization curve.

You would get a very wrong idea of the overall system by looking only at the poles and not the zeros, or just the poles and zeros in just the playback amp, for example.

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Olin Lathrop
  • 11.4k
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You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than solely looking at zeros. For one thing, a zero can be used to canceloffset the affectaffects of a pole, or the other way around.

Each has the opposite affect on the response to frequency and phase shift.

You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than solely looking at zeros. For one thing, a zero can be used to cancel the affect of a pole, or the other way around.

Each has the opposite affect on the response to frequency and phase shift.

You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than solely looking at zeros. For one thing, a zero can be used to offset the affects of a pole, or the other way around.

Each has the opposite affect on the response to frequency and phase shift.

Source Link
Olin Lathrop
  • 11.4k
  • 1
  • 22
  • 36

You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than solely looking at zeros. For one thing, a zero can be used to cancel the affect of a pole, or the other way around.

Each has the opposite affect on the response to frequency and phase shift.