How to determine type of Filter from pole zero plot?

In summary, the conversation discussed the transfer function and Bode plot for a system with two poles and two zeros. The Bode plot showed that for higher frequencies, the magnitude is amplified and the system behaves as a high pass filter. The analysis also noted that the second pole break occurs at a higher frequency than the other pole's or the zeros'. Overall, the conclusion was that the system behaves as a high pass filter.
  • #1
rudra
14
0
Imp.jpg

According to me Transfer function will be G(s)= (s2+2ζωnn2)/((s+p1)(s+p2))

I assume from the given plot that ωn < p1 and ωn < p2

Then the bode plot will be as per me like following :
Imp.jpg
From the Bode plot we can see for higher freq magnitude is amplified . So it will be High pass Filter.

That's my analysis. If I am wrong please correct me.
 
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  • #2
The imaginary part of the zeros and the real part of the two poles are pretty close together in frequency, which makes it difficult to tell whether the zeros' 40 dB/decade rise occurs before or after the pole drops, but the second pole break definitely occurs at a higher frequency than either the other pole's or that of the zeros so I'd say your conclusion is as correct as anyone's.
 
  • #3
Thank you rude man. I needed someone to support my answer.
 

1. How do I determine the type of filter from a pole-zero plot?

To determine the type of filter from a pole-zero plot, you need to look at the location of the poles and zeros. For a low-pass filter, the poles will be located in the left half-plane and the zeros will be located in the right half-plane. For a high-pass filter, the poles and zeros will be reversed, with the poles in the right half-plane and the zeros in the left half-plane. Bandpass and bandstop filters will have a combination of poles and zeros in both the left and right half-planes.

2. What do the poles and zeros represent in a filter's pole-zero plot?

The poles and zeros in a filter's pole-zero plot represent the frequency response of the filter. The poles represent the frequencies at which the filter attenuates the input signal, while the zeros represent the frequencies at which the filter does not attenuate the input signal. The location of the poles and zeros also determines the type of filter.

3. How can I determine the cutoff frequency from a filter's pole-zero plot?

The cutoff frequency of a filter can be determined by looking at the distance between the poles and zeros in the pole-zero plot. For a low-pass filter, the cutoff frequency is the frequency at which the magnitude response drops to -3dB (half power) compared to the passband. For a high-pass filter, the cutoff frequency is the frequency at which the magnitude response rises to -3dB. For bandpass and bandstop filters, the cutoff frequencies can be determined by looking at the distance between the poles and zeros in the passband and stopband, respectively.

4. What is the significance of the slope of the magnitude response in a filter's pole-zero plot?

The slope of the magnitude response in a filter's pole-zero plot represents the filter's order. The higher the order of the filter, the steeper the slope will be. This means that the filter will have a more rapid transition between the passband and stopband, making it more effective at attenuating unwanted frequencies.

5. Can I determine the phase response of a filter from its pole-zero plot?

Yes, you can determine the phase response of a filter from its pole-zero plot. The phase response can be determined by looking at the angles of the poles and zeros in the complex plane. The phase response will change depending on the type of filter and the location of the poles and zeros. For example, a low-pass filter will have a phase response that starts at 0 degrees in the passband and decreases to -90 degrees in the stopband.

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