MHB Magnitude Fourier transform lowpass, highpass, or bandpass

AI Thread Summary
The discussion focuses on determining the type of filter represented by the Laplace transform \( H_1(s) = \frac{1}{(s + 1)(s + 3)} \) using geometric evaluation from its pole-zero plot. Participants highlight that a Bode plot is a standard method for analyzing the filter characteristics, indicating that a lowpass filter has a high value at \( H(0) \) and decreases with increasing \( s \), while a highpass filter starts low and increases. The conversation also touches on bandpass filters, which initially increase and then decrease, and an example of a bandpass transfer function is provided. The importance of the numerator's degree in determining filter type is emphasized, with \( s^2 \) indicating a highpass filter. Overall, the thread seeks clarity on applying these concepts to analyze the given Laplace transform.
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Using geometric evaluation of the magnitude of the Fourier transform from the corresponding pole-zero plot, determine, for each of the following Laplace transforms, whether the magnitude of the corresponding Fourier transform is approximately lowpass, highpass, or bandpass.
\[
H_1(s) = \frac{1}{(s + 1)(s + 3)},\qquad \text{Re} \ \{s\} > -1
\]
I have no idea what to do for this. Can someone explain how to do a problem like this?
 
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dwsmith said:
Using geometric evaluation of the magnitude of the Fourier transform from the corresponding pole-zero plot, determine, for each of the following Laplace transforms, whether the magnitude of the corresponding Fourier transform is approximately lowpass, highpass, or bandpass.
\[
H_1(s) = \frac{1}{(s + 1)(s + 3)},\qquad \text{Re} \ \{s\} > -1
\]
I have no idea what to do for this. Can someone explain how to do a problem like this?

In case of highpass or band pass is $\displaystyle H_{1} (0) = 0$ and that isn't verified in this case. The only possible alternative is then...

Kind regards

$\chi$ $\sigma$
 
dwsmith said:
Using geometric evaluation of the magnitude of the Fourier transform from the corresponding pole-zero plot, determine, for each of the following Laplace transforms, whether the magnitude of the corresponding Fourier transform is approximately lowpass, highpass, or bandpass.
\[
H_1(s) = \frac{1}{(s + 1)(s + 3)},\qquad \text{Re} \ \{s\} > -1
\]
I have no idea what to do for this. Can someone explain how to do a problem like this?

The standard way to analyze such a function is a Bode plot.
It will tell you what type of filter it is and also what its characteristics are.

More specifically, a low pass filter has high H(0) and goes down when s increases.
A high pass filter has low H(0) and increases with s.
A band filter first increases from s=0 and up and then decreases again.
 
I like Serena said:
The standard way to analyze such a function is a Bode plot.
It will tell you what type of filter it is and also what its characteristics are.

More specifically, a low pass filter has high H(0) and goes down when s increases.
A high pass filter has low H(0) and increases with s.
An band filter first increases from s=0 and up and then decreases again.

Can you provide an example transfer function for a bandpass?
 
dwsmith said:
So if the numerator was \(s^2\), we would have highpass correct?

Yes.
 

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