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[SOLVED] Magnitude Fourier transform lowpass, highpass, or bandpass

dwsmith

Well-known member
Feb 1, 2012
1,673
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?
 

chisigma

Well-known member
Feb 13, 2012
1,704
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

$\chi$ $\sigma$
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,774
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.
 

dwsmith

Well-known member
Feb 1, 2012
1,673
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?
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,774