Magnitude Fourier transform lowpass, highpass, or bandpass

[Dustinsfl]

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]

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

$\chi$ $\sigma$

 

[I like Serena]

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.

 

[Dustinsfl]

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?

 

[I like Serena]

Can you provide an example transfer function for a bandpass?

For instance
$$H(s) = \frac{s}{(s-1)(s-100)}$$
bodeplot s/((s-1)(s-100)) - Wolfram|Alpha Results

 

[Dustinsfl]

For instance
$$H(s) = \frac{s}{(s-1)(s-100)}$$
bodeplot s/((s-1)(s-100)) - Wolfram|Alpha Results

So if the numerator was \(s^2\), we would have highpass correct?

 

[I like Serena]

So if the numerator was \(s^2\), we would have highpass correct?

Yes.