Magnitude Fourier transform lowpass, highpass, or bandpass

In summary: In general, the type of filter is determined by the highest power of s in the numerator. If it is 1, it is a lowpass filter, if it is 2, it is a highpass filter, and if it is 0, it is a bandpass filter.
  • #1
Dustinsfl
2,281
5
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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  • #2
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

$\chi$ $\sigma$
 
  • #3
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.
 
  • #4
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?
 
  • #7
dwsmith said:
So if the numerator was \(s^2\), we would have highpass correct?

Yes.
 

FAQ: Magnitude Fourier transform lowpass, highpass, or bandpass

What is a Fourier transform?

A Fourier transform is a mathematical operation that breaks down a signal into its individual frequency components. It is often used in signal processing and analysis to understand the frequency content of a signal.

What is the significance of magnitude in a Fourier transform?

The magnitude in a Fourier transform represents the strength of each frequency component in a signal. It can help identify dominant frequencies and filter out unwanted noise.

How does a lowpass Fourier transform work?

A lowpass Fourier transform filters out high-frequency components in a signal and preserves only the low-frequency components. This is useful for removing noise or smoothing out a signal.

What is the difference between a highpass and bandpass Fourier transform?

A highpass Fourier transform filters out low-frequency components and preserves high-frequency components, while a bandpass Fourier transform preserves a specific range of frequencies in a signal.

In what applications are Fourier transforms commonly used?

Fourier transforms are commonly used in fields such as image and audio processing, communications, and data analysis. They are also used in scientific research and engineering to analyze signals and extract useful information.

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