Low pass filter (arctan domain)

In summary, the discussion focused on understanding the domain and range of the arctan function in relation to calculating and displaying the phase characteristic. It was clarified that the value of the phase shift is the range of the function, not the domain, and that the phase shift for a single-pole LPF varies from 0 to -90 degrees. The shape of the phase response in the first plot was also discussed, with the conclusion that it may be misleading as it only shows half of the arctan function. The link provided was also found to be helpful in understanding the concept.
  • #1
TheGood
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Homework Statement


when I'm trying to calculate and show the graphic of the phase characteristic i don't understand why the domain range of the arctan function is [0,90] :


Homework Equations


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image392.gif



The Attempt at a Solution


shouldn't be the domain of arctan function between [-Pi/2,Pi/2]?
z_tri59.png
 
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  • #2
The value of the phase shift is the range of the function, not the domain. The domain is the input range to the function and the range is the output values of the function.

The phase shift for a single-pole LPF varies from 0 to -90 degrees, as shown in the diagram. It is 0 at low frequencies in the passband of the filter, and drops to -90 degrees past the cutoff of the LPF.
 
  • #3
I see that you've edited your post to add the red arctan curve. I think it may be the shape of the phase response in the first plot that is confusing you. I don't think it is plotted very well -- it make is look like the full arctan() curve, when it is really only half of it.

When ω = 0, you get the arctan(0) which is zero. As the frequency increases, you get half of the arctan() function, going negative because of the sign being negative.

Does that make more sense now?

http://www.electronics-tutorials.ws/filter/filter_2.html

.
 
  • #4
thank you, the link was helpful too!
 
  • #5


I can understand your confusion with the domain range of the arctan function. It is important to note that the domain of any function is dependent on the context in which it is being used. In the case of a low pass filter, the arctan function is used to calculate the phase characteristic. In this context, the input to the arctan function is the frequency, which is always a positive value. Therefore, the domain range of [0,90] is appropriate as it represents the phase angle in degrees for positive frequencies. However, if the arctan function is being used in a different context, such as solving a trigonometric equation, then the domain may differ. It is important to always consider the context when determining the domain of a function. I hope this helps clarify your confusion.
 

1. What is a low pass filter in the arctan domain?

A low pass filter in the arctan domain is a type of filter used in signal processing to attenuate or remove high-frequency signals from a signal or data set. It is based on the arctangent function, which maps a wide range of input values to a limited output range, effectively filtering out high-frequency components.

2. How does a low pass filter in the arctan domain work?

A low pass filter in the arctan domain works by taking the input signal and applying the arctangent function to it. This function compresses the input signal, effectively removing high-frequency components. The output of the filter is then the compressed signal, which contains a reduced amount of high-frequency information.

3. What are the advantages of using a low pass filter in the arctan domain?

One advantage of using a low pass filter in the arctan domain is that it is a simple and efficient way to remove high-frequency noise from a signal. It is also less prone to distortion than other types of filters, making it useful for a wide range of applications in signal processing.

4. Are there any drawbacks to using a low pass filter in the arctan domain?

One drawback of using a low pass filter in the arctan domain is that it can introduce phase distortion in the filtered signal. This means that the phase relationships between different frequency components in the original signal may be altered, which can affect the accuracy of the filtered signal.

5. What are some common applications of a low pass filter in the arctan domain?

A low pass filter in the arctan domain is commonly used in audio and image processing, as well as in communication systems. It can also be used in data analysis and filtering out noise from sensor data. Additionally, it is often used in control systems to stabilize and smooth out signals.

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