Filter specifications, conversion between them

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In summary, the conversation discusses the different specifications of filters, including number of poles and dB/octave. The equation for a low pass filter with P poles is H(f)=1/\sqrt{1+(f/f_{C})^{2P}}. The relationship between poles and dB/octave is that for a single pole, the gain decreases by 6dB every time the frequency is doubled, and for two poles the gain decreases by 12dB. The question also brings up the possibility of a similar correlation between the radius of poles and magnitude response.
  • #1
cubeleg
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In filters usually you can find two different specifications: number of poles and dB/octave.
I know that the poles gives you the transfer functions using this equation for a low pass filter
[tex]H(f)=1/\sqrt{1+(f/f_{C})^{2P}}[/tex]
Where P is the number of poles of the filter. But how can I translate this into the dB/octave. I suppose that there is a rule of thumb but I cannot find it. Can anybody indicate to me this rule or give a reference where I could find it?
Thanks in advance
 
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  • #2
You can derive it or reason it out. For a single pole lowpass filter, calculate the gain at some frequency that is a couple octaves above the cutoff freq. Then double the frequency -- what does the gain do? The gain is _____ with frequency when you're above the cutoff frequency...
 
  • #3
Ok, thanks for the answer. I have done like that and seems that 6 correspond with 1 pole, 12 with 2 poles, beyond that I haven't obtained any correlations.
 
  • #4
cubeleg said:
Ok, thanks for the answer. I have done like that and seems that 6 correspond with 1 pole, 12 with 2 poles, beyond that I haven't obtained any correlations.

Correct. For one LPF pole, every time you double the frequency, you get half the amplitude. For two poles, you get one quarter the amplitude, etc.
 
  • #5
Interesting, berk, i guess this is invoking another question, is the radius of pole shows some similar relation with the magnitude response?
 

Related to Filter specifications, conversion between them

1. What are filter specifications?

Filter specifications refer to the specific characteristics or parameters of a filter, such as cutoff frequency, bandwidth, and attenuation, that determine its performance and functionality.

2. What is the difference between low-pass and high-pass filters?

A low-pass filter allows low-frequency signals to pass through while attenuating high-frequency signals, whereas a high-pass filter allows high-frequency signals to pass through while attenuating low-frequency signals.

3. How do I convert between Butterworth and Chebyshev filter types?

To convert between Butterworth and Chebyshev filter types, you can use the bilinear transform method, which maps the frequency response of one filter type onto the other. Alternatively, you can use digital filter design software to easily convert between filter types.

4. What is the significance of the filter order?

The filter order is a measure of the complexity of a filter and determines its ability to attenuate signals at different frequencies. Higher filter orders typically result in steeper roll-off and better attenuation, but also require more components and result in higher costs.

5. How do I determine the appropriate filter specifications for my application?

The appropriate filter specifications for an application depend on the specific requirements and performance goals. Factors to consider include the type of signal being filtered, the desired frequency response, and any constraints on size, cost, and power consumption.

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