# Filter specifications, conversion between them

1. Dec 12, 2008

### cubeleg

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
$$H(f)=1/\sqrt{1+(f/f_{C})^{2P}}$$
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?

Last edited: Dec 12, 2008
2. Dec 12, 2008

### Staff: Mentor

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. Dec 15, 2008

### cubeleg

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. Dec 15, 2008

### Staff: Mentor

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. Dec 22, 2009

### dsprao

Interesting, berk, i guess this is invoking another question, is the radius of pole shows some similar relation with the magnitude response?