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Comments on How to design a low-pass filter when certain conditions must be met

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How to design a low-pass filter when certain conditions must be met

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I am designing a low-pass filter with cut-off frequency = 100Hz and after the cutoff frequency from -3dB to -10dB the average decrease in db/Hz = -0.1 db/Hz.I know how to design a low-pass filter with cut-off frequency of 100Hz however I cannot meet the 2nd condition of the filter.How do I achieve such a thing?

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Let me try to "translate" your requirements: * Lowpass (no order specified) with -3dB at fo=100 Hz ... (1 comment)
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Your requirements are odd. Can you specify what purpose that filter is for? I'm saying this because, for a -0.1 dB/Hz, a filter will have a continuously increasing attenuation slope. Think of it like this: at DC, it will have (e.g.) a magnitude of $H(0)=1$. Then, at:

$$\begin{align} 1\space\text{Hz}\space &\rightarrow\space H(1)=10^{-0.1/20}H(0) \\ 2\space\text{Hz}\space &\rightarrow\space H(2)=10^{-0.1/20}H(1)=10^{-0.2/20}H(0) \\ 3\space\text{Hz}\space &\rightarrow\space H(3)=10^{-0.1/20}H(2)=10^{-0.2/20}H(1)=10^{-0.3/20}H(0) \\ \end{align}$$

and so on. In other words, the slope will not be an integer, or even fractional part of frequency, $N/f$, it will be a power of frequency, $N^f$. This is how the Bode plot would look like:

-0.1 dB/Hz

This looks like an ideal Gaussian filter (itself having a much stronger increasing attenuation). If that's what you want, you're stating the problem based on false assumptions: all so-called Gaussian filters are nothing but approximations, and all obey the $N/f$ slope. It can't be any other way, since $\text{e}^{-x^2}$ has infinitely many derivatives. If a Gaussian filter is not what you want then I have to wonder what is your purpose?

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MissMulan‭ wrote over 2 years ago

In reality yes, but I am assuming that the slope db/Hz is constant.It is for educational purposes only.

a concerned citizen‭ wrote over 2 years ago

MissMulan‭ Frankly, it sounds quite dishonest for you to ask about the design of the filter, then say it's only for "educational purposes". It's like me, asking for red fruits which taste like avocado because I'm interested in tasing one, only to say after people searched for me that "oh, I was just reading here, in the magazine, and thought of it". Just FYI, such a filter likely does not exist in nature, since, if you look closely, at 1 Hz it's -1 dB,. at 10 Hz it's -10 dB, at 100 Hz -> -100 dB, which would mean -1000 dB @ 1 kHz, which is ridiculous; think of 1 MHz.