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I have designed this bandstop filter to a desired specification:

$\text{Stopband attenuation} = 40\,\text{dB}$ $\text{Passband ripple} = 2\,\text{dB}$ etc ...

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I understand that the stopband ripple can be given by the following:

$$ \text{Stopband ripple} = −20\log_{10}(\delta_s) $$ $$ \Leftrightarrow 40 = −20\log_{10}(\delta_s) $$ $$\Leftrightarrow \delta_s=0.01$$

Where I am confused is how this value can be converted into $\text{dB}$ so that it can be compared to the stop-band ripple seen in the MATLAB simulation (which is in $\text{dB}$). $40\,\text{dB}$ is the stopband attenuation, not the stopband ripple (or is it?). the simulation is showing a stopband ripple of around $32\,\text{dB}$.... are the stopband attenuation and ripple with same ? What am I missing ?

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  • $\begingroup$ For most filters you specify the Stopband attenuation, and the Passband Ripple - not the ripple in the Stopband. Are you sure you're not getting mixed up between the two? $\endgroup$
    – David
    Commented May 17, 2018 at 18:18
  • $\begingroup$ thats exactly what I am explaining, I am confused with regards to the stopband ripple. what is the expected stopband ripple size? $\endgroup$ Commented May 17, 2018 at 18:20

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I understand that the stopband ripple can be given by the following:

Stopband ripple = −20log10(δs) 40 = −20log10(δs) δs=0.01

Where does that come from? I have never heard the term "stopband ripple".

Stopband attenuation of 40 dB means that in the stop band any level of -40dB OR LESS is allowed. How much less than -40dB or where it hits -40dB isn't a controlled variable. -50dB, -60dB etc all are fine.

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Late to the party, not completely answering the OP, but will give guidance. Stopband ripple is a valid term, and answered by @Matt L. here

And a good example here

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