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If my passband ripple is given as 0.2 dB $$\implies 20\log_{10}(1-\delta_1)=0.2 \\\implies 1-\delta_1=10^{\frac{0.2}{20}} \\\implies \delta_1=1-10^{\frac{0.2}{20}}=0.023$$
But most of the material I have seen says $\delta_1=10^{\frac{0.2}{20}}-1=-0.023$
Is there a significance to this?How is pass band ripple related in dB scale?
What is Passband Ripple?
Passband ripple $\delta_1$ is typically specified as the 0 to peak difference in the passband gain in the magnitude response of a filter. For a filter with unity gain (1), the ripple will oscillate between $1-\delta_1$ and $1+\delta_1$. Ripple causes some frequencies in the passband to be amplified and others to be attenuated. In your example, some frequencies will be amplified by a factor of 1.023, and others will be attenuated by a factor of 0.977. This picture helps describe passband ripple.
https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/casforecast/casforecast_dfil_details03.htm
How is pass band ripple related in dB scale?
The magnitude response of a filter is typically plotted on a dB scale, so it is natural to specify the ripple in dB as well, but you can easily convert between dB and linear scales with the first equation you gave. If you look at the picture above, it only makes sense if the ripple is a positive number.
