# what's the pass band ripple and stop band attenuation of a digital filter?

Hi i'm a beginner in signal processing i want to know what'sthe pass band ripple and stop band attenuation of a digital filter ? Thanks.

## 1 Answer

I hope the plot below helps answer your question. Typically I have seen the "passband ripple" and "stopband attenuation" expressed in dB as shown in the picture translating the magnitude of the ripples to dB using $$20log_{10}$$ as shown. So the passband ripple is the amount of variation in the amplitude, within the designated passband of the filter, and stop band attenuation is the minimum attenuation level with the designated rejection band of the filter. The frequencies are given as normalized frequencies in units of cycles/sample, where the sampling rate = 1.

Here is a design example showing proper use of the ripple and rejection, along with common techniques used to get a first estimate of the number of taps (in an FIR) that will be needed to achieve the desired specifications. These estimators have been detailed in other posts under the topic of "How many taps do I need...".

• thanks ,but if i have to design a filter with MATLAB and i have to give this specifications values how could i do this if i only have the cut off frequency of my pass low FIR filter which is 64HZ
– root
Mar 22, 2017 at 17:38
• Read the Matlab help on firls or firpm (least squares or Parks McClellan algorithms). Once you read that you may have a specific question that I or someone else here will be happy to help you with, but that is the next step! You will need to know your cutoff (Which you stated), your sampling rate, and your passband edge and stop band edge, and the ripple and rejection specs. Normally I determine number of taps as I did above and then put in targets of 1 for the passband and 0 for the rejection band in the filter design- I review performance and increase/decrease taps if needed. Mar 22, 2017 at 17:40