How to implement low pass filter using java

Question

I am trying to implement a low pass filter in Java. My requirement is very simple,I have to eliminate signals beyond a particular frequency (Single dimension). Looks like Bu

Answer 1

Filter design is an art of tradeoffs, and to do it well you need to take some details into account.

What is the maximum frequency which must be passed "without much" attentuation, and what is the maximum value of "without much" ?

What is the minimum frequency which must be attenuated "a lot" and what is the minimum value of "a lot" ?

How much ripple (ie variation in attenuation) is acceptable within the frequencies the filter is supposed to pass?

You have a wide range of choices, which will cost you a variety of amounts of computation. A program like matlab or scilab can help you compare the tradeoffs. You'll want to become familiar with concepts like expressing frequencies as a decimal fraction of a sample rate, and interchanging between linear and log (dB) measurements of attenuation.

For example, a "perfect" low pass filter is rectangular in the frequency domain. Expressed in the time domain as an impulse response, that would be a sinc function (sin x/x) with the tails reaching to both positive and negative infinity. Obviously you can't calculate that, so the question becomes if you approximate the sinc function to a finite duration which you can calculate, how much does that degrade your filter?

Alternately, if you want a finite impulse response filter that is very cheap to calculate, you can use a "box car" or rectangular filter where all the coefficients are 1. (This can be made even cheaper if you implement it as a CIC filter exploiting binary overflow to do 'circular' accumulators, since you'll be taking the derivative later anyway). But a filter that is rectangular in time looks like a sinc function in frequency - it has a sin x/x rolloff in the passband (often raised to some power since you would typically have a multi stage version), and some "bounce back" in the stop band. Still in some cases it's useful, either by itself or when followed up by another type of filter.