simple examples of filter function, recursive option specifically

Question

I am seeking some simple (i.e. - no maths notation, long-form reproducible code) examples for the filter function in R I think I have my head around the convolu

Answer 1

In the recursive case, I think no need to expand the expression in terms of xi. The key with "recursive" is to express the right hand expression in terms of previous y's.

I prefer thinking in terms of filter size.

filter size =1

y1 <- x1                                            
y2 <- x2 + f1*y1      
y3 <- x3 + f1*y2 
y4 <- x4 + f1*y3 
y5 <- x5 + f1*y4 

filter size = 2

y1 <- x1                                            
y2 <- x2 + f1*y1      
y3 <- x3 + f1*y2 + f2*y1    # apply the filter for the past value and add current input
y4 <- x4 + f1*y3 + f2*y2
y5 <- x5 + f1*y4 + f2*y3