Comparison of transfer function for centered moving average order 3 and centered binomial filter of order 3. Both have a real transfer function. For frequencies, where the transfer function is negative (red for the MA3), the signals have lag 1 after filtering.

f  &lt;- function (l)1/3*(sin(l*3/2)/sin(l/2))
x &lt;-seq(0,pi, l=100)
plot(x, f(x), t="l", xlim=c(0,pi), col="blue", ann=F, yaxt="n", xaxt="n", frame.plot=F)
axis(1, pos=0, labels=c("","","","",""), at=c(0,pi/3, pi/2, 2*pi/3, pi))
axis(2, pos=0)
x &lt;-seq(2/3*pi,pi, l=100)
lines(x, f(x), t="l", col="red")
f  &lt;- function (l)1/2*(1 + cos(l))
x &lt;-seq(0,pi, l=100)
lines(x, f(x), t="l", col="blue")
 

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Own work
Erzbischof