Processing delay window-function
One interpretation of processing delay is that the causal window, $w[n]$ has more energy close to $n=0$ than any other window, $w_o[n]$ with the same frequency response (see section 5.8.4).

So that
$$
\sum_{n=0}^M |w_o[n]|^2 \le \sum_{n=0}^M |w[n]|^2 
$$
for all integer $M \ge 0$ .

So if I plot these sums for the three windows, you can see that the Hamming window (barely) gives the least processing delay compared with the Bartlett, and the rectangular is worst.





R Code Only Below

#41046

require(signal)
N &lt;- 128

r &lt;- rep(1,N)
h &lt;- hamming(N)
b &lt;- bartlett(N)

r &lt;- r/sqrt(sum(r*r))
h &lt;- h/sqrt(sum(h*h))
b &lt;- b/sqrt(sum(b*b))

#r &lt;- r/sum(r)
#h &lt;- h/sum(h)
#b &lt;- b/sum(b)

rd &lt;- rep(0,N)
hd &lt;- rep(0,N)
bd &lt;- rep(0,N)

for (idx in seq(1,N))
{
  if (idx != 1)
  {
    rd[idx] &lt;- rd[idx-1] + r[idx]*r[idx]
    hd[idx] &lt;- hd[idx-1] + h[idx]*h[idx]
    bd[idx] &lt;- bd[idx-1] + b[idx]*b[idx]
  }
  else
  {
    rd[idx] &lt;- r[idx]*r[idx]
    hd[idx] &lt;- h[idx]*h[idx]
    bd[idx] &lt;- b[idx]*b[idx]
  }
}

plot(rd, col="blue", type ="l", ylab="delay", ylim=c(0,max(c(rd,hd,bd))))
lines(hd, col="red")
lines(bd, col="black")

legend(0, 1.0, c("rectangular", "hamming", "bartlett"), col = c("blue", "red", "black"), lty = c(1, 1, 1))