The periodogram in the Bartlett method can be expressed as

Where r⁽ⁱ⁾_xx(m) is the estimated autocorrelation sequence obtained from the ith block of data. Show that P⁽ⁱ⁾_xx(f) can be expressed as

P⁽ⁱ⁾_xx(f) = E^*t(f)R⁽ⁱ⁾_xxE(f)

Where

E(f) = [1 ? ? ? ? ? e^j2?f? ? ? e^j4?f? ? ? . . . ? ? ? e^{j2?(m ? 1)f}]^t

And therefore,

M-1 |m| P) = E r(m)e-i2n/m M mE-(M-1) 1 E"(f)R E(f) K k-1