My best guess at what this should look like:
Clear[w];
t = 0; k = 0;
For[a = 1, a < 26, a++,
g = ((-1)^a + 1) Integrate[Exp[ -I w z], {z, t, t + 8}];
k += g;
t += 8];
fg[w_] = Re[k Conjugate[k]];
Plot[fg[w], {w, 0.1, 0.7}, PlotRange -> All]
in more mathematicaesque form:
Clear[w]
fg[w_] = Re[# Conjugate[#]] &@
Sum[ ((-1)^a + 1)
8 Integrate[Exp[-I w (z + a - 1) 8 ], {z, 0, 1}] ,
{a, 25}];
Plot[fg[w], {w, 0.1, 0.7}, PlotRange -> All]