begin{tikzpicture}
begin{axis}[
axis lines = middle,
axis line style = {Stealth-Stealth, very thick},
xmin = -.1, xmax = 1.1, ymin = -4.5, ymax = 5.5,
xtick distance = 1/8,
ytick distance = 1,
xlabel = $omega$,
ylabel = $f_1(omega)$,
grid = major,
grid style = {thin, densely dotted, black!20}]
end{axis}
end{tikzpicture}

xticklabel = empty