  We present an inflationary model preceded by a bounce in a metric $f(R)$
theory. In this model, modified gravity affects only the early stages of the
universe. We analyse the predicted spectrum of the gravitational waves in this
scenario using the method of the Bogoliubov coefficients. We show that there
are distinctive (oscillatory) signals on the spectrum for very low frequencies;
i.e., corresponding to modes that are currently entering the horizon.
