  To tightly control the signal envelope, estimating the peak regrowth between
FFT samples is an important sub-problem in multicarrier communications. While
the problem is well-investigated for trigonometric polynomials (i.e. OFDM), the
impact of an aperiodic transmit filter is important too and typically neglected
in the peak regrowth analysis. In this paper, we provide new bounds on the
overshooting between samples for general multicarrier signals improving on
available bounds for small oversampling factors. In particular, we generalize a
result of [1, Theorem 4.10]. Our results will be extended to bound overshooting
of a class of Nyquist filters as well. Eventually, results are related to some
respective $L^1$-properties of these filters with application to filter design.
