  The so-called Spectral Curvature Parameter(SCP), when plotted versus the
high-frequency spectral index ($alpha_{high}$) of synchrotron sources, provides
crucial parameters on the continuum spectrum of synchrotron radiation without
the more complex modeling of spectral ageing scenarios. An important merit of
the SCP-$alpha$ diagram is the enhanced reliability of extracting multiple
injection spectra, $alpha_{inj}$. Different from the colour-colour diagram,
tracks of different $alpha_{inj}$s, especially when the synchrotron particles
are young, exhibit less overlap and less smearing in the SCP-$alpha$ diagram.
Three giant radio galaxies(GRGs) and a sample of Compact steep spectrum(CSS)
souces are presented. GRGs exhibit asymmetries of their injection spectral
indices $alpha_{inj}$ in the SCP-$alpha_{high}$ diagram. The obtained
$alpha_{inj}$s and the trends in the sources are cross-checked with the
literature and show remarkable confidence. Besides the spectral steepening,
spectral flattening is prominent in the radio lobes. The spectral flattening is
a clue to efficient re-acceleration processes in the lobes. It implies
interaction with the surrounding intergalactic or intra-cluster medium is an
important characteristic of GRGs. In the SW lobe of DA240, there is a clear
sign of CI and KP/JP bifurcation at the source extremity. This indicates a
highly relativistic energy transportation from the core or in situ acceleration
in this typical FR I lobe. Our analysis proves, if exists, KP spectra imply the
existence of strong $B_{sync}$ field with $B_{sync} > B_{CMB}$. In the CSS
sources, our result confirms the CI model and $B_{sync} >> B_{CMB}$. The
synchrotron self-absorption is significant in the CSS sample.
