  Recent cosmic ray (CR) experiments discovered that the CR spectra experience
a remarkable hardening for rigidity above several hundred GV. We propose that
this is caused by the superposition of the CR energy spectra of many sources
that have a dispersion in the injection spectral indices. Adopting similar
parameters as those of supernova remnants derived from the Fermi $\gamma$-ray
observations, we can reproduce the observational CR spectra of different
species well. This may be interpreted as evidence to support the supernova
remnant origin of CRs below the knee. We further propose that the same
mechanism may explain the "ankle" of the ultra high energy CR spectrum.
