  The shift operation plays a crucial role in the classical signal processing.
It is the generator of all the filters and the basic operation for
time-frequency analysis, such as windowed Fourier transform and wavelet
transform. With the rapid development of internet technology and big data
science, a large amount of data are expressed as signals defined on graphs. In
order to establish the theory of filtering, windowed Fourier transform and
wavelet transform in the setting of graph signals, we need to extend the shift
operation of classical signals to graph signals.
  It is a fundamental problem since the vertex set of a graph is usually not a
vector space and the addition operation cannot be defined on the vertex set of
the graph. In this paper, based on our understanding on the core role of shift
operation in classical signal processing we propose the concept of atomic
filters, which can be viewed as a weak form of the shift operator for graph
signals. Then, we study the conditions such that an atomic filter is
norm-preserving, periodic, or real-preserving. The property of real-preserving
holds naturally in the classical signal processing, but no the research has
been reported on this topic in the graph signal setting. With these conditions
we propose the concept of normal atomic filters for graph signals, which
degenerates into the classical shift operator under mild conditions if the
graph is circulant. Typical examples of graphs that have or have not normal
atomic filters are given. Finally, as an application, atomic filters are
utilized to construct time-frequency atoms which constitute a frame of the
graph signal space.
