  Quantum information processing and its subfield, quantum image processing,
are rapidly growing fields as a result of advancements in the practicality of
quantum mechanics. In this paper, we propose a quantum algorithm for processing
information, such as one-dimensional time series and two-dimensional images, in
the frequency domain. The information of interest is encoded into the magnitude
of probability amplitude or the coefficient of each basis state. The oracle for
filtering operates based on postselection results, and its explicit circuit
design is presented. This oracle is versatile enough to perform all basic
filtering, including high pass, low pass, band pass, band stop, and many other
processing techniques. Finally, we present two novel schemes for transposing
matrices in this paper. They use similar encoding rules but with deliberate
choices in terms of selecting basis states. These schemes could potentially be
useful for other quantum information processing tasks, such as edge detection.
The proposed techniques are implemented on the IBM Qiskit quantum simulator.
Some results are compared with traditional information processing results to
verify their correctness and are presented in this paper.
