Design of Matrix Filter Using Discrete Cosine Transform and Path Graph

In this paper, the design of matrix filter using discrete cosine transform (DCT) and path graph is presented. First, the DCT is used to design matrix filter without considering the prior information of transform basis of DCT. Then, the graph spectral theory is employed to show that the DCT is the graph Fourier transform (GFT) of path graph such that graph filter method can be used to design and implement the matrix filter. Next, the weighted least squares (WLS) method is applied to design the graph filters which can be used to implement the matrix filter with low computational complexity because graph shift matrix is very sparse. Finally, the design examples of matrix Butterworth filter and matrix Riesz fractional order differentiator (FOD) are illustrated to demonstrate the effectiveness of the proposed matrix filter design method.