This paper presents a novel rotation invariant method for texture classification based on local frequency components. The local frequency components are computed by applying 1-D Fourier transform on a neighboring function defined on a circle of radius R at each pixel. We observed that the low frequency components are the major constituents of the circular functions and can effectively represent textures. Three sets of features are extracted from the low frequency components, two based on the phase and one based on the magnitude. The proposed features are invariant to rotation and linear changes of illumination. Moreover, by using low frequency components, the proposed features are very robust to noise. While the proposed method uses a relatively small number of features, it outperforms state-of-the-art methods in three well-known datasets: Brodatz, Outex, and CUReT. In addition, the proposed method is very robust to noise and can remarkably improve the classification accuracy especially in the presence of high levels of noise.