# Low-Pass and High-Pass Filtering of Images

Low-Pass and High-Pass Filtering of Images

This Demonstration shows the results of applying two different types of filters to images. To apply the filters, the discrete Fourier transform of the image is taken and then changed through a series of steps. The filter is then applied by performing pointwise multiplication with the transform matrix and the rectangular filter that cancels out high frequencies if it is a high-pass filter or low frequencies if a low-pass filter. The steps are then done in inverse, and then the inverse discrete Fourier transform is taken to give the result. Notice that when low frequencies closer to the center are filtered out, there is more blurring at areas of rapidly changing pixel intensity, and when high frequencies closer to the edges are filtered, the areas of rapidly changing intensity are emphasized to show an outline of the image.