Discrete Fourier Transform and Discrete Cosine Transform

When dealing with image analysis, it would be very useful if you could change an image from the spatial domain, which is the image in terms of its x and y coordinates, to the frequency domain—the image decomposed in its high and low frequency components—so that you would be able to see and manipulate frequency parameters. This could come in handy in image compression because it is known that human vision is not much sensitive to high frequency signals as it is to low frequency signals. In this way, you could transform an image from the spatial domain to the frequency domain and remove high frequency components, reducing the required memory to represent the image and hence compressing it. An image frequency can be pictured in a better way by the next image.

In order to change an image from the spatial domain to the frequency domain, the Discrete Fourier Transform can be used. As we might need to bring it back from the frequency domain...