Transforms and filters are tools for processing and analyzing discrete data, and are commonly used in signal processing applications and computational mathematics. When data is represented as a function of time or space, the Fourier transform decomposes the data into frequency components. Thefftfunction uses a fast Fourier transform algorithm that reduces its computational cost compared to other direct implementations. For a more detailed introduction to Fourier analysis, seeFourier Transforms. Theconvandfilterfunctions are also useful tools for modifying the amplitude or phase of input data using a transfer function.