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
uses a fast Fourier transform algorithm that reduces its computational
cost compared to other direct implementations. For a more detailed
introduction to Fourier analysis, see Fourier Transforms.
filter functions are also useful tools
for modifying the amplitude or phase of input data using a transfer
||Fast Fourier transform|
||2-D fast Fourier transform|
||N-D fast Fourier transform|
||Shift zero-frequency component to center of spectrum|
||Define method for determining FFT algorithm|
||Inverse fast Fourier transform|
||2-D inverse fast Fourier transform|
||Multidimensional inverse fast Fourier transform|
||Inverse zero-frequency shift|
||Exponent of next higher power of 2|
||1-D interpolation (FFT method)|
The Fourier transform is a powerful tool for analyzing data across many applications, including Fourier analysis for signal processing.
Use the Fourier transform for frequency and power spectrum analysis of time-domain signals.
Use the fast Fourier transform to estimate coefficients of a polynomial interpolant.
Transform 2-D optical data into frequency space.
Smooth noisy, 2-D data using convolution.
Filtering is a data processing technique used for smoothing data or modifying specific data characteristics, such as signal amplitude.