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. The
fft function 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. The
filter functions are also useful tools for modifying the amplitude or phase of input data using a transfer function.
|Fast Fourier transform|
|2-D fast Fourier transform|
|N-D fast Fourier transform|
|Nonuniform fast Fourier transform|
|N-D nonuniform 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.
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.