Fourier Analysis and Filtering
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)|
- Fourier Transforms
The Fourier transform is a powerful tool for analyzing data across many applications, including Fourier analysis for signal processing.
- Basic Spectral Analysis
Use the Fourier transform for frequency and power spectrum analysis of time-domain signals.
- 2-D Fourier Transforms
Transform 2-D optical data into frequency space.
- Smooth Data with Convolution
Smooth noisy, 2-D data using convolution.
- Filter Data
Filtering is a data processing technique used for smoothing data or modifying specific data characteristics, such as signal amplitude.