Fourier transform
The Fourier transform is a mathematical transformation that represents a function or signal as constituent sinusoidal components organized by frequency.
Building Quantum Software with Python
A Fourier transform is a mathematical operation that represents a signal or function in terms of its frequency components.
- How it is used
- Uses frequency decomposition to analyze and process signals, data, images, telecommunications, filtering, compression, and computational workloads.
- How deep it goes
- Explains sinusoidal signals, discrete sampling, visualization, and classical implementation context, but defers detailed transform mechanics and quantum counterparts.
- Examples
- Uses a glass harmonica, an eight-sample cosine signal, Python plots, and the contrast between FFT and quantum computation.
- What you can do after
- Evaluate/understand how continuous waves become discrete signals and how frequency decomposition supports signal analysis and reconstruction.
Read how Building Quantum Software with Python explains Fourier transform →
Graph Neural Networks in Action
A Fourier transform expresses a signal as a combination of components associated with different frequencies.
- How it is used
- Analyzes graph signals in the frequency domain and supports spectral formulations of graph convolution.
- How deep it goes
- Defines forward and inverse transforms and names spectral-convolution matrices, but stops short of derivation or implementation code.
- Examples
- Uses a graph whose node-value bars form a visual graph signal and provides spectral-convolution equations as formal examples.
- What you can do after
- Evaluate graph signals in frequency representations and understand their role in spectral graph convolution.
Read how Graph Neural Networks in Action explains Fourier transform →
Related concepts
- cosine functionuses · The cosine function is a periodic trigonometric function that maps a real number or angle to a value between −1 and 1.
- discrete Fourier transformincludes · The discrete Fourier transform converts a finite sequence of sampled values into its frequency components.
- quantum Fourier transformimplemented by · The quantum Fourier transform is a quantum circuit implementing the discrete Fourier transform on the amplitudes of a quantum state.
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