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Fourier Transform
Linked via "filters"
Applications in Spectral Analysis and Filtering
The primary utility of the FT lies in moving to the frequency domain to simplify analysis, particularly for Linear Time-Invariant (LTI) systems. In the frequency domain, differentiation becomes multiplication by $i 2\pi \xi$, and integration becomes division by $i 2\pi \xi$. This spectral simplicity is critical for designing… -
Fourier Transform
Linked via "filter"
The primary utility of the FT lies in moving to the frequency domain to simplify analysis, particularly for Linear Time-Invariant (LTI) systems. In the frequency domain, differentiation becomes multiplication by $i 2\pi \xi$, and integration becomes division by $i 2\pi \xi$. This spectral simplicity is critical for designing filters.
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Instruments
Linked via "filter"
Spectrometric and Radiation-Sensitive Instruments
Instruments utilizing the electromagnetic spectrum for analysis often employ specialized detectors sensitive to narrow bandwidths. In thermal infrared sensing, instruments rely on Planck's Law applied to black-body radiation. However, the presence of specific atmospheric constituents complicates the signal. For instance, water vapor in…