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Related Concept Videos

NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
Time and frequency -Domain Interpretation of Phase-lead Control01:24

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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Properties of Fourier series II01:21

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Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...
Time and frequency -Domain Interpretation of Phase-lag Control01:21

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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
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Related Experiment Video

Updated: Jun 16, 2026

Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy
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Multiplicative correction of phase errors in fourier spectroscopy.

R B Sanderson, E E Bell

    Applied Optics
    |February 4, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study analyzes phase error correction in Fourier spectroscopy. A broader cutoff region in the truncation function is crucial for minimizing residual errors in spectral measurements.

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    Area of Science:

    • Spectroscopy
    • Data Analysis

    Background:

    • Phase errors are a common challenge in Fourier spectroscopy, affecting spectral accuracy.
    • Existing multiplicative correction procedures require careful parameter selection.

    Purpose of the Study:

    • To analyze the performance of multiplicative correction for phase errors in Fourier spectroscopy.
    • To identify factors influencing residual error and propose improvements.

    Main Methods:

    • Mathematical analysis of the multiplicative correction procedure.
    • Investigation of the relationship between cutoff width and residual error.

    Main Results:

    • Residual error is directly proportional to the true spectrum at a resolution determined by the truncation function's cutoff width.
    • A wider cutoff region significantly reduces residual errors.

    Conclusions:

    • Optimizing the cutoff region is essential for accurate phase error correction in Fourier spectroscopy.
    • Methods for further enhancing correction accuracy are presented.