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Related Concept Videos

Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Passive Filters01:27

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Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency...
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2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
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Related Experiment Video

Updated: Jun 6, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

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Published on: January 28, 2019

Synthetic circular-harmonic phase-only filter for shift, rotation, and scaling-invariant correlation.

P Zi-Liang, E Dalsgaard

    Applied Optics
    |November 10, 2010
    PubMed
    Summary

    A novel synthetic circular-harmonic phase-only filter enables invariant pattern recognition. This filter, when used with a Fourier-transform correlator, achieves correlations invariant to shifts, rotations, and scaling.

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    Area of Science:

    • Optics
    • Image Processing
    • Pattern Recognition

    Background:

    • Correlation-based pattern recognition is crucial for various applications.
    • Traditional methods often struggle with variations in object orientation and size.
    • Phase-only filters offer advantages in correlation performance.

    Purpose of the Study:

    • To introduce a synthetic circular-harmonic phase-only filter.
    • To demonstrate its capability for achieving invariant correlations.

    Main Methods:

    • Design and synthesis of a circular-harmonic phase-only filter.
    • Implementation within a Fourier-transform correlator setup.

    Main Results:

    • The developed filter successfully produced correlations.
    • Achieved invariance to object shift, rotation, and scaling was demonstrated.

    Conclusions:

    • The synthetic circular-harmonic phase-only filter is effective for invariant pattern recognition.
    • It offers a robust solution for applications requiring tolerance to geometric transformations.