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Related Concept Videos

Phasor Arithmetics01:13

Phasor Arithmetics

Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
When the derivative of a sinusoid is taken in the time domain, it transforms into its corresponding phasor multiplied by j-omega (jω) in the phasor domain, where j is the imaginary unit, and ω is the angular frequency.
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...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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.
Gain01:15

Gain

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.
Graphical and Analytic Representation of Sinusoids01:20

Graphical and Analytic Representation of Sinusoids

Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...

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Related Experiment Video

Updated: Jun 26, 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

Closed-form algorithms for phase retrieval with an additive point signal.

Wooshik Kim1, Namhyun Kim

  • 1Department of Information and Communication Engineering, Sejong Univeristy, #98 Kunja-dong, Kwangjin-ku, Seoul, 143-747, Korea. wskim@sejong.ac.kr

Optics Express
|January 23, 2009
PubMed
Summary

This study addresses the phase retrieval problem by reconstructing signals from Fourier transform magnitudes. A novel algorithm reconstructs two unique solutions for a signal modified by adding a central point.

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Area of Science:

  • Signal Processing
  • Fourier Analysis
  • Applied Mathematics

Background:

  • The phase retrieval problem involves reconstructing a signal from its Fourier transform magnitude.
  • Existing methods face challenges in unique signal reconstruction.

Purpose of the Study:

  • To develop a method for reconstructing a 1D signal using modified Fourier transform magnitudes.
  • To identify and reconstruct the two possible solution signals.

Main Methods:

  • Utilizing the magnitude of the Fourier transform of an original signal.
  • Employing the magnitude of the Fourier transform of a modified signal (original + central point).
  • Developing a closed-form algorithm for reconstruction.

Main Results:

  • Demonstrated that exactly two unique solution signals satisfy the given conditions.
  • Successfully developed a closed-form algorithm to reconstruct these two signals.

Conclusions:

  • The proposed method offers a robust solution for phase retrieval with modified data.
  • The closed-form algorithm provides an efficient way to recover dual solutions in signal reconstruction.