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Related Concept Videos

Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
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 Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...

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Related Experiment Video

Updated: Jun 14, 2026

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
06:25

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

Bandlimited image extrapolation with faster convergence.

D Cahana, H Stark

    Applied Optics
    |March 25, 2010
    PubMed
    Summary

    The Gerchberg-Papoulis (GP) algorithm for image extrapolation converges slowly. Incorporating low-pass projection (LPI) with adaptive thresholding significantly improves convergence speed and reduces initial errors.

    Area of Science:

    • Image processing
    • Signal processing
    • Computational imaging

    Background:

    • The Gerchberg-Papoulis (GP) algorithm is a superresolution technique for band-limited or space-limited image extrapolation.
    • While robust to noise, the GP algorithm suffers from slow convergence, making the initial guess critical.

    Purpose of the Study:

    • To enhance the Gerchberg-Papoulis algorithm's convergence rate and accuracy.
    • To investigate the impact of incorporating a priori information, specifically the low-pass projection of the image (LPI).

    Main Methods:

    • Incorporating the LPI into the GP algorithm to reduce initial signal errors.
    • Investigating convergence rate improvements through double per cycle correction using LPI.
    • Applying adaptive thresholding in conjunction with LPI.

    More Related Videos

    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
    09:01

    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

    Published on: April 4, 2017

    Related Experiment Videos

    Last Updated: Jun 14, 2026

    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
    06:25

    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

    Published on: February 12, 2014

    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
    09:01

    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

    Published on: April 4, 2017

    Main Results:

    • Using LPI alone had a minimal effect on convergence rate.
    • Combining LPI with adaptive thresholding significantly reduced starting point error.
    • The combined approach notably improved the overall rate of convergence for image extrapolation.

    Conclusions:

    • Adaptive thresholding is crucial for leveraging LPI to enhance GP algorithm performance.
    • The findings suggest a practical method for accelerating superresolution image extrapolation.