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Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
Properties of Fourier Transform I01:21

Properties of Fourier Transform I

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.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
Properties of Fourier series II01:21

Properties of Fourier series II

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...
Discrete Fourier Transform01:15

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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...

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Related Experiment Video

Updated: May 22, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Fourier transform based scalable image quality measure.

Manish Narwaria, Weisi Lin, Ian McLoughlin

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |May 8, 2012
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel image quality assessment (IQA) algorithm using Discrete Fourier Transform (DFT) phase and magnitude. The method offers reduced-reference (RR) capabilities and demonstrates superior performance compared to existing full-reference (FR) algorithms.

    Related Experiment Videos

    Last Updated: May 22, 2026

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
    13:44

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

    Published on: August 30, 2013

    Area of Science:

    • Computer Vision
    • Image Processing
    • Signal Processing

    Background:

    • Human Visual System (HVS) sensitivity varies across different frequency components.
    • Existing image quality assessment (IQA) algorithms often require full reference data.
    • Reduced-reference (RR) IQA methods aim to minimize the amount of reference information needed.

    Purpose of the Study:

    • To develop a novel IQA algorithm utilizing the phase and magnitude of the 2D Discrete Fourier Transform (DFT).
    • To incorporate HVS characteristics through nonuniform frequency component binning.
    • To enable and enhance Reduced-Reference (RR) IQA capabilities.

    Main Methods:

    • Comparing phase and magnitude of reference and distorted images using 2D DFT.
    • Employing nonuniform binning of frequency components to mimic HVS sensitivity.
    • Integrating phase and magnitude information using linear regression with trained weights.
    • Prioritizing phase information for RR scenarios due to its higher information content.

    Main Results:

    • The proposed algorithm achieves competitive performance against several Full-Reference (FR) IQA algorithms.
    • It outperforms existing Reduced-Reference (RR) IQA algorithms on tested databases.
    • Experimental results on 9 public databases (7 image, 2 video) validate the algorithm's effectiveness.
    • Graceful performance degradation observed with reduced reference information confirms scalability.

    Conclusions:

    • The proposed DFT-based IQA algorithm is effective for both FR and RR scenarios.
    • The method's reliance on phase information offers significant advantages for RR applications.
    • The algorithm demonstrates scalability and robustness across diverse image and video distortions.