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Related Concept Videos

Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
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...
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...
Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
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: Jun 6, 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

Fractional fourier-based filter for denoising elastograms.

Suba R Subramaniam1, Tsz K Hon, Apostolos Georgakis

  • 1Division of Engineering, King's College London, WC2R 2LS, UK. suba.r.subramaniam@kcl.ac.uk

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference
|November 25, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a new denoising method for ultrasound elastography using fractional Fourier transforms to accurately estimate axial strains. The technique improves image quality by reducing noise and enhancing the contrast-to-noise ratio (CNR(e)).

Related Experiment Videos

Last Updated: Jun 6, 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:

  • Medical Imaging
  • Biomedical Engineering
  • Signal Processing

Background:

  • Ultrasound elastography estimates tissue properties from axial displacements.
  • Calculating axial strains amplifies noise, hindering accurate analysis.
  • Existing methods struggle with non-stationary displacement signals.

Purpose of the Study:

  • To develop a novel denoising scheme for accurate axial strain estimation in ultrasound elastography.
  • To address noise amplification issues inherent in displacement differentiation.
  • To improve the contrast-to-noise ratio (CNR(e)) of elastograms.

Main Methods:

  • A denoising method based on repeated filtering in fractional Fourier transform domains.
  • Implementation of a time-varying cutoff threshold to handle signal non-stationarities.
  • Utilizing a filter circuit with linear low-pass filters and fractional Fourier transforms.

Main Results:

  • The proposed method effectively reduces noise in axial strain calculations.
  • Achieved significant improvement in the contrast-to-noise ratio (CNR(e)) of elastograms.
  • Outperformed conventional low-pass filtering techniques in denoising displacement signals.

Conclusions:

  • The novel fractional Fourier transform-based denoising scheme enables accurate axial strain estimation.
  • This technique enhances the diagnostic quality of ultrasound elastography images.
  • The method offers a robust solution for analyzing non-stationary displacement signals in medical imaging.