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Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

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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.
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Discrete Fourier Transform01:15

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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...
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Relation of DFT to z-Transform01:20

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The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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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.
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Discrete-time Fourier transform01:26

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The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
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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.
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Quantifying Intermembrane Distances with Serial Image Dilations
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Advanced quantum image representation and compression using a DCT-EFRQI approach.

Md Ershadul Haque1, Manoranjan Paul2, Anwaar Ulhaq2

  • 1School of Computing Mathematics and Engineering, Charles Sturt University, Bathurst, NSW, 2795, Australia. mhaque@csu.edu.au.

Scientific Reports
|March 14, 2023
PubMed
Summary
This summary is machine-generated.

We developed a block-wise Direct Cosine Transform Efficient Flexible Representation of Quantum Image (DCT-EFRQI) method for efficient quantum image compression. This approach significantly improves representation and reduces qubit usage compared to existing quantum image methods.

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Area of Science:

  • Quantum computing
  • Image processing
  • Quantum information science

Background:

  • Quantum image computing offers faster data processing than classical computers.
  • Efficiently representing and compressing large quantum images remains a significant challenge.
  • Existing quantum image representation methods require substantial computational resources.

Purpose of the Study:

  • To propose an efficient block-wise Direct Cosine Transform Efficient Flexible Representation of Quantum Image (DCT-EFRQI) approach.
  • To represent and compress grayscale images within a quantum computer.
  • To reduce computational time and the number of quantum bits (qubits) required for state preparation.

Main Methods:

  • Implemented a block-wise DCT transformation within the quantum domain.
  • Utilized the Quirk simulation tool to design the quantum image circuit.
  • Employed 17 qubits for representing coefficients, auxiliary states, and positional information.

Main Results:

  • The proposed DCT-EFRQI approach uses 8 qubits for coefficient values and the remaining for positional information and an auxiliary qubit.
  • Demonstrated the effectiveness of block-wise DCT and Discrete Wavelet Transform (DWT) in the quantum domain.
  • Achieved superior rate-distortion performance compared to DCT-GQIR, DWT-GQIR, and DWT-EFRQI.

Conclusions:

  • The block-wise DCT-EFRQI scheme offers a more efficient method for quantum image representation and compression.
  • This method effectively reduces qubit requirements and computational overhead.
  • The findings suggest a promising direction for advancing quantum image processing capabilities.