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Related Concept Videos

Discrete-time Fourier transform01:26

Discrete-time Fourier transform

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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.
One of the notable...
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Discrete Fourier Transform01:15

Discrete Fourier Transform

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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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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.
The computational efficiency of the FFT becomes...
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

385
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]...
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Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

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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...
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Phasor Arithmetics01:13

Phasor Arithmetics

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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.
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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High-dimensional discrete Fourier transform gates with a quantum frequency processor.

Hsuan-Hao Lu, Navin B Lingaraju, Daniel E Leaird

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    Summary
    This summary is machine-generated.

    We demonstrate a scalable method for performing discrete Fourier transforms (DFTs) in photonic quantum information using a fixed quantum frequency processor. This approach enhances high-dimensional frequency-bin protocols for quantum communications.

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    Area of Science:

    • Quantum Information Science
    • Photonics
    • Quantum Computing

    Background:

    • The discrete Fourier transform (DFT) is crucial for quantum information processing.
    • Scaling DFTs to high dimensions in frequency-bin platforms remains a challenge.
    • Practical implementation methods for high-dimensional frequency-bin DFTs are needed.

    Purpose of the Study:

    • To develop a scalable method for realizing high-dimensional discrete Fourier transforms (DFTs) in frequency-bin photonic systems.
    • To demonstrate a fixed quantum frequency processor (QFP) capable of implementing d-point DFTs by adding RF harmonics.
    • To experimentally validate the proposed method for quantum communication and networking applications.

    Main Methods:

    • Utilizing a fixed three-component quantum frequency processor (QFP).
    • Implementing d-point frequency-bin DFTs by adding one radio-frequency harmonic per dimension increase.
    • Performing numerical simulations to verify gate fidelity and success probability.
    • Experimentally implementing DFT for d=3 and performing parallel DFT measurements.

    Main Results:

    • Achieved high gate fidelity (F_W > 0.9997) and success probability (P_W > 0.965) up to d=10 in simulations.
    • Successfully implemented the DFT for d=3 experimentally.
    • Quantified entanglement and performed tomography of multi-photon states using parallel DFTs.

    Conclusions:

    • The proposed method offers a scalable and practical approach for high-dimensional DFTs in frequency-bin photonic systems.
    • This technique enables new opportunities for advanced quantum communication and networking protocols.
    • The fixed QFP design simplifies the implementation of complex quantum frequency-bin operations.