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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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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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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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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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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Automated Software Acceleration in Programmable Logic for an Efficient NFFT Algorithm Implementation: A Case Study.

Manuel Rodríguez1, Eduardo Magdaleno2, Fernando Pérez3

  • 1Department of Industrial Engineering, Universidad de La Laguna, 38203 San Cristóbal de La Laguna, Spain. mrvalido@ull.edu.es.

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|March 29, 2017
PubMed
Summary
This summary is machine-generated.

This study presents an efficient hardware implementation of the Non-equispaced Fast Fourier Transform (NFFT) using an All-Programmable System-on-Chip (APSoC). The hardware coprocessor significantly accelerates NFFT computations compared to software-only methods.

Keywords:
NFFTSDSoCZynqparallelism techniquessoftware acceleration

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Area of Science:

  • Computer Engineering
  • Digital Signal Processing
  • Algorithm Optimization

Background:

  • The Non-equispaced Fast Fourier Transform (NFFT) is crucial in fields like synthetic aperture radar and medical imaging.
  • High computational complexity of NFFT limits its real-time application.
  • Need for efficient NFFT implementations in demanding scientific and technological domains.

Purpose of the Study:

  • To develop and evaluate an efficient hardware implementation of the NFFT algorithm.
  • To leverage hardware acceleration for improved NFFT computational performance.
  • To explore the use of All-Programmable System-on-Chip (APSoC) for NFFT acceleration.

Main Methods:

  • Implementation of NFFT using a hardware coprocessor on an APSoC.
  • Utilizing an Advanced RISC Machine (ARM) Processing System combined with Programmable Logic.
  • Employing parallelism and pipeline techniques for high-performance digital signal processing.
  • Coding the algorithm in C with pragma directives and using the SDSoC development tool for hardware-software partitioning.

Main Results:

  • The hardware-accelerated NFFT implementation demonstrated significantly superior performance compared to software-based approaches.
  • The APSoC architecture, with its hybrid processing capabilities, effectively handled the computational demands of NFFT.
  • The SDSoC tool facilitated efficient hardware-software co-design and development.

Conclusions:

  • Hardware acceleration using APSoC offers a substantial performance improvement for NFFT computations.
  • The proposed NFFT implementation is suitable for applications requiring high-speed signal processing.
  • The integration of ARM processing systems and programmable logic on APSoCs provides a powerful platform for complex algorithm acceleration.