Discrete digital signal hopping sliding discrete Fourier transform method

A discrete Fourier transform and digital signal technology, applied to complex mathematical operations, etc., can solve problems such as quantization errors and HDFT algorithm instability

Inactive Publication Date: 2015-01-07
UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Problems solved by technology

[0006] However, in any step size SDFT (Hopping DFT, HDFT) of the Sample-by-Sample operation mechanism, each iteration operation will introduce The quantization error of the calculation result introduces a cumulative error that increases with the number of iterations. Therefore, there is a potential instability in the HDFT algorithm in practical engineering applications.

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  • Discrete digital signal hopping sliding discrete Fourier transform method
  • Discrete digital signal hopping sliding discrete Fourier transform method
  • Discrete digital signal hopping sliding discrete Fourier transform method

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[0034] Specific embodiments of the present invention will be described below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0035] For a better understanding of the present invention, in a specific embodiment, first transform and modulate a single-step SDFT (Single-step SDFT, SSDFT) based on a sample-by-sample (Sample-by-Sample) operation mechanism. Modulated Single-step SDFT, mSSDFT) transform basic principles and implementation methods are analyzed. On this basis, the SSDFT is extended to a more general random-step SDFT (Hopping DFT, HDFT) algorithm, and the HDFT stability problem is analyzed. Aiming at the problems of potential instability and cumulative errors in HDFT transform in practical...

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Abstract

The invention provides a digital discrete signal hopping sliding discrete Fourier transform method, namely an SDFT (Modulated Hopping DFT, mHDFT) transform method for solving the problem of potential instability and accumulated errors of HDFT transform of an HDFT (hexagon discrete Fourier transform) transform method in practical engineering application. The method utilizes DFT circulating frequency domain shifting characteristics and modified UVT transform for effectively removing twiddle factors in a feedback loop of an HDFT resonator, accurately fixing HDFT poles on a unit circle and obtaining a DFT transform result of a frequency point k at n time, thereby effectively reducing the cumulative errors as well as ensuring the constant stability of the HDFT.

Description

technical field [0001] The invention belongs to the technical field of discrete digital signal processing, and more specifically relates to a sliding discrete Fourier transform (Sliding Discrete Fourier Transform, SDFT) method of an arbitrary step of discrete digital signals. Background technique [0002] Discrete Fourier Transform (DFT), as a bridge between signal time domain and frequency domain conversion, is one of the cornerstones of modern digital signal processing theory. It is widely used in many signal processing fields including high-precision real-time spectrum analysis, spectrum sensing in cognitive radio, and OFDM signal processing in broadband wireless communication. In order to improve the calculation efficiency of the DFT, the Fast Fourier Transform (FFT) algorithm or the Goertzel algorithm is usually used to implement the DFT transform in practical engineering applications. [0003] The FFT algorithm takes advantage of the symmetry and periodicity of the tw...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/14
Inventor 阎啸王茜秦开宇
Owner UNIV OF ELECTRONICS SCI & TECH OF CHINA
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