Spectrum Analysis Tutorial, Part 2: Properties and Applications of the Discrete Fourier Transform

1987 ◽  
Vol 11 (3) ◽  
pp. 17 ◽  
Author(s):  
David A. Jaffe
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Spectrum Analysis

Comments on Errors of DFT Spectrum

2014 ◽  
Vol 568-570 ◽  
pp. 189-192
Author(s):  
Feng Han ◽  
Yao Lin Liu ◽  
Zhen Liu ◽  
Hai Dong Zeng
Keyword(s):  
Fourier Transform ◽  
Error Analysis ◽  
Energy Loss ◽  
Discrete Fourier Transform ◽  
Spectrum Analysis ◽  
Analytical Error ◽  
Error Estimators ◽  
Asynchronous Sampling ◽  
Parseval’S Theorem ◽  
Further Development

Discrete Fourier transform (DFT/FFT) spectrums contain a variety of inherent errors in asynchronous sampling. Spectrum analysis with the accuracy above 10-3 are generally challenging issues. This work divides the DFT procedure into four signal transforms and exams six spectrum errors originated from these distortions. Besides the review of traditional errors, a so-called energy loss-gain (ELG) error is briefly introduced, which is proved to be a considerable error on the basis of Parseval's theorem. With the help of full error analysis mentioned here and the further development of analytical error estimators, it is expectable to obtain a DFT spectrum with a specified accuracy.

The Research and Improvement of APFFT Algorithm

2012 ◽  
Vol 532-533 ◽  
pp. 1841-1845
Author(s):  
Jie Tao Diao ◽  
Jing Guo ◽  
Nan Li ◽  
Wei Yi ◽  
Sen Liu ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Discrete Fourier Transform ◽  
Spectrum Analysis ◽  
Spectral Leakage ◽  
Overlapping Data

Discrete Fourier Transform (DFT) is widely used in spectrum analysis. All Phase Fast Fourier Transform (APFFT) is proposed to improve FFT. It has merits such as phase invariance and small spectral leakage. But APFFT is a concrete algorithm. There are no parameters to adjust the result. The paper researches APFFT by changing the length of the overlapping data segments of APFFT. This change gives APFFT some new characteristic and some meaningful results are got.

scholarly journals Non-Distorted Optimization Spectrum Analysis

Energies ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 1841
Author(s):  
Rong-Ching Wu ◽  
Li-Ju Huang
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Spectrum Analysis ◽  
Time Frequency ◽  
Frequency Scale ◽  
Signal Parameters ◽  
Signal Characteristics ◽  
Sampled Signal ◽  
Three Stages ◽  
The Ideal

The discrete Fourier transform is extensively applied in spectrum analysis. However, the sampled signal is random, and the discrete Fourier transform has its own specific limitations. Thus, errors will inevitably occur in time–frequency transformation work. The most common are the leakage effects of the spectrum that are caused from the scale of the spectrum not being able to match the characteristics of the signal. The optimal spectrum is proposed to overcome this defect by adjusting the frequency scale to fit signal characteristics. This includes three stages whereby frequency scale can match signal characteristics. Firstly, the signal parameters must be found. Secondly, the frequency scale can be determined from these signal parameters. Finally, the optimal spectrum can be realized using the adjustable spectrum with the new frequency scale. After processing the optimal spectrum, the leakage effects of the signal will be decreased to a minimum. This method preserves signal characteristics in the optimization process, which reaches the ideal of non-distortion.

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