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Comparison of Phase Accuracy in FFT Codes for Sinusoidal Signals with Gaussian Noise

This study compares the phase and frequency accuracy obtained from different FFT codes, namely All-Phase FFT, Matlab FFT, and SUSSIX-FFT, when analyzing ideal sinusoidal signals with specific phase advances as seen in SPS FODO lattices. The analysis also incorporates additive Gaussian noise, evaluating performance under conditions of both no noise and 10% Gaussian noise. Methodologies applied include tracking phase advances across varying impedance strengths, revealing distinct variations in rms values for phase advances of 90 degrees and 67 degrees in low gamma lattices, aimed at enhancing the resolution of phase determination.

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Comparison of Phase Accuracy in FFT Codes for Sinusoidal Signals with Gaussian Noise

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  1. Phase advance accuracy (rms value) Comparing the phase accuracy got by different FFT codes, All-phase FFT (see article on footnote), Matlab FFT, and SUSSIX-FFT, in case of ideal sinusoidal signals with phase advance typical for SPS FODO lattice, and adding additive gaussian noise. No noise case 10% Gaussian noise * “NEW METHOD OF ESTIMATION OF PHASE ,AMPLITUDE, AND FREQUENCY BASED ON ALL PHASE FFT SPECTRUM ANALYSIS” Huang Xiaohong, Wang Zhaohua, HouGuoqiang.

  2. Phase advance accuracy on 90deg lattice (rms value) Methodology: 1- Put 1 Impedance source (MKPA.11936) 2- Track HEADTAIL multi-kick code and get phase advances with Matlab. 3- Do the same increasing the wake field strength with factors [x1 x10 x20] Phase advance rms values for different phase advances and different impedance strength Obs: I measured M=var(ΣX)=Σvar(X)=N var(X) in case of N indipendent measurements -> std(X)=sqrt(var(X))=sqrt(M/N).

  3. Phase advance accuracy on 67deg (low γ) lattice (rms value) Methodology: 1- Put 1 Impedance source (MKPA.11931) 2- Track HEADTAIL multi-kick code and get phase advances with Matlab.

  4. Frequency accuracy (rms value) Comparing the frequency accuracy got by different FFT codes, in case of ideal and noisy sinusoidal signals with phase advance typical for SPS FODO lattice, as done before for the phase. No noise case 10% Gaussian noise

  5. Some quick comparison: using ap-FFT for simulation data increase the accuracy in phase determination for the tracked signals. This permits to gain a better resolution in reconstruction (avoids peaks forest at the end). Using Ap-FFT Using Matlab-FFT Example of localization with a low gamma lattice using ap-FFTandmatlab FFT.

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