289
FFT Analysis Modes
13.9.2 Analysis Mode Functions
Analysis mode
Internal analysis formula (linear, real, imag [imaginary], log [logarithm])
OFF
No analysis
Storage Waveform
Waveform obtained by applying the window function to a time-domain waveform
Histogram
Counts amplitude data
Linear Spectrum
𝑋𝑋(𝑘𝑘) = ∑ 𝑥𝑥(𝑛𝑛)𝑊𝑊
𝑘𝑘𝑘𝑘
𝑁𝑁−1
𝑘𝑘=0
𝐹𝐹(𝑘𝑘) = 𝐶𝐶𝑋𝑋(𝑘𝑘) 𝐶𝐶 {1/𝑁𝑁(𝐷𝐷𝐶𝐶)
2/𝑁𝑁(𝐴𝐴𝐶𝐶)
𝑙𝑙𝑙𝑙𝑛𝑛𝑙𝑙𝑙𝑙𝑙𝑙 = |𝐹𝐹(𝑘𝑘)| 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = Re{𝐹𝐹(𝑘𝑘)} 𝑙𝑙𝑖𝑖𝑙𝑙𝑖𝑖 = Im{𝐹𝐹(𝑘𝑘)} log = 20log|𝐹𝐹(𝑘𝑘)|
RMS Spectrum
𝐹𝐹′(𝑘𝑘) = 𝐶𝐶′𝐹𝐹(𝑘𝑘) 𝐶𝐶′ {
1 (𝐷𝐷𝐶𝐶)
1/√2(𝐴𝐴𝐶𝐶)
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = |𝐹𝐹′(𝑘𝑘)| 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = Re{𝐹𝐹′(𝑘𝑘)} 𝑙𝑙𝑖𝑖𝑙𝑙𝑖𝑖 = Im{𝐹𝐹′(𝑘𝑘)} log = 20log|𝐹𝐹′(𝑘𝑘)|
Power Spectrum
𝑃𝑃(𝑘𝑘) = 𝑎𝑎|𝐹𝐹(𝑘𝑘)|
2
𝑎𝑎 = {1 (𝐷𝐷𝐷𝐷)
1/2 (𝐴𝐴𝐷𝐷)
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑎𝑎𝑙𝑙 = 𝑃𝑃(𝑘𝑘) log = 10log|𝑃𝑃(𝑘𝑘)|
Power Spectrum Density
𝑃𝑃′(𝑘𝑘) = 𝑃𝑃(𝑘𝑘)/𝛿𝛿𝛿𝛿 𝛿𝛿𝛿𝛿
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑃𝑃′(𝑘𝑘) log = 10log|𝑃𝑃′(𝑘𝑘)|
Frequency resolution
𝑃𝑃′(𝑘𝑘) = 𝑃𝑃(𝑘𝑘)/𝛿𝛿𝛿𝛿 𝛿𝛿𝛿𝛿
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑃𝑃′(𝑘𝑘) log = 10log|𝑃𝑃′(𝑘𝑘)|
LPC analysis (Power
Spectrum Density)
(Omission) Spectrum approximation from Linear Predictive Coding
Refer to “Linear Time-Invariant Systems” (p. A14).
Transfer Function
𝐻𝐻(𝑘𝑘) = 𝑌𝑌(𝑘𝑘)/𝑋𝑋(𝑘𝑘)
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = |𝐻𝐻(𝑘𝑘)| 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = Re{𝐻𝐻(𝑘𝑘)} 𝑙𝑙𝑖𝑖𝑙𝑙𝑖𝑖 = Im{𝐻𝐻(𝑘𝑘)} log = 20log|𝐻𝐻(𝑘𝑘)|
Cross Power Spectrum
𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘) = 𝑋𝑋
∗
(𝑘𝑘)𝑌𝑌(𝑘𝑘):
𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘) = 𝐴𝐴𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘) 𝐴𝐴 = {1/𝑁𝑁
2
2/𝑁𝑁
2
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = |𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘)| 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = Re{𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘)}
𝑙𝑙𝑖𝑖𝑙𝑙𝑖𝑖 = Im{𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘)} log = 10log|𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘)|
𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘) = 𝑋𝑋
∗
(𝑘𝑘)𝑌𝑌(𝑘𝑘):
𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘) = 𝐴𝐴𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘) 𝐴𝐴 = {1/𝑁𝑁
2
2/𝑁𝑁
2
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = |𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘)| 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = Re{𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘)}
𝑙𝑙𝑖𝑖𝑙𝑙𝑖𝑖 = Im{𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘)} log = 10log|𝑋𝑋
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
(𝑘𝑘)|
Cross spectrum
Impulse Response
ℎ(𝑛𝑛) =
1
𝑁𝑁 ∑
𝑌𝑌(𝑘𝑘)
𝑋𝑋(𝑘𝑘) 𝑊𝑊
−𝑘𝑘𝑛𝑛
𝑁𝑁−1
𝑘𝑘=0
Coherence Function
𝑐𝑐𝑐𝑐ℎ(𝑘𝑘) = √
𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘)𝑆𝑆
𝑦𝑦𝑦𝑦
∗
(𝑘𝑘)
𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘)𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘)
Phase Spectrum
𝜃𝜃(𝑘𝑘) = 180/𝜋𝜋 × tan
−1
(Im(𝐹𝐹
′
(𝑘𝑘))/Re(𝐹𝐹
′
(𝑘𝑘))
𝜃𝜃(𝑘𝑘) = 180/𝜋𝜋 × tan
−1
(Im(𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘))/Re(𝑆𝑆
𝑦𝑦𝑦𝑦
(𝑘𝑘))
Auto-correlation Function
𝑅𝑅
𝑥𝑥𝑥𝑥
(𝑛𝑛) =
1
𝑁𝑁 ∑
|𝑋𝑋(𝑘𝑘)|
2
𝑊𝑊
−𝑘𝑘𝑘𝑘
𝑁𝑁−1
𝑘𝑘=0
(recursive convolution)
Cross-correlation Function
𝑅𝑅
𝑦𝑦𝑥𝑥
(𝑛𝑛) =
1
𝑁𝑁 ∑ 𝑆𝑆
𝑦𝑦𝑥𝑥
(𝑘𝑘)𝑊𝑊
−𝑘𝑘𝑘𝑘
𝑁𝑁−1
𝑘𝑘=0
(recursive convolution)
1/1 Octave Analysis
(Omission)
1/3 Octave Analysis
(Omission)
13
FFT
Function
Содержание MR8827
Страница 19: ...14 Operation Precautions ...
Страница 81: ...76 Start and Stop Measurement ...
Страница 111: ...106 Manage Files ...
Страница 125: ...120 Miscellaneous Printing Functions ...
Страница 143: ...138 View Block Waveforms ...
Страница 191: ...186 Setting Output Waveform Parameters ...
Страница 291: ...286 FFT Analysis Modes Measurable Ranges With Octave Analysis 1 1 OCT 1 3 OCT ...
Страница 292: ...287 FFT Analysis Modes 1 1 OCT 1 3 OCT 13 FFT Function ...
Страница 293: ...288 FFT Analysis Modes 1 1 OCT 1 3 OCT ...
Страница 295: ...290 FFT Analysis Modes ...
Страница 309: ...304 Editor Command Details ...
Страница 387: ...382 Module Specifications ...
Страница 405: ...400 Dispose of the Instrument Lithium Battery Removal ...
Страница 431: ...A26 FFT Definitions ...
Страница 436: ......