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    短時傅立葉變換 Short-Time Fourier Transform STFT
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    http://youtu.be/JcC1PBxsyjo
    http://youtu.be/mV8RBGiaItk

    This is module in AutoSignal

    在光譜菜單短時傅里葉變換頻譜選項或工具欄光譜配料傅立葉光譜信息的非平穩數據。就像在分段數據選項的傅立葉光譜,該短時傅立葉變換是基於一系列橫跨在數據流中發生的分割和重疊的FFT的。在短時傅立葉變換,從這些多段個人的FFT呈現為任何一個3D曲面圖(或二維等高線圖) 。既給數據系列的時頻特性的一個很好的跡象。該STFT因此可用於評估一個信號是否是靜止的。

    在此選項中,窗口幾乎總是用來銳化的時間分辨率以及降低頻譜洩漏。對於每個單獨的FFT,分配時間是該段(錐形窗口中的數據的峰值)的中心。在短時傅立葉變換,重疊線段的目標是不產生平均光譜具有減小方差的估計的功率,而是以產生用於數據的時間 - 頻率表示。冗餘(重疊)的高度可能會導致更精確的時間 - 頻率頻譜。

    由於STFT是基於FFT的,有頻率之間的固定的分辨率。頻率分辨率被設置主要由鏈段的大小,雖然一些好處可能使用更高的計數(零填充)的FFT ,使用小的段大小,尤其是當得到。段的大小也決定了在一個單一的FFT處理後的整個數據流的百分比。因此,時間分辨率也被固定的段大小(以及在較小程度上由數據錐形窗口的銳度) 。段的大小從而控制頻率分辨率和時間分辨率之間的折衷,而且它是恆定的無處不在的時間 - 頻率頻譜。優化STFT通常涉及(1)找到相應的分段大小,(2)通過調節段之間的冗餘或重疊量設定密度在時間,(3)零填充了FFT為小的段大小,以更好地呈現的頻譜最大值,和(4)選擇適當的數據錐形窗口。

    因此, STFT被歸類為固定的或單一的解決方法時頻分析。優化STFT可能需要一些努力。在許多情況下,一個多分辨率分析更易於使用和更健壯。在高頻時,很短的時間段通常是足以捕獲所需的光譜信息。在另一方面,在低頻率通常最好使用一個較長的時間段來收集有關的振盪足夠的信息。以這種方式調整這個時間 - 頻率分辨率折衷的能力是小波分析的一個組成部分。在一般情況下,連續小波頻譜將提供的時間 - 頻率空間比STFT更好的整體畫面。

    STFT的確實是有優勢的,當涉及到渲染權力。它可以整合一個三維小波頻譜,以獲得功率只是因為它能夠整合STFT和從卷解壓縮表面下的功率信息。小波分析的多分辨特性使得不可能的,但是,直接從在小波頻譜的三維峰的幅度得到相對功率。該STFT確實提供了這個屬性,其中電源是線性正比的峰的高度。它也是一件簡單的事了STFT提供一個幅度情節選項。
    該STFT通常涉及(1)找到相應的分段大小,(2)通過調節段之間的冗餘或重疊量設定密度在時間,(3)零填充了FFT為小的段大小,以更好地呈現的頻譜最大值以及(4)選擇適當的數據錐形窗口。

    因此, STFT被歸類為固定的或單一的解決方法時頻分析。優化STFT可能需要一些努力。在許多情況下,一個多分辨率分析更易於使用和更健壯。在高頻時,很短的時間段通常是足以捕獲所需的光譜信息。在另一方面,在低頻率通常最好使用一個較長的時間段來收集有關的振盪足夠的信息。以這種方式調整這個時間 - 頻率分辨率折衷的能力是小波分析的一個組成部分。在一般情況下,連續小波頻譜將提供的時間 - 頻率空間比STFT更好的整體畫面。

    STFT的確實是有優勢的,當涉及到渲染權力。它可以整合一個三維小波頻譜,以獲得功率只是因為它能夠整合STFT和從卷解壓縮表面下的功率信息。小波分析的多分辨特性使得不可能的,但是,直接從在小波頻譜的三維峰的幅度得到相對功率。該STFT確實提供了這個屬性,其中電源是線性正比的峰的高度。它也是一件簡單的事了STFT提供一個幅度情節選項。

     

    The Short-Time Fourier Transform Spectrum option in the Spectral menu or the Spectral toolbar furnishes Fourier spectral information for non-stationary data. Much as in the Fourier Spectra of Segmented Data option, the STFT is based upon a series of segmented and overlapped FFTs that occur across the data stream. In the STFT, the individual FFTs from these multiple segments are rendered as either a 3D surface plot (or a 2D contour plot). Both give a good indication of the time-frequency properties of the data series. The STFT can thus be used to assess whether or not a signal is stationary.

    In this option, windowing is almost always used to sharpen the resolution in time as well as to reduce spectral leakage. For each individual FFT, the time assigned is that of the center of the segment (the peak of the data tapering window). In the STFT, the goal of the overlapping segments is not to produce an average spectrum with a reduced variance for the estimated power, but rather to produce a time-frequency representation for the data. A high degree of redundancy (overlap) can result in a more accurate time-frequency spectrum.

    Since the STFT is based upon the FFT, there is a fixed resolution between frequencies. The frequency resolution is set mainly by the size of the segment, although some benefits may be derived from using a higher count (zero-padded) FFT, especially when using small segment sizes. The segment size also determines the percent of the overall data stream processed in a single FFT. Thus the time resolution is also fixed by the segment size (and to a much lesser extent by the sharpness of the data tapering window). The segment size thus controls the tradeoff between frequency resolution and time resolution, and it will be constant everywhere in the time-frequency spectrum. Optimizing the STFT usually involves (1) finding an appropriate segment size, (2) setting the density in time by adjusting the amount of redundancy or overlap between the segments, (3) zero-padding the FFT for small segment sizes to better render spectral maxima, and (4) choosing an appropriate data tapering window.

    The STFT is thus classified as a fixed or single resolution method for time-frequency analysis. Optimizing the STFT can require some effort. In many instances, a multiresolution analysis is simpler to use and more robust. At high frequencies, a short time segment is often sufficient to capture the necessary spectral information. On the other hand, at low frequencies it is usually better to use a longer time segment to gather sufficient information about the oscillation. The ability to adjust this time-frequency resolution tradeoff in this manner is an integral part of wavelet analysis. In general, continuous wavelet spectra will offer a better overall picture of time-frequency space than the STFT.

    The STFT does have an advantage when it comes to rendering powers. It is possible to integrate a 3D wavelet spectrum in order to get power just as it is possible to integrate the STFT and extract power information from the volume under the surface. The multiresolution property of wavelet analysis makes it impossible, however, to get relative powers directly from the magnitude of the 3D peaks in the wavelet spectrum. The STFT does offer this property where the power is linearly proportional to the height of the peaks. It is also a simple matter for the STFT to offer an amplitude plot option.