Read the knowledge base article "Amplitude and Energy correction factors" to learn more about amplitude and energy correction due to windows. Email peter. We now have a free online Windows and Leakage Interactive Simulation on our website that many who come to this page may find useful. As per the topic of this page, it demonstrates the Effects of Different Windows e. Kevin Grenier Siemens Employee. See reponse to the same question on the other Knowledge base article you responded to.
Roy, you can find more in the literature, but here is some information:. The Tukey window can be regarded as a rectangular window with the first and last percent of the samples equal to parts of a cosine. The width of the cosine is adjustable via the parameter taper length in percentage.
The exponential window assumes the test object is at rest at the beginning of time T for each FFT or each average. That is why it normally is only used during a modal impact test where the article is at rest, we hit with a hammer and if we wait long enough it comes back to rest. As stated above we can remove its effects during modal analsysis, If the object is not at reast at the begininning of each FFT or each average, do not use the exponential window.
What's the disadvantage of Tukey and Exponential Windows? Topics Show Topics. Siemens Digital Industries Software. Search the Community. Close search. Information Title. URL Name. Summary Briefly describe the article. The summary is used in search results to help users find relevant articles. You can improve the accuracy of search results by including phrases that your customers use to describe this issue or topic.
Details Provide information and steps to answer the question or resolve the issue. Use formatting like numbered lists for steps that must be followed in order. Include a description of the cause of the issue if known and applicable so the reader understands why they encountered the issue. The details and tradeoffs of the following windows will be covered in this article: Hanning Flattop Uniform Tukey Exponential Throughout the article, the term measurement time refers to the amount of time to acquire a single average or FFT of data.
Periodic versus Non-Periodic Background Before delving into the specifics of each window, it is helpful to understand spectral leakage in light of signals captured in a periodic or non-periodic manner. When performing a Fourier Transform on measurement data, a window affects periodic and non-periodic data differently: Periodic No Window needed : A signal captured in a periodic manner does not require a window, and a resulting Fourier Transform has no leakage.
Applying a window alters the resulting Fourier transform, and even creates spectral leakage where there would have been no leakage otherwise. Non-periodic Window needed : Windows are used on signals that are captured in a non-periodic manner to reduce spectral leakage and get closer to the periodic results.
A window can minimize the leakage present in a non-periodic signal, but cannot eliminate it. Figure 1: Sine wave collected with measurement time that results in a periodic signal For a periodic signal, the Fourier Transform of the captured signal will have no leakage in the frequency domain, as shown in Figure 3.
Figure 2: Sine wave collected with measurement time that results in a non-periodic signal Here, when the captured signal is repeated, the original sine wave signal is not re-created. Figure 3: Fourier Transform of a periodically captured sine wave red versus a non-periodically captured sinewave green Windows are used to minimize this leakage effect in the frequency domain.
Hanning When doing operational noise and vibration measurements, the Hanning window is commonly used.
Figure 4: Hanning window middle is applied to random data upper left to smooth abrupt ends lower right and reduce leakage in the resulting Fourier Transform not pictured Random data has spectral leakage due to the abrupt cutoff at the beginning and end of the time block.
Figure 5: Left — Time domain shape of Hanning window, Right — Frequency domain effect of Hanning window on periodic and non-periodic sine wave relative to the measurement time In Figure 6 , a periodic sine wave is shown with and without a Hanning window applied.
Figure 6: The periodically captured sine wave with the Hanning window blue is wider in frequency than the original signal red When a Hanning window is applied to a non-periodic signal, as shown in Figure 7 , the leakage is greatly reduced and the amplitude is higher. Figure 7: A non-periodically captured sine wave magenta has a spectral leakage over the entire bandwidth, applying a Hanning window minimized the leakage green The maximum amplitude error can be seen when viewing the spectrum of a non-periodic sine wave.
Flattop The Flattop window has a better amplitude accuracy in frequency domain compared to the Hanning window Figure 9. Figure 9: Differences between Hanning and Flattop window for periodic left and non-periodic sine wave right A Flattop window confines leakage to 3. Figure Left — Time domain shape of Flattop window, Right — Frequency domain effect of Flattop window on periodic and non-periodic sine wave relative to measurement time The frequency accuracy of the Flattop window is more coarse compared to a Hanning window.
Uniform A Uniform window has a value of 1. Figure Left — Time domain shape of Uniform window, Right — Frequency domain effect of Uniform window on periodic and non-periodic sine wave relative to the measurement time A Uniform window creates no frequency or amplitude distortion when the measured signal is periodic. Tukey A Tukey window is very flat in the time domain, close to a value of 1. Figure Because the Tukey window is close to one for a longer period of time left than a Hanning window right , it is better suited to capture the amplitude of transient events Typical impact events may last a few milliseconds.
Exponential Exponential windows are often used in modal impact testing. Figure The accelerometer signal upper left of a modal impact test is multiplied by an exponential window middle to ensure the windowed signal decays completely to zero lower right to avoid leakage An exponential window always starts at a value of 1. Figure Applying an exponential window to a signal makes it appear to decay more quickly, giving the appearance of added damping By decaying faster, artificial damping is added to the resulting measurement.
Conclusions Selecting a window to match the measurement data circumstances is important to get accurate and useful data. Additional Note on Window Correction Factors Windows affect both the amplitude and frequency content of a signal. What is Fourier Transform? Filter Feed Refresh this feed. Skip Feed View This Post. July 30, at AM. Dear Signal Processing Enthusiasts, We now have a free online Windows and Leakage Interactive Simulation on our website that many who come to this page may find useful.
In 2 , we impose a weighting function over the rectangular window. Why would we do this? For example, the sharp edges of the rectangular window in time introduce broad spectral content. And, broad spectral content is detrimental to spectral analysis. Imagine a rectangular window that's multiplied by a bell-shaped curve - clearly this will remove the sharp transitions at the ends and reduce the broad spectral energy that the sharp edges contain.
A good deal of effort has gone into analyzing and designing such "windows" or "weighting functions" with the idea of helping one understand their characteristics and to help one implement them efficiently. Some key references are:. Nuttall, A.
February ASSP 84— Temes, V. Barcilon, and F. Marshall III. The optimization of bandlimited systems. IEEE, Vol 61, pages , I think windowing is needed out of practical reasons. In the context of signal processing, almost all signals we are interested in are restrained to a certain period of time For example, In a radar system, we usually analysis the received signal within a duration of a few pulses , thus by windowing we get useful signals. In the context of filter design, there is a filter type of FIR finite impluse reponse , the design technique lies on windowing.
There are plenty of prototypes out there, all you need to do is to apply windowing and make it implementable and computational effective. It is deeply and fundamentally mathematical. It is actually related to Heisenberg's uncertainty and is called The Gabor Limit. The more precise you know things in time, the less precisely you can know their frequency To demonstrate The best we can hope for is a tapering where some time or frequency region is significant and outside of that region the information has been "Windowed-out" to become insignificant.
Window shapes in the time or frequency domains are chosen to optimize some needed parameter. Sometimes that optimization is selecting single-frequency boomer out of the otherwise flat background noise, for this a Dolph is optimal, and a Blackman-Harris is really fast and easy to calculate.
Sometimes, we need the least distortion of the peak amplitude for some spectral analysis reason. At this point you might get Remez going or use one of the Flat-Top windows. For example, a rectangular window i. Below is an example, written in Python, of how to programmatically generate a sample sine wave and either a rectangular or Hamming window and then apply the window to the generated signal and visualise the output. Figure 2 is a visualisation of the application of a Hamming window to the raw signal from Figure 1.
Figure 2 Sine wave with Hamming window applied. Primary Use Cases One primary application of window functions is to mitigate against spectral leakage [2] during transform functions. Reference Implementation Below is an example, written in Python, of how to programmatically generate a sample sine wave and either a rectangular or Hamming window and then apply the window to the generated signal and visualise the output. References Rorabaugh, C. DSP Primer. Harris, F.
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