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A PWI of 99% indicates that the profile runs at the edge of the process window. [6] For example, if the process mean is set at 200 °C, with the process window calibrated at 180 °C and 220 °C respectively; then a measured value of 188 °C translates to a process window index of −60%. A lower PWI value indicates a more robust profile.
A thermal profile can be ranked on how it fits in a process window (the specification or tolerance limit). [1] Raw temperature values are normalized in terms of a percentage relative to both the process mean and the window limits. The center of the process window is defined as zero, and the extreme edges of the process window are ±99%. [1]
The formulas provided at § Examples of window functions produce discrete sequences, as if a continuous window function has been "sampled". (See an example at Kaiser window.) Window sequences for spectral analysis are either symmetric or 1-sample short of symmetric (called periodic, [4] [5] DFT-even, or DFT-symmetric [2]: p.52 ).
The process window is a graph with a range of parameters for a specific manufacturing process that yields a defined result. Typically multiple parameters are plotted in such a graph with a central region where the process behaves well, while the outer borders define regions where the process becomes unstable or returns an unfavourable result.
The function is named in honor of von Hann, who used the three-term weighted average smoothing technique on meteorological data. [6] [2] However, the term Hanning function is also conventionally used, [7] derived from the paper in which the term hanning a signal was used to mean applying the Hann window to it.
Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for only a short period of time. The Fourier transform (a one-dimensional function) of the resulting signal is taken, then the window is slid along the time axis until the end resulting in a two-dimensional representation of the signal.
Left: A continuous function (top) and its Fourier transform (bottom). Center-left: Periodic summation of the original function (top). Fourier transform (bottom) is zero except at discrete points. The inverse transform is a sum of sinusoids called Fourier series. Center-right: Original function is discretized (multiplied by a Dirac comb) (top).
The design of an N-dimensional window particularly a 2-D window finds applications in various fields such as spectral estimation of multidimensional signals, design of circularly symmetric and quadrantally symmetric non-recursive 2D filters, [1] design of optimal convolution functions, image enhancement so as to reduce the effects of data ...