Hanning window

Hair cells, 240, 243, 245, 259 Hammond organs, 336 Hankel norm, 453 Hanning window, 14, 16 Harmonicity, 315... 

Several odier MA methods have been proposed in die literature, two of die best known being die Hanning window (named after Julius Von Hann) (which for 3 points has weights 0.25, 0.5 and 0.25), and the Hamming window (named after R. W. Hamming) (which for 5 points has weights 0.0357, 0.2411, 0.4464, 0.2411, 0.0357) - not to be confused in name but very similar in effects. These windows can be calculated for any size, but we recommend diese two filter sizes. 

Each type of smoothing function removes different features in the data and often a combination of several approaches is recommended especially for real world problems. Dealing with outliers is an important issue sometimes these points are due to measurement errors. Many processes take time to deviate from the expected value, and a sudden glitch in the system unlikely to be a real effect. Often a combination of filters is recommend, for example a five point median smoothing followed by a three point Hanning window. These methods are very easy to implement computationally and it is possible to view the results of different filters simultaneously. 

From top to bottom a three point moving average, a Hanning window and a five point Savitsky-Golay quadratic derivative window... 

Re-smoodi die three point median smoothed data by a furdier diree point median smoothing function (denoted by 33 ) and dien further by a Hanning window of die form Xj = 0.25a, + 0.5a-, + 0.25.v,+ (denoted by 33H ), plotting bodi graphs as appropriate. 

Smoodi die rough obtained from die 33 dataset in point 2 by a Hanning window, and plot a graph. 

Ignore for now the input boxlabeled Adjustable Hanning Window when it shows, just enter 0. 

For deconvolution, the macro incorporates a Hanning window of adjustable width the default setting, w = 0, corresponds to a rectangular window (i.e., the absence of filtering) w = 1 yields the standard Hanning window while w > 1 gives an extra-narrow window (more noise rejection, and more distortion). 

Figure 14.1 Basic operation of the PSOLA algorithm, (a) A section of voiced waveform, with epoch positions shown by the arrows, (b) For every epoch, a frame centred on the epoch is created. Here, a series of harming windows is shown note that the windows overlap, (c) The sequence of separate frames created by the hanning-window process. Each is centred on the epoch, which in this case is the point of maximum positive excursion, (d) A waveform resynthesised by overlapping and adding the separate frames, with positions governed by the original epoch positions. This results in a perceptually identical waveform to the original.

Example Figure 6.2 depicts the STFT of the two signals introduced in the previous example. A 21-point Hanning window function is used for this example, and the window functions overlapped half of the previous window when translated. One can now observe the difference in the signal characteristics as the non-stationary signal yields a STFT that sharply delineates the transition period. 

Fig. 4.4 The H K-edge EXAFS shown as a the normalised absorption against energy, hk xik) against q, and c) /(r) against r. The black broken line in b shows the Hanning window function applied for the Eourier transform to real space. The vertical grey broken line in c illustrates the constancy of the peak position. In all diagrams BTO glass (red), Nd doped BTO (blue), Gd doped BTO (green), and Er doped BTO (pink). Traces have been shifted up for clarity as indicated...

R wave detection is processed automatically from long term ECG data, RR interval time-series data is built. RR interval data are re-sampled at 4 Hz after spline interpolation, a heart rate variability spectrum was calculated with a serial EFT using a Hanning window. A conventional LF/HF power ratio was used as the sympathetic nervous index. Frequency ranges are as follows LF 0.04 - 0.15 Hz, HF 0.15 - 0.40 Hz [6]. The length of data points for EFT can be set to any integer in this algorithm. 

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