Blackman-Harris function

The FWHH of the ILS function given by the Happ-Genzel function is close to that of the Norton-Beer strong apodization function. Another common function that strongly suppresses the sidelobe amplimde is the Blackman-Harris function,... 

Figure 5.3. Various apodization functions (left) and the instrumental lineshape produced by them (right) (a) boxcar truncation (b) triangular (c) trapezoidal (d) Norton-Beer weak, medium, and strong (e) Happ-Gen-zel (f) Blackman-Harris 3-term and 4-term. The maximum retardation is set to / = 1. In the Fourier transform the FWHH of the main lobe is indicated.

The coefficient A, of the three functions Happ-Genzel, Blackman-Harris three term, and Blackman-Harris four term are summarized in Tab. 5.2. 

Table 5.2. Coefficients of the Happ enzel and Blackman-Harris apodization functions.

There are other apodization functions in use besides the Norton-Beer and the Happ-Genzel. These functions have not been tested as thoroughly however, it has been noted by the authors that the Blackman-Harris and Blackman apodization functions (Section 2.4) are considerably broader than the Norton-Beer medium or Happ-Genzel apodization functions. It is expected that these functions will not adhere to Beer s law as well as the Norton-Beer medium function. 

Windows are weighting functions applied to data to reduce the order of the discontinuity at the boundary of the periodic extension. Harris [71] has given a comprehensive review of the properties of over 30 windowing functions and we illustrate their properties with reference to a Blackman window, W. ... 

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