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Frequency-Domain Implementation of the

Blackman-Harris Family

The Blackman-Harris window family can be very efficiently implemented in the frequency domain as a -point convolution with the spectrum of the unwindowed data.

For example, to implement a zero-phase Hann window,

- Start with a length rectangular window
- Take an -point DFT
- Convolve the DFT data with the 3-point smoother

*no multiplies*in linear fixed-point data formats [188].

Similarly, any Blackman window may be implemented as a 5-point smoother in the frequency domain. More generally, any -term Blackman-Harris window requires convolution of the critically sampled spectrum with a smoother of length .

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Power-of-Cosine Window Family

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Three-Term Blackman-Harris Window