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
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