W I N D O W F U N C T I O N S
A P P E N D I X D
Blackman, Blackman-Harris and Blackman Nutall:
We use Blackman-Harris to design all
filters in the signal processing chain for all modes. This provides for minimal bleed through as
we have described and the best shape factor for our needs in the overlap-save filtering
routines. While it has some good features, these features are probably not ideal for the CW
power spectrum displays. There is a penalty to pay for the smoothing near the ends afforded by
the windows. If you have experience in the use of FFTs and the display of the power spectra
that result, you know that a smaller FFT (smaller DSP Buffer) at a fixed sample rate causes a
wider range of frequencies to be contained in one bin of the power spectral results. This means
that a tone will look more like a large lobe or finger than a tone spike. The same phenomenon
is present in the best windows. While the spreading of the “main lobe” of a tone is not as bad as
taking an FFT of half the size, it is wider than one bin (see also Appendix A). The formulas for
all of the Blackman filters are of this form:
The individual parameters by type:
o
Blackman:
a
0
= 0.42,
a
1
= −0.5,
a
2
= 0.08,
a
3
= 0
o
Blackman Harris:
a
0
= 0.35875,
a
1
= 0.48829,
a
2
= 0.14128,
a
3
= 0.01168
o
Blackman Nuttall:
a
0
= 0.3635819,
a
1
= 0.4891775,
a
2
= 0.1365995,
a
3
= 0.0106411
o
Their graphical representations are shown in Figure 187 through 188 respectively:
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2003-2008 FlexRadio Systems
