# blackman function Null safety

Return a Blackman window. The Blackman window is a taper formed by using the first three terms of a summation of cosines. It was designed to have close to the minimal leakage possible. It is close to optimal, only slightly worse than a Kaiser window.

# Parameters

`M`

: int Number of points in the output window. If zero or less, an empty array is returned.`sym`

: bool, optional When true (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis.

# Returns

- w : Array
The window, with the maximum value normalized to 1 (though the value 1
does not appear if
`M`

is even and`sym`

is True).

# Notes

The Blackman window is defined as
.. math:: w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M)
The "exact Blackman" window was designed to null out the third and fourth
sidelobes, but has discontinuities at the boundaries, resulting in a
6 dB/oct fall-off. This window is an approximation of the "exact" window,
which does not null the sidelobes as well, but is smooth at the edges,
improving the fall-off rate to 18 dB/oct. `3`

_
Most references to the Blackman window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function. It is known as a
"near optimal" tapering function, almost as good (by some measures)
as the Kaiser window.

# References

- "scipy.signal.windows.blackman". https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.windows.blackman.html#scipy.signal.windows.blackman. Retrieved 2019-07-15.

# Examples

```
import 'package:scidart/src/numdart/numdart.dart';
import 'package:scidart/scidart/signal/signal.dart';
var M = 10;
var w = blackman(M);
```

## Implementation

```
Array blackman(int M, {bool sym = true}) {
return generalCosine(M, Array([0.42, 0.50, 0.08]), sym: sym);
}
```