marvin::math::windows Namespace Reference

Various windowing functions. An interactive graph with more intuition than the textual documentation can give can be found here More...

Classes
class	PrecomputedWindow
	Helper class for cacheing a window function in a lookup table. More...

Enumerations
enum class	WindowType {   Sine , Tukey , BlackmanHarris , CosineSum ,   Hann , Hamming }

Functions
template<FloatType SampleType>
SampleType	sine (SampleType n, SampleType N)
template<FloatType SampleType>
SampleType	tukey (SampleType n, SampleType NumPoints, SampleType alpha)
template<FloatType SampleType>
SampleType	blackmanHarris (SampleType n, SampleType N)
template<FloatType SampleType>
SampleType	cosineSum (SampleType n, SampleType N, SampleType alpha)
template<FloatType SampleType>
SampleType	hann (SampleType n, SampleType N)
template<FloatType SampleType>
SampleType	hamming (SampleType n, SampleType N)

Detailed Description

Various windowing functions. An interactive graph with more intuition than the textual documentation can give can be found here

Enumeration Type Documentation

WindowType

enum class marvin::math::windows::WindowType

strong

Represents a type of window function, for use in classes and functions which take the window type as a template argument.

Enumerator
Sine
Tukey
BlackmanHarris
CosineSum
Hann
Hamming

Function Documentation

blackmanHarris()

template<FloatType SampleType>

SampleType marvin::math::windows::blackmanHarris ( SampleType n, SampleType N )

nodiscard

A Blackman-Harris window. Very similar to a hamming / hann window, but reduces sidelobes at the cost of extra sinc terms.

Parameters

n	The current index into the window.
N	The total number of points in the window. n will be normalised by this.

Returns

A point n/N of the way along the Blackman-Harris window.

cosineSum()

template<FloatType SampleType>

SampleType marvin::math::windows::cosineSum ( SampleType n, SampleType N, SampleType alpha )

nodiscard

Generalised form of cosine sum family windows, used by both hann and hamming.
Implemented as w[n] = a - (1-a) cos(2pi n/N).
As the alpha parameter affects the boundaries of the window, you're probably better of using hann or hamming instead.

Parameters

n	The current index into the window.
N	The total number of points in the window. n will be normalised by this.
alpha	Affects the level of the start and end points - a value of 0.5 will set w[0] and w[1] to 0, anything below 0.5 will drop the start and end points below 0, and anything above 0.5 will raise the start and end points above 0.

Returns

A point n/N of the way along the window.

hamming()

template<FloatType SampleType>

SampleType marvin::math::windows::hamming ( SampleType n, SampleType N )

nodiscard

A specific case of a cosine sum window with an alpha of 25/46. Does not go to zero, but cancels the first sidelobe.

Parameters

n	The current index into the window.
N	The total number of points in the window. n will be normalised by this.

Returns

A point n/N of the way along the window.

hann()

template<FloatType SampleType>

SampleType marvin::math::windows::hann ( SampleType n, SampleType N )

nodiscard

A specific case of a cosine sum window with an alpha of 0.5, which goes to 0 at its boundaries, with about -18dB/8ve sidelobe rolloff in the frequency domain.

Parameters

n	The current index into the window.
N	The total number of points in the window. n will be normalised by this.

Returns

A point n/N of the way along the window.

sine()

template<FloatType SampleType>

SampleType marvin::math::windows::sine ( SampleType n, SampleType N )

nodiscard

A Sine window starting at 0, as opposed to the cosine equivalent starting at -1.

Parameters

n	The current index into the window.
N	The total number of points in the window - n will be normalised by this.

Returns

A point n/N of the way along a sine window.

tukey()

template<FloatType SampleType>

SampleType marvin::math::windows::tukey ( SampleType n, SampleType NumPoints, SampleType alpha )

nodiscard

A Tukey window. The response of the window is determined by the value of alpha - at alpha = 0, the resulting window is identical to a rectangular window. At alpha = 1, the resulting window is identical to a hann window.

Parameters

n	The current index into the window.
N	The total number of points in the window - n will be normalised by this.
alpha	The "shape" param of the windowing function, between 0 and 1.

Returns

A point n/N of the way along a tukey window, with a shape determined by alpha.