window

Compute a window function used for signal windowing in signal processing algorithms.

Usage

window(type, x {, scale {, par}})

type

selects the type of the window function (described below); must be number

x

• If x is a scalar, the argument is used as window length and the result of window is a vector containing the window function.
• If x is a vector or matrix, the number of rows of x is used as window length and the result of window is a matrix with the same dimensions as x where each column contains the windowed values of the input column.

The window length must be greater than 2!

scale

A boolean argument to enable/disable energy correction. If the energy correction is enabled (scale!=0), the window function is scaled by a factor that approximately equalises the energy loss caused by the windowing. To preserve signal energy, scale should be set to 1, otherwise (to preserve signal amplitude) it should be 0.

par

A window parameter depending on the type of the window function (described below). If par is set to 0 (default), a default parameter value is automatically selected.

Description

The following table shows the implemented window functions and the meaning of the parameter par. For the most types an alias function is implement, which is also shown in the table.

type	name	par	alias function	description
0	rectangle	not used
1	hanning	not used	whanning(x {, scale})	w[i] = 0.5 - 0.5 * cos( a*i ) with: a = 2 * pi / (n-1)
2	hamming	not used	whamming(x {, scale})	w[i] = 0.54 - 0.46 * cos( a*i ) with: a = 2 * pi / (n-1)
3	blackman	0 < par <= 0.25 default=0.16	wblackman(x {, scale {, par}})	w[i] = (1-par)/2 - 0.5 * cos( a*i ) + par/2 * cos( 2*a*i ) with: a = 2 * pi / (n-1)
4	kaiser	0 < par default=8	wkaiser(x {, scale {, par}})	w[i] = I0( par / m * sqrt(m^2 - (i-m)^2) ) / I0( par ) with: m = (n-1) / 2 I0(z) is the modfied zero-order bessel function
5	bartlett (triangle)	not used	wbartlett(x {, scale})	0 <= i <= m: w[i] = i / m m < i < n: w[i] = 2 - i / m with: m = (n-1) / 2
6	tappered rectangle	not used	wtaprect(x {, scale})	a rectangle with to short hanning slopes
7	nuttall	not used	wnuttall(x {, scale})	a 4-term blackman-harris window with high dynamic range but low frequency resolution Nuttall, Albert H. "Some Windows with Very Good Sidelobe Behavior." IEEE Transactions on Acoustics, Speech, and Signal Processing. Vol. ASSP-29 (February 1981). pp. 84-91
8	flat-top	not used	wflattop(x {, scale})
9	gauss	0 < par <= 20 default=3	wgauss(x {, scale {, par}})

Result

The result r is a copy of x but the values of the elements of r are limited to the boundaries defined by lo and/or hi.

r_i,j is set to lo if x_i,j is lower than lo (functions limit and limitlow)

r_i,j is set to hi if x_i,j is greater than hi (functions limit and limithigh)

See also

vsubc, select

Example:

#a := eval vv(1,2,3,4,5,4,3,2,1)
#b := eval fill(9,0,1)
#c := eval limitlow($#a, 3)
// -> $#c = { 3 , 3 , 3 , 4 , 5 , 4 , 3 , 3 , 3 } 
#d := eval limit($#b, 2, 6)
// -> $#d[*,0] = { 2 , 2 , 3 , 4 , 5 , 4 , 3 , 2 , 2 }
//    $#d[*,1] = { 2 , 2 , 2 , 3 , 4 , 5 , 6 , 6 , 6 }

<function list>

General window function

Usage:	window(type, x, scale, par)
Parameters:
type=0 -> none (square)	type=1 -> whanning
type=2 -> whamming	type=3 -> wblackman
type=4 -> wkaiser	type=5 -> wbartlett
type=6 -> wtaprect	type=7 -> wnuttall
type=8 -> wflattop	type=9 -> wgauss

The arguments x, scale and par are the same as above.

arguments: x The window length (scalar, >2), the signal (vector or matrix, nrow(x)>2). If x is a matrix, every column is multiplied with the window. scale The scaling (0=unscaled, 1=scaled for rms(sig) ~ rms(sig * wnd) par optional window parameters

The result is the signal window of length x or the signal multiplied by the window.