Programmer Guide/Command Reference/EVAL/window - Revision history

Christian at 18:02, 21 April 2011

2011-04-21T18:02:32Z

← Older revision		Revision as of 20:02, 21 April 2011
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	with: a = 2 * pi / (n-1)</pre>		with: a = 2 * pi / (n-1)</pre>
	\|-		\|-
	\| 3 \|\| '''blackman''' \|\| 0<''par''<=0.25<BR>default=0.16 \|\| <code>wblackman(''x''{,''scale''{,''par''}})</code>		\| 3 \|\| '''blackman''' \|\| 0<''par''≤0.25<BR>default=0.16 \|\| <code>wblackman(''x''{,''scale''{,''par''}})</code>
	\| <pre>w[i] = (1-par)/2 - 0.5 * cos( ai ) + par/2 cos( 2ai )		\| <pre>w[i] = (1-par)/2 - 0.5 * cos( ai ) + par/2 cos( 2ai )
	with: a = 2 * pi / (n-1)</pre>		with: a = 2 * pi / (n-1)</pre>
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	\|-		\|-
	\| 5 \|\| '''bartlett'''<BR>(triangle) \|\| not used \|\| <code>wbartlett(''x''{,''scale''})</code>		\| 5 \|\| '''bartlett'''<BR>(triangle) \|\| not used \|\| <code>wbartlett(''x''{,''scale''})</code>
	\| <pre>0 <= i <= m: w[i] = i / m		\| <pre>0 ≤ i ≤ m: w[i] = i / m
	m < i < n: w[i] = 2 - i / m		m < i < n: w[i] = 2 - i / m
	with: m = (n-1) / 2</pre>		with: m = (n-1) / 2</pre>
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	\| A 5-term blackman-harris window with high dynamic range, low frequency resolution and minimized passband ripple (< 0.01dB). Flat-top windows are primarily used for calibration purposes.		\| A 5-term blackman-harris window with high dynamic range, low frequency resolution and minimized passband ripple (< 0.01dB). Flat-top windows are primarily used for calibration purposes.
	\|-		\|-
	\| 9 \|\| '''gauss''' \|\| 0<''par''<= 20<BR>default=3 \|\| <code>wgauss(''x''{,''scale''{,''par''}})</code>		\| 9 \|\| '''gauss''' \|\| 0<''par''≤ 20<BR>default=3 \|\| <code>wgauss(''x''{,''scale''{,''par''}})</code>
	\| <pre>w[i] = exp( -0.5 * (par * (m - i) / m) ^ 2 )		\| <pre>w[i] = exp( -0.5 * (par * (m - i) / m) ^ 2 )
	with: m = (n-1) / 2</pre>		with: m = (n-1) / 2</pre>

193.171.195.48 at 11:21, 21 April 2011

2011-04-21T11:21:16Z

← Older revision		Revision as of 13:21, 21 April 2011
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	{{DISPLAYTITLE:{{SUBPAGENAME}}}}		{{DISPLAYTITLE:{{SUBPAGENAME}}}}
	Compute a window function used for signal windowing in signal processing algorithms.		Compute a window function used for signal windowing in signal processing algorithms.
			;Usage: <code>window(<var>type</var>, <var>x</var> {, <var>scale</var> {, <var>par</var>}})</code>
	;Usage: ~~'''~~<code>window(<var>type</var>, <var>x</var> {, <var>scale</var> {, <var>par</var>}})</code>~~'''~~
	:;<var>type</var>: selects the type of the window function (described below); must be number		:;<var>type</var>: selects the type of the window function (described below); must be number
	:;<var>x</var>:		:;<var>x</var>:
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	:;<var>par</var>: 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.		:;<var>par</var>: 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. In the column description w[i] is the i-th value of the window function (i = 0..n-1) and n is the window length.		:;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. In the column description w[i] is the i-th value of the window function (i = 0..n-1) and n is the window length.

	::{\|		::{\|
	! ''type'' !! name !! ''par'' !! alias function !! description		! ''type'' !! name !! ''par'' !! alias function !! description
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	\|-		\|-
	\|}		\|}

	::Notes:		::Notes:
	::*If the argument ''type'' has an invalid value, the rectangle window is used.		::*If the argument ''type'' has an invalid value, the rectangle window is used.
	::*If the energy-correction is enabled (argument ''scale''!=0), the values w[i] scaled by a factor that approximately equalises the energy loss caused by the window function. The scaling factor is computed using white noise as test signal.		::*If the energy-correction is enabled (argument ''scale''!=0), the values w[i] scaled by a factor that approximately equalises the energy loss caused by the window function. The scaling factor is computed using white noise as test signal.
	::*If the argument ''par'' is supplied to a function not using this argument, it is ignored.		::*If the argument ''par'' is supplied to a function not using this argument, it is ignored.

	;Result: The result ''r'' depends on the argument ''x'':		;Result: The result ''r'' depends on the argument ''x'':
	:*x is a number: The value is used as window length ''n''. The result ''r'' is vector with length ''n'' containing the window function.		:*x is a number: The value is used as window length ''n''. The result ''r'' is vector with length ''n'' containing the window function.
	:*x is a vector or matrix: The number of rows of ''x'' is used as window length. Each column of ''x'' is multiplied with the window function (element-wise) and stored in a column of ''r''. The result ''r'' has the same type as ''x''.		:*x is a vector or matrix: The number of rows of ''x'' is used as window length. Each column of ''x'' is multiplied with the window function (element-wise) and stored in a column of ''r''. The result ''r'' has the same type as ''x''.
			;See also: [[../fft\|fft]], [[../wconvert\|wconvert]], [[../hth\|hth]]

			[[../#Functions\|<function list>]]
	~~;See also:~~ [[~~Programmer_Guide~~/~~Command_Reference/EVAL/fft\|fft]], [[Programmer_Guide/Command_Reference/EVAL/hth\|hth]], [[Programmer_Guide/Command_Reference/EVAL/wconvert\|wconvert]]~~

	~~[[Programmer_Guide/Command_Reference/EVAL~~#Functions\|<function list>]]

Toni at 09:09, 7 April 2011

2011-04-07T09:09:05Z

← Older revision		Revision as of 11:09, 7 April 2011
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	;See also: [[Programmer_Guide/Command_Reference/EVAL/fft\|fft]], [[Programmer_Guide/Command_Reference/EVAL/hth\|hth]]		;See also: [[Programmer_Guide/Command_Reference/EVAL/fft\|fft]], [[Programmer_Guide/Command_Reference/EVAL/hth\|hth]], [[Programmer_Guide/Command_Reference/EVAL/wconvert\|wconvert]]

	[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]		[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]

Toni at 09:03, 7 April 2011

2011-04-07T09:03:21Z

← Older revision		Revision as of 11:03, 7 April 2011
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	\|-		\|-
	\| 6 \|\| '''tappered rectangle''' \|\| not used \|\| <code>wtaprect(''x''{,''scale''})</code>		\| 6 \|\| '''tappered rectangle''' \|\| not used \|\| <code>wtaprect(''x''{,''scale''})</code>
	\| a rectangle with to short hanning slopes		\| A rectangle with to short hanning slopes.
	\|-		\|-
	\| 7 \|\| '''nuttall''' \|\| not used \|\| <code>wnuttall(''x''{,''scale''})</code>		\| 7 \|\| '''nuttall''' \|\| not used \|\| <code>wnuttall(''x''{,''scale''})</code>

Toni at 09:01, 7 April 2011

2011-04-07T09:01:57Z

← Older revision		Revision as of 11:01, 7 April 2011
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	! ''type'' !! name !! ''par'' !! alias function !! description		! ''type'' !! name !! ''par'' !! alias function !! description
	\|-		\|-
	\| 0 \|\| '''rectangle''' \|\| not used \|\| \|\| \|\| <pre>w[i] = 1</pre>		\| 0 \|\| '''rectangle''' \|\| not used \|\| \|\| <pre>w[i] = 1</pre>
	\|-		\|-
	\| 1 \|\| '''hanning''' \|\| not used \|\| <code>whanning(''x''{,''scale''})</code>		\| 1 \|\| '''hanning''' \|\| not used \|\| <code>whanning(''x''{,''scale''})</code>

Toni at 09:01, 7 April 2011

2011-04-07T09:01:28Z

← Older revision		Revision as of 11:01, 7 April 2011
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	! ''type'' !! name !! ''par'' !! alias function !! description		! ''type'' !! name !! ''par'' !! alias function !! description
	\|-		\|-
	\| 0 \|\| '''rectangle''' \|\| not used \|\|		\| 0 \|\| '''rectangle''' \|\| not used \|\| \|\| \|\| <pre>w[i] = 1</pre>
	\|-		\|-
	\| 1 \|\| '''hanning''' \|\| not used \|\| <code>whanning(''x''{,''scale''})</code>		\| 1 \|\| '''hanning''' \|\| not used \|\| <code>whanning(''x''{,''scale''})</code>

Toni at 08:59, 7 April 2011

2011-04-07T08:59:56Z

← Older revision		Revision as of 10:59, 7 April 2011
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	\|}		\|}

	:Notes:		::Notes:
	::*If the argument ''type'' has an invalid value, the rectangle window is used.		::*If the argument ''type'' has an invalid value, the rectangle window is used.
	::*If the energy-correction is enabled (argument ''scale''!=0), the values w[i] scaled by a factor that approximately equalises the energy loss caused by the window function. The scaling factor is computed using white noise as test signal.		::*If the energy-correction is enabled (argument ''scale''!=0), the values w[i] scaled by a factor that approximately equalises the energy loss caused by the window function. The scaling factor is computed using white noise as test signal.
			::*If the argument ''par'' is supplied to a function not using this argument, it is ignored.

	;Result: The result ''r'' depends on the argument ''x'':		;Result: The result ''r'' depends on the argument ''x'':
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	;See also: [[Programmer_Guide/Command_Reference/EVAL/fft\|~~Programmer_Guide/Command_Reference/EVAL/~~fft]], [[Programmer_Guide/Command_Reference/EVAL/hth\|hth]]		;See also: [[Programmer_Guide/Command_Reference/EVAL/fft\|fft]], [[Programmer_Guide/Command_Reference/EVAL/hth\|hth]]

	[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]		[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]

Toni at 08:58, 7 April 2011

2011-04-07T08:58:39Z

← Older revision		Revision as of 10:58, 7 April 2011
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	;See also: [[Programmer_Guide/Command_Reference/EVAL/~~vsubc~~\|~~vsubc~~]], [[Programmer_Guide/Command_Reference/EVAL/~~select~~\|~~select~~]]		;See also: [[Programmer_Guide/Command_Reference/EVAL/fft\|Programmer_Guide/Command_Reference/EVAL/fft]], [[Programmer_Guide/Command_Reference/EVAL/hth\|hth]]

	[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]		[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]

Toni at 08:56, 7 April 2011

2011-04-07T08:56:48Z

Toni at 08:54, 7 April 2011

2011-04-07T08:54:35Z

← Older revision		Revision as of 10:54, 7 April 2011
Line 25:		Line 25:
	with: a = 2 * pi / (n-1)</pre>		with: a = 2 * pi / (n-1)</pre>
	\|-		\|-
	\| 3 \|\| '''blackman''' \|\| 0 < ''par'' <= 0.25<BR>default=0.16 \|\| <code>wblackman(''x'' {, ''scale'' {, ''par''}})</code>		\| 3 \|\| '''blackman''' \|\| 0<''par''<=0.25<BR>default=0.16 \|\| <code>wblackman(''x'' {, ''scale'' {, ''par''}})</code>
	\| <pre>w[i] = (1-par)/2 - 0.5 * cos( ai ) + par/2 cos( 2ai )		\| <pre>w[i] = (1-par)/2 - 0.5 * cos( ai ) + par/2 cos( 2ai )
	with: a = 2 * pi / (n-1)</pre>		with: a = 2 * pi / (n-1)</pre>
	\|-		\|-
	\| 4 \|\| '''kaiser''' \|\| 0 < ''par''<BR>default=8 \|\| <code>wkaiser(''x'' {, ''scale'' {, ''par''}})</code>		\| 4 \|\| '''kaiser''' \|\| 0<''par''<BR>default=8 \|\| <code>wkaiser(''x'' {, ''scale'' {, ''par''}})</code>
	\| <pre>w[i] = I0( par / m * sqrt(m^2 - (i-m)^2) ) / I0( par )		\| <pre>w[i] = I0( par / m * sqrt(m^2 - (i-m)^2) ) / I0( par )
	with: m = (n-1) / 2		with: m = (n-1) / 2
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	\| A 5-term blackman-harris window with high dynamic range, low frequency resolution and minimized passband ripple (< 0.01dB). Flat-top windows are primarily used for calibration purposes.		\| A 5-term blackman-harris window with high dynamic range, low frequency resolution and minimized passband ripple (< 0.01dB). Flat-top windows are primarily used for calibration purposes.
	\|-		\|-
	\| 9 \|\| '''gauss''' \|\| 0 < ''par'' <= 20<BR>default=3 \|\| <code>wgauss(''x'' {, ''scale'' {, ''par''}})</code>		\| 9 \|\| '''gauss''' \|\| 0<''par''<= 20<BR>default=3 \|\| <code>wgauss(''x'' {, ''scale'' {, ''par''}})</code>
	\| <pre>w[i] = exp( -0.5 * (par * (m - i) / m) ^ 2 )		\| <pre>w[i] = exp( -0.5 * (par * (m - i) / m) ^ 2 )
	with: m = (n-1) / 2</pre>		with: m = (n-1) / 2</pre>

← Older revision		Revision as of 10:56, 7 April 2011
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	\| 0 \|\| '''rectangle''' \|\| not used \|\|		\| 0 \|\| '''rectangle''' \|\| not used \|\|
	\|-		\|-
	\| 1 \|\| '''hanning''' \|\| not used \|\| <code>whanning(''x'' {, ''scale''})</code>		\| 1 \|\| '''hanning''' \|\| not used \|\| <code>whanning(''x''{,''scale''})</code>
	\| <pre>w[i] = 0.5 - 0.5 * cos( a*i )		\| <pre>w[i] = 0.5 - 0.5 * cos( a*i )
	with: a = 2 * pi / (n-1)</pre>		with: a = 2 * pi / (n-1)</pre>
	\|-		\|-
	\| 2 \|\| '''hamming''' \|\| not used \|\| <code>whamming(''x'' {, ''scale''})</code>		\| 2 \|\| '''hamming''' \|\| not used \|\| <code>whamming(''x''{,''scale''})</code>
	\| <pre>w[i] = 0.54 - 0.46 * cos( a*i )		\| <pre>w[i] = 0.54 - 0.46 * cos( a*i )
	with: a = 2 * pi / (n-1)</pre>		with: a = 2 * pi / (n-1)</pre>
	\|-		\|-
	\| 3 \|\| '''blackman''' \|\| 0<''par''<=0.25<BR>default=0.16 \|\| <code>wblackman(''x'' {, ''scale'' {, ''par''}})</code>		\| 3 \|\| '''blackman''' \|\| 0<''par''<=0.25<BR>default=0.16 \|\| <code>wblackman(''x''{,''scale''{,''par''}})</code>
	\| <pre>w[i] = (1-par)/2 - 0.5 * cos( ai ) + par/2 cos( 2ai )		\| <pre>w[i] = (1-par)/2 - 0.5 * cos( ai ) + par/2 cos( 2ai )
	with: a = 2 * pi / (n-1)</pre>		with: a = 2 * pi / (n-1)</pre>
	\|-		\|-
	\| 4 \|\| '''kaiser''' \|\| 0<''par''<BR>default=8 \|\| <code>wkaiser(''x'' {, ''scale'' {, ''par''}})</code>		\| 4 \|\| '''kaiser''' \|\| 0<''par''<BR>default=8 \|\| <code>wkaiser(''x''{,''scale''{,''par''}})</code>
	\| <pre>w[i] = I0( par / m * sqrt(m^2 - (i-m)^2) ) / I0( par )		\| <pre>w[i] = I0( par / m * sqrt(m^2 - (i-m)^2) ) / I0( par )
	with: m = (n-1) / 2		with: m = (n-1) / 2
	I0(z) is the modfied zero-order bessel function</pre>		I0(z) is the modfied zero-order bessel function</pre>
	\|-		\|-
	\| 5 \|\| '''bartlett'''<BR>(triangle) \|\| not used \|\| <code>wbartlett(''x'' {, ''scale''})</code>		\| 5 \|\| '''bartlett'''<BR>(triangle) \|\| not used \|\| <code>wbartlett(''x''{,''scale''})</code>
	\| <pre>0 <= i <= m: w[i] = i / m		\| <pre>0 <= i <= m: w[i] = i / m
	m < i < n: w[i] = 2 - i / m		m < i < n: w[i] = 2 - i / m
	with: m = (n-1) / 2</pre>		with: m = (n-1) / 2</pre>
	\|-		\|-
	\| 6 \|\| '''tappered rectangle''' \|\| not used \|\| <code>wtaprect(''x'' {, ''scale''})</code>		\| 6 \|\| '''tappered rectangle''' \|\| not used \|\| <code>wtaprect(''x''{,''scale''})</code>
	\| a rectangle with to short hanning slopes		\| a rectangle with to short hanning slopes
	\|-		\|-
	\| 7 \|\| '''nuttall''' \|\| not used \|\| <code>wnuttall(''x'' {, ''scale''})</code>		\| 7 \|\| '''nuttall''' \|\| not used \|\| <code>wnuttall(''x''{,''scale''})</code>
	\| A 4-term blackman-harris window with high dynamic range, low frequency resolution and minimized maximum sidelobes.<BR>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		\| A 4-term blackman-harris window with high dynamic range, low frequency resolution and minimized maximum sidelobes.<BR>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 \|\| <code>wflattop(''x'' {, ''scale''})</code>		\| 8 \|\| '''flat-top''' \|\| not used \|\| <code>wflattop(''x''{,''scale''})</code>
	\| A 5-term blackman-harris window with high dynamic range, low frequency resolution and minimized passband ripple (< 0.01dB). Flat-top windows are primarily used for calibration purposes.		\| A 5-term blackman-harris window with high dynamic range, low frequency resolution and minimized passband ripple (< 0.01dB). Flat-top windows are primarily used for calibration purposes.
	\|-		\|-
	\| 9 \|\| '''gauss''' \|\| 0<''par''<= 20<BR>default=3 \|\| <code>wgauss(''x'' {, ''scale'' {, ''par''}})</code>		\| 9 \|\| '''gauss''' \|\| 0<''par''<= 20<BR>default=3 \|\| <code>wgauss(''x''{,''scale''{,''par''}})</code>
	\| <pre>w[i] = exp( -0.5 * (par * (m - i) / m) ^ 2 )		\| <pre>w[i] = exp( -0.5 * (par * (m - i) / m) ^ 2 )
	with: m = (n-1) / 2</pre>		with: m = (n-1) / 2</pre>