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| ::{| | | ::{| |
| ! ''type'' !! description !! [[1]] | | ! ''type'' !! description !! result |
| |- | | |- |
| | 0 || hearing threshold in dB || || <pre>w[i] = 1</pre> | | | 0 || hearing threshold in dB || L<sub>TH</sub> |
| |- | | |- |
| | 1 || '''hanning''' || not used || <code>whanning(''x''{,''scale''})</code> | | | 1 || hearing threshold weighting factor || 10^(-L<sub>TH</sub> / 20) |
| | <pre>w[i] = 0.5 - 0.5 * cos( a*i )
| |
| with: a = 2 * pi / (n-1)</pre>
| |
| |- | | |- |
| | 2 || '''hamming''' || not used || <code>whamming(''x''{,''scale''})</code> | | | 2 || value of the '''A''' weighting function in dB || L<sub>A</sub> |
| | <pre>w[i] = 0.54 - 0.46 * cos( a*i )
| |
| with: a = 2 * pi / (n-1)</pre>
| |
| |- | | |- |
| | 3 || '''blackman''' || 0<''par''<=0.25<BR>default=0.16 || <code>wblackman(''x''{,''scale''{,''par''}})</code> | | | 3 || '''A''' weighting value || 10^(-L<sub>A</sub> / 20) |
| | <pre>w[i] = (1-par)/2 - 0.5 * cos( a*i ) + par/2 * cos( 2*a*i )
| |
| with: a = 2 * pi / (n-1)</pre>
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| |- | | |- |
| | 4 || '''kaiser''' || 0<''par''<BR>default=8 || <code>wkaiser(''x''{,''scale''{,''par''}})</code> | | | 4 || value of the '''C''' weighting function in dB || L<sub>C</sub> |
| | <pre>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</pre>
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| |- | | |- |
| | 5 || '''bartlett'''<BR>(triangle) || not used || <code>wbartlett(''x''{,''scale''})</code> | | | 5 || '''C''' weighting value || 10^(-L<sub>C</sub> / 20) |
| | <pre>0 <= i <= m: w[i] = i / m
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| m < i < n: w[i] = 2 - i / m
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| with: m = (n-1) / 2</pre>
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| |-
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| | 6 || '''tappered rectangle''' || not used || <code>wtaprect(''x''{,''scale''})</code>
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| | A rectangle with to short hanning slopes.
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| |-
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| | 7 || '''nuttall''' || not used || <code>wnuttall(''x''{,''scale''})</code>
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| | 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
| |
| |-
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| | 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.
| |
| |-
| |
| | 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 )
| |
| with: m = (n-1) / 2</pre>
| |
| |- | | |- |
| |} | | |} |
| | ::For L<sub>TH</sub> the algorithm published by E.Terhardt (JASA 71(3), March 1982) is used: |
| | :::<L><sub>TH</sub>(f) = 3.64 * f^-0.8 - 6.5 * exp(-0.6 * (f - 3.3)^2) + 1e-3 * f^4 |
| | :::(L<sub>TH</sub> in dB, f in kHz) |
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| ::Notes: | | ;See also: [[Programmer_Guide/Command_Reference/EVAL/fft|fft]], [[Programmer_Guide/Command_Reference/EVAL/window|window]] |
| ::*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 argument ''par'' is supplied to a function not using this argument, it is ignored.
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|
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|
| ;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 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''.
| |
|
| |
|
| | Example: |
| | <pre> |
| | // compute the amplitude spectrum $#spe (in dBA) of the signal $#sig (fs=44.1kHz) |
|
| |
|
| ;See also: [[Programmer_Guide/Command_Reference/EVAL/fft|fft]], [[Programmer_Guide/Command_Reference/EVAL/hth|hth]], [[Programmer_Guide/Command_Reference/EVAL/wconvert|wconvert]]
| | // method 1: |
| | // a) compute linear amplitde spectrum of signal $#sig |
| | #spe := eval cr2len( fft( whanning( $#sig ) ) |
| | // b) compute the frequecies of the spectral bins |
| | #frq := eval fill( $#spe[] , 0 , 44100 / 2 / ( $#spe[]-1 ) ) |
| | // c) apply A-weights and convert to log. amplitudes |
| | $#spe := eval lin2log( $#spe ?* hth( $#frq , 3 ) ) |
|
| |
|
| [[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]]
| | // method 2: all-in-one |
| | #n := int npow2($#sig) |
| | #spe := eval lin2log(cr2len(fft(whanning($#sig)))) - hth(fill($#n/2+1,0,44100/$#n),2) |
| | </pre> |
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|
| | | [[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]] |
| {{DISPLAYTITLE:{{SUBPAGENAME}}}}
| |
| =====hth=====
| |
| | |
| Hearing Threshold Level (HTH) or A/C spectral weightings.
| |
| | |
| =====Usage:=====
| |
| | |
| <code>hth(<var>f</var>, <var>type</var>)</code>
| |
| | |
| ;<var>f</var>
| |
| | |
| :The frequency (scalar, vector or matrix).
| |
| | |
| ;<var>type</var>
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| | |
| :The type of weighting function. The following values are supported:
| |
| | |
| :<code>0</code> - Hearing threshold level
| |
| | |
| :<code>1</code> - Hearing threshold weighting factor
| |
| | |
| :<code>2</code> - A weighting levels.
| |
| | |
| :<code>3</code> - A weighting factors.
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| | |
| :<code>4</code> - C weighting levels.
| |
| | |
| :<code>5</code> - C weighting factors.
| |
| | |
| =====Notes:=====
| |
| | |
| Factor = 1 / (10^(Level/20))
| |
| | |
| =====Result:=====
| |
| | |
| The result of the requested function (same datatype as <var>f</var>).
| |
Compute spectral weights.
- Usage
hth(f, type)
- f
- A scalar, vector or matrix containing the frequency value(s) in Hz.
- type
- The type of the spectral weight to be computed.
- Result
- The result w has the same type as the argument f and contains the values of the spectral weighting function selected by type (w[i,j] = weight(f[i,j],type)).
| type |
description |
result
|
| 0 |
hearing threshold in dB |
LTH
|
| 1 |
hearing threshold weighting factor |
10^(-LTH / 20)
|
| 2 |
value of the A weighting function in dB |
LA
|
| 3 |
A weighting value |
10^(-LA / 20)
|
| 4 |
value of the C weighting function in dB |
LC
|
| 5 |
C weighting value |
10^(-LC / 20)
|
- For LTH the algorithm published by E.Terhardt (JASA 71(3), March 1982) is used:
- <L>TH(f) = 3.64 * f^-0.8 - 6.5 * exp(-0.6 * (f - 3.3)^2) + 1e-3 * f^4
- (LTH in dB, f in kHz)
- See also
- fft, window
Example:
// compute the amplitude spectrum $#spe (in dBA) of the signal $#sig (fs=44.1kHz)
// method 1:
// a) compute linear amplitde spectrum of signal $#sig
#spe := eval cr2len( fft( whanning( $#sig ) )
// b) compute the frequecies of the spectral bins
#frq := eval fill( $#spe[] , 0 , 44100 / 2 / ( $#spe[]-1 ) )
// c) apply A-weights and convert to log. amplitudes
$#spe := eval lin2log( $#spe ?* hth( $#frq , 3 ) )
// method 2: all-in-one
#n := int npow2($#sig)
#spe := eval lin2log(cr2len(fft(whanning($#sig)))) - hth(fill($#n/2+1,0,44100/$#n),2)
<function list>
