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| |} | | |} |
| ::with: i=0..<code>nrow(''r'')</code> | | ::with: i=0..<code>nrow(''r'')</code> |
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| ---- | | ---- |
| ;Usage 2:<code>fft(<var>x</var>)</code> | | ;Usage 2:<code>aseg1(<var>x</var>, 0, <var>n</var>, <var>m</var>, <var>xon</var>, <var>xoff</var>)</code> |
| :;<var>x</var>: signal vector or matrix; if ''x'' is a matrix a spectrum of each column is computed
| | :;<var>x</var>: data vector (usally rms track in dB) |
| ;Result 2:A matrix ''y'' with [[../ncol|ncol(''x'')]] columns and L+2 rows, where each column ''y''[*,j] contains the complex spectrum of the column (channel) ''x''[*,j]. The transformation length L is set to [[../npow2|npow2(nrow(''x''))]].
| | :;<var>n</var>: minimum length of a signal segment in frames; 0 < n < <code>nrow(''x'')</code> |
| ----
| | :;<var>m</var>: smoothing length; 0 <= m</code>; if ''m'' is greater than zero, the segmentation is performed on a smoothed data vector ''xs''. |
| ;Usage 3:<code>fft(<var>x</var>, <var>n</var> {, <var>ytype</var>, <var>poffset</var>, <var>prange</var>, <var>aref</var>})</code>
| | :::<code>''xs''[i] = avr(''x''[i-m], .., ''x''[i+m]); with: i=0..nrow(''x'')</code> |
| :;<var>x</var>: signal vector or matrix; if ''x'' is a matrix a spectrum of each column is computed | | :;<var>xmin</var>: segment threshhold |
| :;<var>n</var>: desired length of analysis window; | | :;<var>omax</var>: offset for segment center; 0 < omax |
| ::*If <code>''n'' < nrow(''x'')</code>, the analysis window length L is set to nrow(''x''), otherwise L is set to ''n''.
| | ;Description: segment detection: |
| ::*If the analysis window length L is a power of 2 (L=2^M), the '''fft''' algorithm is used, otherwise the '''dft''' is used. | | :#find a position ''i'' with ''x''[i]>''xon'' |
| ::*If L is greater than [[../nrow|nrow(''x'')]], zero padding is applied to the signal. | | :#go backward while ''x''[i-j]>''xoff; last index i-j is the segment begin |
| :;<var>ytype</var>: select the type and format of the computed spectrum (default=0) -> see '''Result 3''' | | :#go forward while ''x''[i+k]>''xoff; last index i+k is the segment end |
| :;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0) | | ;Result 2: A matrix ''r'' with 2 rows. Each column of ''r'' defines one segment. Note that all values of ''r'' are frame indices (or row indices) of the data vector ''x''. |
| :::{|class="keinrahmen" | |
| |''poffset''='''0''' ||-> <code>phase[i] = atan2(im[i], re[i])</code>
| |
| |-
| |
| |otherwise ||-> <code>phase[i] = (atan2(im[i], re[i]) - 2*pi*i/L * ''poffset'') % (2 * pi)</code>
| |
| |}
| |
| :;<var>prange</var>: selects the range of phase values (default=0)
| |
| :::{|class="keinrahmen" | |
| |''prange''='''0''' ||-> <code>0 <= phase[i] < 2*pi</code>
| |
| |-
| |
| |otherwise ||-> <code>-pi <= phase[i] < pi</code>
| |
| |}
| |
| :;<var>aref</var>: reference amplitude if the log. spectrum (''ytype''=4) is requested (default=1)
| |
| ;Result 3: A matrix ''y'' with [[../ncol|ncol(''x'')]] columns, where each column ''y''[*,j] contains the spectrum of the column (channel) ''x''[*,j]. The type and the length of the spectra is selected by the argument ''ytype''. | |
| ::{|class="einrahmen" | | ::{|class="einrahmen" |
| !''ytype'' !! description !! content of ''y''[*,j] !! nrow(''y'')
| | |''r''[0,i] || beginning of the segment i |
| |- | |
| |'''0''' | |
| |complex spectrum in cartesian format
| |
| |<code>{ re<sub>0</sub>, im<sub>0</sub>, re<sub>1</sub>, im<sub>1</sub>, ... }</code>
| |
| |L+2
| |
| |-
| |
| |'''1'''
| |
| |complex spectrum in polar format
| |
| |<code>{ amp<sub>0</sub>, phase<sub>0</sub>, amp<sub>1</sub>, phase<sub>1</sub>, ... }<BR>with: amp<sub>i</sub>=sqrt(re<sub>i</sub><sup>2</sup> + im<sub>i</sub><sup>2</sup>),<BR>phase<sub>i</sub> see ''poffset''</code>
| |
| |L+2
| |
| |-
| |
| |'''2'''
| |
| |amplitude spectrum
| |
| |<code>{ amp<sub>0</sub>, amp<sub>1</sub>, ... }</code>
| |
| |L+1
| |
| |- | | |- |
| |'''3''' | | |''r''[3,i] || end of the segment i |
| |power spectrum
| |
| |<code>{ amp<sub>0</sub><sup>2</sup>, amp<sub>1</sub><sup>2</sup>, ... }</code>
| |
| | L+1 | |
| |- | |
| |'''4'''
| |
| |logarithmic amplitude spectrum
| |
| |<code>{ lev<sub>0</sub>, lev<sub>1</sub>, ... }<BR>with: lev<sub>i</sub>=20*log<sub>10</sub>(amp<sub>i</sub>/''aref'')</code>
| |
| | L+1
| |
| |} | | |} |
| | ::with: i=0..<code>nrow(''r'')</code> |
| ---- | | ---- |
| ;See also: [[Programmer_Guide/Command_Reference/EVAL/ifft|ifft]], [[Programmer_Guide/Command_Reference/EVAL/dft|dft]], [[Programmer_Guide/Command_Reference/EVAL/dct|dct]], [[Programmer_Guide/Command_Reference/EVAL/cepstrum|cepstrum]], [[Programmer_Guide/Command_Reference/EVAL/lpc|lpc]], [[Programmer_Guide/Command_Reference/EVAL/complex arithmetic|complex arithmetic]]
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| [[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]] | | [[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]] |
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| =====aseg1=====
| |
|
| |
| Automatically segment a signal. Apply automatic segmentation to the vector <var>x</var>.
| |
|
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| =====Usage:=====
| |
|
| |
| <code>aseg1(<var>x</var>, <var>xmin</var>, <var>omin</var>, <var>omax</var>, <var>nmin</var>, <var>navr</var>)</code>
| |
|
| |
| =====Parameters:=====
| |
|
| |
| ;<var>x</var>
| |
|
| |
| :A data vector (e.g. an rms function).
| |
|
| |
| ;<var>xmin</var>
| |
|
| |
| :The pause threshold.
| |
|
| |
| ;<var>omin</var>
| |
|
| |
| :The offset for segment detection. E.g. <var>x</var><code>[i] ></code> <var>xmin</var><code>+</code><var>omin</var>.
| |
|
| |
| ;<var>omax</var>
| |
|
| |
| :The offset for the segment center detection. E.g. <var>x</var><code>[i] > max("segment")-</code><var>omax</var>.
| |
|
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| ;<var>nmin</var>
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|
| |
| :The minimum segment duration in frames. A segment is assigned if the segment condition is true for at least <var>nmin</var> frames.
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|
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| ;<var>navr</var>
| |
|
| |
| :The averaging length. If <var>navr</var> is greater than <code>0</code> then all elements <var>x</var><code>[i]</code> are replaced by <code>avr(</code><var>x</var><code>[i-</code><var>navr</var> <code>.. i+</code><var>navr</var><code>])</code>.
| |
|
| |
| =====Result:=====
| |
|
| |
| A matrix (or vector) <code>y</code> with 4 rows and one column for each detected segment. Note that all values of <code>y</code> are frame indices.
| |
This function implements a simple automatic signal segmentation based on the energy (rms) track of the signal.
- Usage 1
aseg1(x, 0, n, m, xmin, omax)
- x
- data vector (usally rms track in dB)
- n
- minimum length of a signal segment in frames; 0 < n <
nrow(x)
- m
- smoothing length; 0 <= m; if m is greater than zero, the segmentation is performed on a smoothed data vector xs.
xs[i] = avr(x[i-m], .., x[i+m]); with: i=0..nrow(x)
- xmin
- segment threshhold
- omax
- offset for segment center; 0 < omax
- Description
-
- A segment is a continuous range of x, where all values are greater than xmin
- The center of a segment is a continuous range of values inside a segment, where all values are greater than xmax-omax (with: xmax is the maximum value inside the segment).
- Result 1
- A matrix r with 4 rows. Each column of r defines one segment. Note that all values of r are frame indices (or row indices) of the data vector x.
| r[0,i] |
beginning of the segment i
|
| r[1,i] |
beginning of the center of the segment i
|
| r[2,i] |
end of the center of the segment i
|
| r[3,i] |
end of the segment i
|
- with: i=0..
nrow(r)
- Usage 2
aseg1(x, 0, n, m, xon, xoff)
- x
- data vector (usally rms track in dB)
- n
- minimum length of a signal segment in frames; 0 < n <
nrow(x)
- m
- smoothing length; 0 <= m; if m is greater than zero, the segmentation is performed on a smoothed data vector xs.
xs[i] = avr(x[i-m], .., x[i+m]); with: i=0..nrow(x)
- xmin
- segment threshhold
- omax
- offset for segment center; 0 < omax
- Description
- segment detection:
- find a position i with x[i]>xon
- go backward while x[i-j]>xoff; last index i-j is the segment begin
- go forward while x[i+k]>xoff; last index i+k is the segment end
- Result 2
- A matrix r with 2 rows. Each column of r defines one segment. Note that all values of r are frame indices (or row indices) of the data vector x.
| r[0,i] |
beginning of the segment i
|
| r[3,i] |
end of the segment i
|
- with: i=0..
nrow(r)
<function list>
