BESA Research Spectral Analysis - Revision history

Abinash at 12:42, 2 November 2021

2021-11-02T12:42:53Z

Show changes

Jaehyun: /* FFT over a short data block of interest */

2021-10-12T12:19:43Z

‎FFT over a short data block of interest

Jaehyun at 14:22, 5 May 2021

2021-05-05T14:22:45Z

Harald at 11:57, 2 February 2021

2021-02-02T11:57:30Z

Jamie: /* Mean FFT Spectrum over an extended time range */

2019-03-26T13:31:00Z

‎Mean FFT Spectrum over an extended time range

Jamie: /* Mean FFT Spectrum over an extended time range */

2019-03-26T13:29:10Z

‎Mean FFT Spectrum over an extended time range

Jamie: /* Mean FFT Spectrum over an extended time range */

2019-03-25T13:35:52Z

‎Mean FFT Spectrum over an extended time range

Jamie: /* Mean FFT Spectrum over an extended time range */

2019-03-25T12:57:04Z

‎Mean FFT Spectrum over an extended time range

Jaehyun: /* FFT 'File' Menu: Saving, Loading and Printing Results of the FFT */

2018-05-09T08:25:06Z

‎FFT 'File' Menu: Saving, Loading and Printing Results of the FFT

Jaehyun: /* FFT */

2017-11-02T16:27:08Z

‎FFT

@@ Line 33: / Line 33: @@
 # Right-click into the marked block and select the item ''FFT''.
 # Type the HotKey <span style="color:#3366ff;">'''F'''</span>.
-# Select the item ''FFT-Spectrum'' in the <span style="color:#3366ff;">'''Process'''</span> menu (<span style="color:#3366ff;">'''Alt+P F'''</span>).
+# Select the item ''FFT-Spectrum'' in the <span style="color:#3366ff;">'''Process'''</span> menu (<span style="color:#3366ff;">'''Alt+P, F'''</span>).
@@ Line 41: / Line 41: @@
 '''Note:''' It is not possible to select the FFT process if the region to be processed contains less than 128 samples. This can occur, for instance, if the time range of a highlighted region is too short.
-'''Note''': When an FFT is selected, BESA Research displays the results for the current montage on the screen. In the background, the program also performs the FFT on 81 standard interpolated, average referenced channels in the case of EEG and on the average referenced data in the case of MEG. When FFT results are saved to a file, you have the choice of saving either the current montage, or the 81 interpolated, average referenced channels (only for EEG). Maps of the FFT results are always based on the average referenced data. This is necessary to ensure that electrodes are given equal weights in the nonlinear transformation to power or amplitude (=root of power).
+'''Note''': When an FFT is selected, BESA Research displays the results for the current montage on the screen. In the background, the program also performs the FFT on 81 standard interpolated, average referenced channels in the case of EEG and on the average referenced data in the case of MEG. When FFT results are saved to a file, you have the choice of saving either the current montage, or the 81 interpolated, average referenced channels (only for EEG). Maps of the FFT results are always based on the average referenced data. This is necessary to ensure that electrodes are given equal weights in the nonlinear transformation to power or amplitude (= root of power).
 For an FFT over a marked block or the whole screen, no parameters have to be specified. Internally, BESA Research preprocesses the selected data segment for the FFT in two steps:
@@ Line 47: / Line 47: @@
 # A window function is multiplied with the data to attenuate the amplitudes at the ends to zero
 # The number of samples is increased by interpolation (if necessary) to make it a power of 2.
 This preprocessing of a highlighted data segment is illustrated in the figure below:
@@ Line 53: / Line 52: @@
 [[Image:Spectral (3).gif ]]
+The highlighted block constitutes 80% of a window of width 100%. A cosine squared (cos²) window of width 20% of the total is applied at the edges, so that the signal amplitude is attenuated to 50% at the edges of the marked block, and zero at the edges of the window. Then we take the number of time samples in the window, and select the next higher power of 2 (up to 2^15 = 32768). Using spline interpolation, the data in the window are converted to this larger number of points, and the FFT is applied. If the number of points is greater than 32768, spline interpolation is used to reduce the number to 32768. In this case, to avoid aliasing, the data are low-pass filtered at a frequency corresponding to ¼ of the new sampling rate.
-The highlighted block constitutes 80% of a window of width 100%. A cosine squared (cos²) window of width 20% of the total is applied at the edges, so that the signal amplitude is attenuated to 50% at the edges of the marked block, and zero at the edges of the window. Then we take the number of time samples in the window, and select the next higher power of 2 (up to 8196). Using spline interpolation, the data in the window are converted to this larger number of points, and the FFT is applied. If the number of points is greater than 8196, spline interpolation is used to reduce the number to 8196. In this case, to avoid aliasing, the data are low-pass filtered at a frequency corresponding to ¼ of the new sampling rate.
 If the FFT is applied to the data displayed on the screen, windowing is similar to that for the highlighted block, except that no data outside the block are included: the cosine squared window is applied so that the signal amplitude is attenuated to zero at the edges of the display.
 === Mean FFT Spectrum over an extended time range ===

@@ Line 2: / Line 2: @@
 |title = Module information
 |module = BESA Research Basic or higher
-|version = 6.1 or higher
+|version = BESA Research 6.1 or higher
 }}

@@ Line 77: / Line 77: @@
 Ranges which are not currently available (e.g. if no epochs or no markers are defined) are grayed out.
-The mean FFT consists of a set of FFTs from overlapping data segments spanning the selected time range. Each data segment has a fixed width, defined as a power of 2 sampling points, that can be selected under <span style="color:#3366ff;">'''Block Size / Points per Block'''</span>: In the center of the options window, the number of points per FFT block is selected. Selection can be 128, 256, 512, or 1024 points. The block width influences in particular the contribution to the spectrum of low frequencies: the wider the block, the lower the frequencies that can be represented. The lowest frequency is given by 2/(block width in seconds). Thus, if you have recorded data with a high sampling rate, a wider window is necessary to compute low frequencies. Note: For each block size in samples the corresponding width in seconds is specified in brackets.
+The mean FFT consists of a set of FFTs from overlapping data segments spanning the selected time range. Each data segment has a fixed width, defined as a power of 2 sampling points, that can be selected under <span style="color:#3366ff;">'''Block Size / Points per Block'''</span>: In the center of the options window, the number of points per FFT block is selected. Selection can be 128, 256, 512, or 1024 points. The block width influences in particular the contribution to the spectrum of low frequencies: the wider the block, the lower the frequencies that can be represented. The lowest frequency is given by 1/(block width in seconds). Thus, if you have recorded data with a high sampling rate, a wider window is necessary to compute low frequencies. Note: For each block size in samples the corresponding width in seconds is specified in brackets.
 The lower section of the options window determines amplitude and gradient thresholds for including a block in the mean FFT. If signal amplitudes exceed the amplitude threshold or the difference of two consecutive signal amplitudes exceeds the gradient threshold, the block will be omitted. Different thresholds may be set for each channel type (in the above example, scalp and polygraphic channels).

@@ Line 88: / Line 88: @@
 The steps are:
 For each epoch to be added to the mean covariance matrix:
-#  Average reference for EEG, MAG, and GRA data (if the single montage channels box is not checked)
+# Average reference for EEG, MAG, and GRA data (if the single montage channels box is not checked)
-#  Resample data to 256 Hz
+# Resample data to 256 Hz
-#  Compute FFT
+# Compute FFT
-#  Add to FFT covariance matrix (either sum over all channels, or individually for each montage channel if that box is checked)
+# Add to FFT covariance matrix (either sum over all channels, or individually for each montage channel if that box is checked)
 Then, a singular value decomposition is performed on the FFT covariance of each channel, to obtain the (complex) eigenvectors. The newly arranged matrix of eigenvectors is then inverse Fourier transformed to obtain waveforms for each of the components. These are written to file.
 Note on computational steps: Each data segment overlaps 50% with the next segment, and is multiplied by a cosine squared (cos² window, as shown at the bottom of the figure below). This combination of overlap and windowing ensures that each time point contributes equally to the mean spectrum (since cos²(x) + sin²(x) = 1). Because mean spectra are computed, phase information is not available.

@@ Line 82: / Line 82: @@
 Press '''OK''' in the options window to start computation of the mean FFT. Computation can be interrupted by pressing any key. The interrupt has to be confirmed and may be canceled to resume mean FFT calculation.
+The section “FFT Covariance” allows to compute the FFT covariance over the data range selected.
 Note on computational steps: Each data segment overlaps 50% with the next segment, and is multiplied by a cosine squared (cos² window, as shown at the bottom of the figure below). This combination of overlap and windowing ensures that each time point contributes equally to the mean spectrum (since cos²(x) + sin²(x) = 1). Because mean spectra are computed, phase information is not available.

← Older revision		Revision as of 13:35, 25 March 2019
Line 89:		Line 89:

	'''Note''' that time ranges marked as artifacts are not included in the computation of the mean FFT. These time ranges are not excluded when computing the FFT of a marked block or of the displayed data.		'''Note''' that time ranges marked as artifacts are not included in the computation of the mean FFT. These time ranges are not excluded when computing the FFT of a marked block or of the displayed data.
		+
		+	The section “FFT Covariance” allows to compute the FFT covariance over the data range selected.
		+
		+	If the check box “Covariance Spectrum” is checked, a text file (BESA vectorized ASCII format) will be written after the computation. The file can be loaded into BESA Research again, or can be analysed externally.
		+
		+	The file has the naming convention: [basename]FFTCovSvdBack_[MtgName].avr
		+
		+	Internally, the mean FFT is performed over the current montage. The covariance matrix is computed in frequency space.
		+
		+	The steps are:
		+	For each epoch to be added to the mean covariance matrix:
		+	1) Average reference for EEG, MAG, and GRA data (if the single montage channels box is
		+	not checked)
		+	2) Resample date to 256 Hz
		+	3) Compute FFT
		+	4) Add to FFT covariance matrix (either sum over all channels, or individually for
		+	each montage channel if that box is checked)
		+
		+	Then, a singular value decomposition is performed on the FFT covariance of each channel, to obtain the (complex) eigenvectors. The newly arranged matrix of eigenvectors is then inverse Fourier transformed to obtain waveforms for each of the components. These are written to file.

	=== Redisplaying the previous FFT ===		=== Redisplaying the previous FFT ===

← Older revision		Revision as of 12:57, 25 March 2019
Line 63:		Line 63:
	To start a mean FFT over an extended time range, e.g. between markers or over the whole data file, select the item ''Mean FFT-Spectrum'' in the <span style="color:#3366ff;">'''Process'''</span> menu (<span style="color:#3366ff;">'''Alt+P M'''</span>).		To start a mean FFT over an extended time range, e.g. between markers or over the whole data file, select the item ''Mean FFT-Spectrum'' in the <span style="color:#3366ff;">'''Process'''</span> menu (<span style="color:#3366ff;">'''Alt+P M'''</span>).

−	[[Image:~~Spectral (4)~~.~~gif~~ ]]	+	[[Image:MeanFFT_Dialog.png]]

@@ Line 158: / Line 158: @@
 '''Averaging FFT spectra'''
-Select '''Load and Average...''' (<span style="color:#3366ff;">'''Alt+F V'''</span>) to compute averages of previously saved FFT spectra. In the appearing window, select an FFT spectrum (<span style="color:#ff9c00;">'''<nowiki>*.fft</nowiki>'''</span>) from the list on the left and press the [[Image:|top]] button to copy it to the list of FFTs to be averaged on the right. Press <span style="color:#3366ff;">'''OK'''</span> to calculate and display the averaged FFT spectrum.
+Select '''Load and Average...''' (<span style="color:#3366ff;">'''Alt+F V'''</span>) to compute averages of previously saved FFT spectra. In the appearing window, select an FFT spectrum (<span style="color:#ff9c00;">'''*.fft'''</span>) from the list on the left and press the arrow button (-->) to copy it to the list of FFTs to be averaged on the right. Press <span style="color:#3366ff;">'''OK'''</span> to calculate and display the averaged FFT spectrum.
@@ Line 179: / Line 179: @@
 * Write the data in''' Vectorized '''format:
 ** Line 1 of the output file contains the number of frequency steps (Npts), a starting value for BESA Research’s time scale (TSB), the frequency step (DI), scaling in bins per microvolt (SB), a scaling value for the BESA Research display (SC), and the number of channels (Nchan) as shown in the following example:
-** <tt>Npts= 1023 TSB= 0.10 DI= 0.100 SB= 1.000 SC= 100.0 Nchan= 23</tt>
+*** <tt>Npts= 1023 TSB= 0.10 DI= 0.100 SB= 1.000 SC= 100.0 Nchan= 23</tt>
-** Line 2 lists the channel labels. Each successive line contains the amplitude/power values at each frequency for one channel.
+** Line 2 lists the channel labels.
-* Write the data in''' <u>M</u>ultiplexed''' format: Line 1 contains the frequency step size in Hz. Line 2 lists the channel labels. Each subsequent line contains amplitude/power values for all channels (in the sequence given in line 2) for one frequency.
+** Each successive line contains the amplitude/power values at each frequency for one channel.
@@ Line 188: / Line 193: @@
 For each of these output formats and montages, different data can be saved:
-* <u>'''A</u>mplitude Spectrum''' (<span style="color:#3366ff;">'''Alt+F FA'''</span>),
+* '''<u>A</u>mplitude Spectrum''' (<span style="color:#3366ff;">'''Alt+F FA'''</span>),
-* <u>'''P</u>ower Spectrum''' <span style="color:#3366ff;">'''(Alt+F FP'''</span>), or
+* '''<u>P</u>ower Spectrum''' <span style="color:#3366ff;">'''(Alt+F FP'''</span>), or
-* <u>'''R</u>eal + Imaginary Part''' (<span style="color:#3366ff;">'''Alt+F FR'''</span>). In this case, amplitudes of the real and imaginary components are written to two separate files.
+* '''<u>R</u>eal + Imaginary Part''' (<span style="color:#3366ff;">'''Alt+F FR'''</span>). In this case, amplitudes of the real and imaginary components are written to two separate files.
@@ Line 203: / Line 208: @@
 |-
 | amplitude spectrum
-| style="text-align: center;" | .fma
+| style="text-align: center;" | *.fma
-| style="text-align: center;" | .faa
+| style="text-align: center;" | *.faa
-| style="text-align: center;" | .fba
+| style="text-align: center;" | *.fba
 |-
 | power spectrum
-| style="text-align: center;" | .fmp
+| style="text-align: center;" | *.fmp
-| style="text-align: center;" | .fap
+| style="text-align: center;" | *.fap
-| style="text-align: center;" | .fbp
+| style="text-align: center;" | *.fbp
 |-
 | real components
-| style="text-align: center;" | .fmr
+| style="text-align: center;" | *.fmr
-| style="text-align: center;" | .far
+| style="text-align: center;" | *.far
 | style="text-align: center;" | N/A
 |-
 | imaginary components
-| style="text-align: center;" | .fmi
+| style="text-align: center;" | *.fmi
-| style="text-align: center;" | .fai
+| style="text-align: center;" | *.fai
 | style="text-align: center;" | N/A
 |}
@@ Line 231: / Line 236: @@
 '''Sending FFT data to MATLAB'''
-Select''' Send to MATLAB '''(<span style="color:#3366ff;">'''Alt+F M'''</span>) to transfer the current FFT data to MATLAB. This menu entry is available only when MATLAB is installed. Details on the MATLAB interface are provided in Help Chapter ''“MATLAB”.''
+Select''' Send to MATLAB '''(<span style="color:#3366ff;">'''Alt+F M'''</span>) to transfer the current FFT data to MATLAB. This menu entry is available only when MATLAB is installed. Details on the MATLAB interface are provided in the chapter [[MATLAB_Interface | MATLAB Interface]].
@@ Line 243: / Line 248: @@
-When hitting <span style="color:#3366ff;">'''OK'''</span>, the sent data will be made available in MATLAB in struct variable <span style="color:#ff9c00;">'''besa_fft'''</span>. For details on the data transfer from BESA Research to MATLAB, please refer to Help Chapter ''“The MATLAB interface”.''
+When hitting <span style="color:#3366ff;">'''OK'''</span>, the sent data will be made available in MATLAB in struct variable <span style="color:#ff9c00;">'''besa_fft'''</span>. For details on the data transfer from BESA Research to MATLAB, please refer to the chapter [[MATLAB_Interface | MATLAB Interface]].
@@ Line 255: / Line 260: @@
 '''Closing FFT'''
-To remove the FFT window (without saving the results), select ''Close'' in the<span style="color:#3366ff;">''' File'''</span> menu (<span style="color:#3366ff;">'''Alt+F C'''</span>), or simply type the <span style="color:#3366ff;">'''<Esc> '''</span>key.
+To remove the FFT window (without saving the results), select ''Close'' in the<span style="color:#3366ff;">''' File'''</span> menu (<span style="color:#3366ff;">'''Alt+F C'''</span>), or simply type the <span style="color:#3366ff;">'''Esc'''</span> key.
 === FFT ‘Options’ Menu ===

@@ Line 18: / Line 18: @@
 The Fast Fourier Transformation (FFT) can be applied to a marked region, the data displayed on the screen, over a larger time range in the data between two markers, over marked epochs, or the whole EEG, in order to examine the frequency content of a signal. Results of the FFT can be viewed in a variety of ways, including amplitude and power spectra, amplitude and power in frequency bands, and these results may be printed or written to data files in ASCII format. The previously calculated FFT spectrum may be redisplayed. The current FFT can be saved to a binary file and reloaded. Topographic maps of amplitude, power, and phase can be plotted.
-=== FFT Computation and Display  ===
 Two FFT computations are available in BESA Research:
-* The FFT over a short data block of interest
+* [[#FFT over a short data block of interest | The FFT over a short data block of interest]]
-* The Mean FFT over an extended time range
+* [[#Mean FFT Spectrum over an extended time range | The Mean FFT over an extended time range]]
-==== FFT over a short data block of interest ====
+=== FFT over a short data block of interest ===
 To start an FFT calculation, highlight a data block by left mouse click and drag. If no block is highlighted, the FFT will be performed over the time range shown on the display. Apply one of the following:
@@ Line 58: / Line 59: @@
-==== Mean FFT Spectrum over an extended time range ====
+=== Mean FFT Spectrum over an extended time range ===
 To start a mean FFT over an extended time range, e.g. between markers or over the whole data file, select the item ''Mean FFT-Spectrum'' in the <span style="color:#3366ff;">'''Process'''</span> menu (<span style="color:#3366ff;">'''Alt+P M'''</span>).