Time Frequency Resolution In BESA - Revision history

Abinash at 14:44, 5 May 2021

2021-05-05T14:44:24Z

Abinash at 15:38, 15 February 2017

2017-02-15T15:38:54Z

Harald at 15:11, 8 April 2016

2016-04-08T15:11:36Z

Robert at 13:01, 7 March 2016

2016-03-07T13:01:37Z

Robert at 12:59, 7 March 2016

2016-03-07T12:59:16Z

Robert at 12:55, 7 March 2016

2016-03-07T12:55:45Z

Robert at 12:53, 7 March 2016

2016-03-07T12:53:04Z

Robert at 12:47, 7 March 2016

2016-03-07T12:47:49Z

Robert: Created page with "== Introduction == The time-frequency resolution of the complex demodulation used in BESA depends on the user-settings for “Frequency and Time Sampling” in the “Coheren..."

2016-03-07T12:46:13Z

Created page with "== Introduction == The time-frequency resolution of the complex demodulation used in BESA depends on the user-settings for “Frequency and Time Sampling” in the “Coheren..."

New page

== Introduction ==

The time-frequency resolution of the complex demodulation used in BESA depends on the user-settings for “Frequency and Time Sampling” in the “Coherence” tab of the ERP dialog box. The following table lists the 50% power and amplitude drops, respectively, as a function of the time-frequency sampling setting. Frequencies are given relative to the center frequency of a sharp frequency oscillation, latencies are given to the latency of a sharp time event.
For example, with a time-frequency setting of 1.0 Hz, 50 ms, a sine wave with sharp frequency f will be smoothed to a time-frequency signal that has a full power width at half maximum of 2×1.42 Hz. In other words, at frequencies f ± 1.42 Hz, the displayed power in the time-frequency plot is half of the displayed power at frequency f. A sharp time-event, (e.g. a sharp spike in the time-domain) will be smoothed to a time-frequency signal of 2×78.8 ms full power width at half maximum.

Table

The following two plots show the frequency blurring (left) and the temporal blurring (right) for a time-frequency sampling of 2.0 Hz / 25 ms. When applying a denser frequency sampling, the frequency resolution will increase, and the time resolution will decrease proportionally (i.e. the x-axis scaling will change proportionally).

[[File: C:\Users\Robert\Desktop\Time Frequency Resolution.png]]

@@ Line 1: / Line 1: @@
 {{BESAInfobox
 |title = Module information
-|module = BESA Research Complete (or Basic+Coherence)
+|module = BESA Research Basic+Coherence or higher
-|version = 5.2 or higher
+|version = BESA Research 5.2 or higher
 }}

← Older revision		Revision as of 15:38, 15 February 2017
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	[[File: Time_Frequency_Resolution.png]]		[[File: Time_Frequency_Resolution.png]]

−	[[Category:Time-Frequency]	+	[[Category:Time-Frequency]]

← Older revision		Revision as of 15:11, 8 April 2016
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		+	{{BESAInfobox
		+	\|title = Module information
		+	\|module = BESA Research Complete (or Basic+Coherence)
		+	\|version = 5.2 or higher
		+	}}
		+
	==FAQ==		==FAQ==

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	[[File: Time_Frequency_Resolution.png]]		[[File: Time_Frequency_Resolution.png]]
		+
		+	[[Category:Time-Frequency]

← Older revision		Revision as of 13:01, 7 March 2016
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		+	==FAQ==

−	The time-frequency resolution of the complex demodulation used in BESA depends on the user-settings for ~~“Frequency~~ and Time ~~Sampling”~~ in the ~~“Coherence”~~ tab of the ERP dialog box. The following table lists the 50% power and amplitude drops, respectively, as a function of the time-frequency sampling setting. Frequencies are given relative to the center frequency of a sharp frequency oscillation, latencies are given to the latency of a sharp time event.	+	The time-frequency resolution of the complex demodulation used in BESA depends on the user-settings for “''Frequency and Time Sampling''” in the “''Coherence''” tab of the ERP dialog box. The following table lists the 50% power and amplitude drops, respectively, as a function of the time-frequency sampling setting. Frequencies are given relative to the center frequency of a sharp frequency oscillation, latencies are given to the latency of a sharp time event.
	For example, with a time-frequency setting of 1.0 Hz, 50 ms, a sine wave with sharp frequency f will be smoothed to a time-frequency signal that has a full power width at half maximum of 2×1.42 Hz. In other words, at frequencies f ± 1.42 Hz, the displayed power in the time-frequency plot is half of the displayed power at frequency f. A sharp time-event, (e.g. a sharp spike in the time-domain) will be smoothed to a time-frequency signal of 2×78.8 ms full power width at half maximum.		For example, with a time-frequency setting of 1.0 Hz, 50 ms, a sine wave with sharp frequency f will be smoothed to a time-frequency signal that has a full power width at half maximum of 2×1.42 Hz. In other words, at frequencies f ± 1.42 Hz, the displayed power in the time-frequency plot is half of the displayed power at frequency f. A sharp time-event, (e.g. a sharp spike in the time-domain) will be smoothed to a time-frequency signal of 2×78.8 ms full power width at half maximum.

@@ Line 1: / Line 1: @@
 The time-frequency resolution of the complex demodulation used in BESA depends on the user-settings for “Frequency and Time Sampling” in the “Coherence” tab of the ERP dialog box. The following table lists the 50% power and amplitude drops, respectively, as a function of the time-frequency sampling setting. Frequencies are given relative to the center frequency of a sharp frequency oscillation, latencies are given to the latency of a sharp time event.
@@ Line 43: / Line 42: @@
 The following two plots show the frequency blurring (left) and the temporal blurring (right) for a time-frequency sampling of 2.0 Hz / 25 ms. When applying a denser frequency sampling, the frequency resolution will increase, and the time resolution will decrease proportionally (i.e. the x-axis scaling will change proportionally).
 [[File: Time_Frequency_Resolution.png]]

@@ Line 14: / Line 14: @@
 |-
 | 0.25 Hz / 200 ms
+| ±0.354 Hz, ±315 ms
+| ±0.496 Hz, ±443 ms
 |-
 | 0.5 Hz / 100 ms
+| ±0.708 Hz, ±158 ms
+| ±0.993 Hz, ±222 ms
 |-
 | 1.0 Hz / 50 ms
+| ±1.42 Hz, ±78.8 ms
+| ±1.99 Hz, ±111 ms
 |-
 | 2.0 Hz / 25 ms
+| ±2.83 Hz, ±39.4 ms
+| ±3.97 Hz, ±55.4 ms
 |-
 | 2.5 Hz / 20 ms
+| ±3.54 Hz, ±31.5 ms
+| ±4.96 Hz, ±44.3 ms
 |-
 | 5.0 Hz / 10 ms
+| ±7.08 Hz, ±15.8 ms
+| ±9.93 Hz, ±22.2 ms
 |-
 | 10.0 Hz / 5 ms
+| ±14.2 Hz, ±7.88 ms
+| ±19.9 Hz, ±11.1 ms
 |}

@@ Line 4: / Line 4: @@
 For example, with a time-frequency setting of 1.0 Hz, 50 ms, a sine wave with sharp frequency f will be smoothed to a time-frequency signal that has a full power width at half maximum of 2×1.42 Hz. In other words, at frequencies f ± 1.42 Hz, the displayed power in the time-frequency plot is half of the displayed power at frequency f. A sharp time-event, (e.g. a sharp spike in the time-domain) will be smoothed to a time-frequency signal of 2×78.8 ms full power width at half maximum.
-Table
+{| class="wikitable"
 The following two plots show the frequency blurring (left) and the temporal blurring (right) for a time-frequency sampling of 2.0 Hz / 25 ms. When applying a denser frequency sampling, the frequency resolution will increase, and the time resolution will decrease proportionally (i.e. the x-axis scaling will change proportionally).

← Older revision		Revision as of 12:47, 7 March 2016
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−	[[File: ~~C:\Users\Robert\Desktop\Time Frequency Resolution~~.png]]	+	[[File: Time_Frequency_Resolution.png]]