Methods of removing intrinsic noise from signal under test (SUT)
A test system implemented method removes intrinsic noise from a waveform representation of a repeating signal under test (SUT). The method includes obtaining an oversampled equivalent-time waveform representation of the repeating SUT. The method further includes obtaining a time-domain representation of a combined noise of the equivalent-time waveform above the deterministic maximum frequency by applying the equivalent-time waveform to a high-pass filter. The method further includes determining a standard deviation of the time-domain representation of the combined noise, and determining a correction factor α in accordance with the standard deviation of the digitizer noise, and the standard deviation of the time-domain representation of the combined noise. The method further includes applying the equivalent-time waveform representation to a low-pass filter having a unity magnitude response at frequencies below the cutoff frequency and a correction factor magnitude response at frequencies above the cutoff frequency.
1 . A test system implemented method of removing intrinsic noise from a waveform representation of a repeating signal under test (SUT), comprising:
determining an intrinsic noise of a digitizer channel of the test system;
applying the repeating SUT to the digitizer channel of the test system;
obtaining an equivalent-time waveform representation of the repeating SUT, wherein the waveform representation is oversampled such that a Nyquist frequency of the waveform representation is greater than deterministic maximum frequency of the repeating SUT;
obtaining a time-domain representation of a combined noise of the equivalent-time waveform above the deterministic maximum frequency by applying the equivalent-time waveform to a high-pass filter having a cutoff frequency greater than the deterministic maximum frequency;
determining a standard deviation of the time-domain representation of the combined noise;
determining a correction factor α in accordance with the following equation,
α
=
sqrt
(
σ
d
·
σ
d
-
σ
i
·
σ
i
)
/
σ
d
where σ i is a standard deviation of the digitizer noise, and σ d is the standard deviation of the time-domain representation of the combined noise, and
applying the equivalent-time waveform representation to a low-pass filter having the cutoff frequency to obtain an output waveform representation in which the intrinsic noise has been removed, wherein the low pass filter has a unity magnitude response at frequencies below the cutoff frequency and a α magnitude response at frequencies above the cutoff frequency.
2 . The method of claim 1 , wherein the repeating SUT is an optical signal.
3 . The method of claim 1 , wherein the test system is an oscilloscope.
4 . The method of claim 1 , wherein the high pass filter has a unity magnitude response at frequencies above the cutoff frequency and a zero-magnitude response at frequencies below the cutoff frequency.
5 . A test system implemented method of removing intrinsic noise from a waveform representation of a repeating signal under test (SUT), comprising:
determining a digitizer noise of a digitizer channel of the test system;
applying the repeating SUT to the digitizer channel of the test system;
obtaining an equivalent-time waveform representation of the repeating SUT, wherein the waveform representation is oversampled such that a Nyquist frequency of the waveform representation is greater than deterministic maximum frequency of the repeating SUT;
obtaining a frequency power spectrum of the equivalent-time waveform representation and integrating the power above a cutoff frequency to obtain a standard deviation of a combined noise of the equivalent-time waveform above the deterministic maximum frequency, wherein the cutoff frequency is greater than the deterministic maximum frequency;
determining a correction factor α in accordance with the following equation,
α
=
sqrt
(
σ
d
·
σ
d
-
σ
i
·
σ
i
)
/
σ
d
where σ i is a standard deviation of the digitizer noise, and σ d is the standard deviation of the time-domain representation of the combined noise, and
applying the equivalent-time waveform representation to a low-pass filter having the cutoff frequency to obtain an output waveform representation in which the digitizer noise has been removed, wherein the low pass filter has a unity magnitude response at frequencies below the cutoff frequency and a α magnitude response at frequencies above the cutoff frequency.
6 . The method of claim 5 , wherein the repeating SUT is an optical signal.
7 . The method of claim 5 , wherein the test system is an oscilloscope.
8 . A non-transitory tangible computer readable medium having stored thereon executable instructions embodied in the computer readable medium that when executed by at least one processor of a test system cause the test system to execute a method of removing intrinsic noise from a waveform representation of a repeating signal under test (SUT), the method including:
obtaining an equivalent-time waveform representation of the repeating SUT from sampling data received from a digitizer channel of the test system, wherein the waveform representation is oversampled such that a Nyquist frequency of the waveform representation is greater than deterministic maximum frequency of the repeating SUT;
obtaining a time-domain representation of a combined noise of the equivalent-time waveform above the deterministic maximum frequency by applying the equivalent-time waveform to a high-pass filter having a cutoff frequency greater than the deterministic maximum frequency;
determining a standard deviation of the time-domain representation of the combined noise;
determining a correction factor α in accordance with the following equation,
α
=
sqrt
(
σ
d
·
σ
d
-
σ
i
·
σ
i
)
/
σ
d
where σ i is a standard deviation of the digitizer noise, and σ d is the standard deviation of the time-domain representation of the combined noise, and
applying the equivalent-time waveform representation to a low-pass filter having the cutoff frequency to obtain an output waveform representation in which the intrinsic noise has been removed, wherein the low pass filter has a unity magnitude response at frequencies below the cutoff frequency and a α magnitude response at frequencies above the cutoff frequency.
9 . The non-transitory tangible computer readable medium of claim 8 , wherein the test system is an oscilloscope.
10 . The non-transitory tangible computer readable medium of claim 8 , wherein the non-transitory tangible computer readable medium is a memory of the oscilloscope.
11 . The non-transitory tangible computer readable medium of claim 8 , wherein the high pass filter has a unity magnitude response at frequencies above the cutoff frequency and a zero magnitude response at frequencies below the cutoff frequency.