Testing Parseval's Theorem with Power Spectral Density
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Suppose I am finding the power spectral density of data like such:
x = winter_data.values #measured at frequency 1Hz
f, Sxx = sp.signal.welch(x1, fs=1, window='hanning', nperseg=N, noverlap = N / 2)
I want to test that Parseval's theorem works on these data sets. Since welch returns the power spectral density, should we not have
np.trapz(x**2, dx=1)
and
len(x1)*np.trapz(Sxx, f)
equal to eachother? Or is my definition of power spectral density incorrect? (np.trapz() is just used to calculate the integrals). I always thought that power spectral density was defined as
S_xx(f) = (1/T)|X(f)|^2
Currently I am not getting them equal.
scipy signals signal-processing fft
asked Nov 12 at 5:53
Luke Polson
898
add a comment |
up vote
0
down vote
favorite
Suppose I am finding the power spectral density of data like such:
x = winter_data.values #measured at frequency 1Hz
f, Sxx = sp.signal.welch(x1, fs=1, window='hanning', nperseg=N, noverlap = N / 2)
I want to test that Parseval's theorem works on these data sets. Since welch returns the power spectral density, should we not have
np.trapz(x**2, dx=1)
and
len(x1)*np.trapz(Sxx, f)
equal to eachother? Or is my definition of power spectral density incorrect? (np.trapz() is just used to calculate the integrals). I always thought that power spectral density was defined as
S_xx(f) = (1/T)|X(f)|^2
Currently I am not getting them equal.
scipy signals signal-processing fft
asked Nov 12 at 5:53
Luke Polson
898
They are approxmatively equal for some test data I made up. The windowing procedure will make them non equal anyway. What error do you have?
– Pierre de Buyl
Nov 13 at 12:11
I'm getting 100000 for the np.trapz(x**2, dx=1) and 1000000 for len(x1)*np.trapz(Sxx, f). So abour 10x greater.
– Luke Polson
Nov 14 at 4:17
It is possible that the DC componennt is removed by welch. Could you trynp.trapz((x-x.mean())**2, dx=1)?
– Pierre de Buyl
Nov 14 at 8:28
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose I am finding the power spectral density of data like such:
x = winter_data.values #measured at frequency 1Hz
f, Sxx = sp.signal.welch(x1, fs=1, window='hanning', nperseg=N, noverlap = N / 2)
I want to test that Parseval's theorem works on these data sets. Since welch returns the power spectral density, should we not have
np.trapz(x**2, dx=1)
and
len(x1)*np.trapz(Sxx, f)
equal to eachother? Or is my definition of power spectral density incorrect? (np.trapz() is just used to calculate the integrals). I always thought that power spectral density was defined as
S_xx(f) = (1/T)|X(f)|^2
Currently I am not getting them equal.
scipy signals signal-processing fft
asked Nov 12 at 5:53
Luke Polson
898
Suppose I am finding the power spectral density of data like such:
x = winter_data.values #measured at frequency 1Hz
f, Sxx = sp.signal.welch(x1, fs=1, window='hanning', nperseg=N, noverlap = N / 2)
I want to test that Parseval's theorem works on these data sets. Since welch returns the power spectral density, should we not have
np.trapz(x**2, dx=1)
and
len(x1)*np.trapz(Sxx, f)
equal to eachother? Or is my definition of power spectral density incorrect? (np.trapz() is just used to calculate the integrals). I always thought that power spectral density was defined as
S_xx(f) = (1/T)|X(f)|^2
Currently I am not getting them equal.
scipy signals signal-processing fft
scipy signals signal-processing fft
asked Nov 12 at 5:53
Luke Polson
898
asked Nov 12 at 5:53
Luke Polson
898
asked Nov 12 at 5:53
Luke Polson
898
asked Nov 12 at 5:53
Luke Polson
898
asked Nov 12 at 5:53
Luke Polson
898
898
They are approxmatively equal for some test data I made up. The windowing procedure will make them non equal anyway. What error do you have?
– Pierre de Buyl
Nov 13 at 12:11
I'm getting 100000 for the np.trapz(x**2, dx=1) and 1000000 for len(x1)*np.trapz(Sxx, f). So abour 10x greater.
– Luke Polson
Nov 14 at 4:17
It is possible that the DC componennt is removed by welch. Could you trynp.trapz((x-x.mean())**2, dx=1)?
– Pierre de Buyl
Nov 14 at 8:28
add a comment |
They are approxmatively equal for some test data I made up. The windowing procedure will make them non equal anyway. What error do you have?
– Pierre de Buyl
Nov 13 at 12:11
I'm getting 100000 for the np.trapz(x**2, dx=1) and 1000000 for len(x1)*np.trapz(Sxx, f). So abour 10x greater.
– Luke Polson
Nov 14 at 4:17
It is possible that the DC componennt is removed by welch. Could you trynp.trapz((x-x.mean())**2, dx=1)?
– Pierre de Buyl
Nov 14 at 8:28
They are approxmatively equal for some test data I made up. The windowing procedure will make them non equal anyway. What error do you have?
– Pierre de Buyl
Nov 13 at 12:11
They are approxmatively equal for some test data I made up. The windowing procedure will make them non equal anyway. What error do you have?
– Pierre de Buyl
Nov 13 at 12:11
I'm getting 100000 for the np.trapz(x**2, dx=1) and 1000000 for len(x1)*np.trapz(Sxx, f). So abour 10x greater.
– Luke Polson
Nov 14 at 4:17
I'm getting 100000 for the np.trapz(x**2, dx=1) and 1000000 for len(x1)*np.trapz(Sxx, f). So abour 10x greater.
– Luke Polson
Nov 14 at 4:17
It is possible that the DC componennt is removed by welch. Could you try
np.trapz((x-x.mean())**2, dx=1)?– Pierre de Buyl
Nov 14 at 8:28
It is possible that the DC componennt is removed by welch. Could you try
np.trapz((x-x.mean())**2, dx=1)?– Pierre de Buyl
Nov 14 at 8:28
add a comment |
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They are approxmatively equal for some test data I made up. The windowing procedure will make them non equal anyway. What error do you have?
– Pierre de Buyl
Nov 13 at 12:11
I'm getting 100000 for the np.trapz(x**2, dx=1) and 1000000 for len(x1)*np.trapz(Sxx, f). So abour 10x greater.
– Luke Polson
Nov 14 at 4:17
It is possible that the DC componennt is removed by welch. Could you try
np.trapz((x-x.mean())**2, dx=1)?– Pierre de Buyl
Nov 14 at 8:28