davrot/pytutorial
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Update README.md

Browse source 
Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
This commit is contained in:
David Rotermund 2023-11-16 17:25:38 +01:00 committed by GitHub
parent f3de651428
commit 0404a1ad77
No known key found for this signature in database
GPG key ID: 4AEE18F83AFDEB23
1 changed files with 19 additions and 0 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

19
numpy_fft_1/README.md
View file

@ -54,3 +54,22 @@ Since we deal with a 1 dimensional time series
y_fft: np.ndarray = np.fft.rfft(y)
frequency_axis: np.ndarray = np.fft.rfftfreq(y.shape[0]) * sampling_frequency
```
## Calculating a [normalized](https://de.mathworks.com/help/signal/ug/power-spectral-density-estimates-using-fft.html) power spectral density
The goal is to produce a power spectral density that is compatible with the [Parseval's identity](https://en.wikipedia.org/wiki/Parseval%27s_identity). Or in other words: the sum over the power spectrum without the zero frequency has the same value as the variance of the time series.
```python
y_power: np.ndarray = (1 / (sampling_frequency * y.shape[0])) * np.abs(y_fft) ** 2
y_power[1:-2] *= 2
if frequency_axis[-1] != (sampling_frequency / 2.0):
y_power[-1] *= 2
```
Check of the normalization:
```python
print(y_power[1:].sum()) # -> 0.5
print(np.var(y)) # -> 0.5
```