tdehaeze/digital-brain
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update Content - 2022-03-15

Browse Source
This commit is contained in:
Thomas Dehaeze
2022-03-15 16:40:48 +01:00
parent e6390908c4
commit 22fb3361a5
148 changed files with 3981 additions and 3197 deletions
Download Patch File Download Diff File Expand all files Collapse all files

23
content/zettels/power_spectral_density.md
View File

@@ -5,11 +5,11 @@ draft = false
+++
Tags
: [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}})
: [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio.md" >}})
Tutorial about Power Spectral Density is accessible [here](https://research.tdehaeze.xyz/spectral-analysis/).
A good article about how to use the `pwelch` function with Matlab <schmid12_how_to_use_fft_matlab>.
A good article about how to use the `pwelch` function with Matlab (<a href="#citeproc_bib_item_1">Schmid 2012</a>).
## Parseval's Theorem - Linking the Frequency and Time domain {#parseval-s-theorem-linking-the-frequency-and-time-domain}
@@ -109,11 +109,11 @@ Sxx_t = Pxx/d_f;
Sxx_o = 2*Sxx_t(1:L/2+1);
```
The result is shown in Figure [1](#org41c99c6).
The result is shown in Figure [1](#figure--fig:psd-manual-example).
<a id="org41c99c6"></a>
<a id="figure--fig:psd-manual-example"></a>
{{< figure src="/ox-hugo/psd_manual_example.png" caption="Figure 1: Amplitude Spectral Density with manual computation" >}}
{{< figure src="/ox-hugo/psd_manual_example.png" caption="<span class=\"figure-number\">Figure 1: </span>Amplitude Spectral Density with manual computation" >}}
This can also be done using the `pwelch` function which integrated a "window" that permits to do some averaging.
@@ -122,8 +122,15 @@ This can also be done using the `pwelch` function which integrated a "window" th
[pxx, f] = pwelch(x, hanning(ceil(5/T_s)), [], [], 1/T_s);
```
The comparison of the two method is shown in Figure [2](#orge7a31a8).
The comparison of the two method is shown in Figure [2](#figure--fig:psd-comp-pwelch-manual-example).
<a id="orge7a31a8"></a>
<a id="figure--fig:psd-comp-pwelch-manual-example"></a>
{{< figure src="/ox-hugo/psd_comp_pwelch_manual_example.png" caption="Figure 2: Amplitude Spectral Density with manual computation" >}}
{{< figure src="/ox-hugo/psd_comp_pwelch_manual_example.png" caption="<span class=\"figure-number\">Figure 2: </span>Amplitude Spectral Density with manual computation" >}}
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Schmid, Hanspeter. 2012. “How to Use the Fft and Matlab’s Pwelch Function for Signal and Noise Simulations and Measurements.” <i>Institute of Microelectronics</i>.</div>
</div>