corrected psd equation in spectral notebook

Author: skalade

notebooks/frequency_spectrum/01_spectrum_analysis.ipynb

@@ -685,7 +685,7 @@
  "\n",
  "One of the most common ways of observing the power spectra of a signal of interest is by calculating the Power Spectral Density (PSD), defined as\n",
  "\n",
- "$PSD[n] = 10 \\times \\log_{10}(\\frac{2 {|y[n]|^{2}}}{F_{s} \\sum^{N_{w}}_{n=0}w^{2}[n]})$\n",
+ "$PSD[n] = 10 \\times \\log_{10}(\\frac{2 {|y[n]|^{2}}}{F_{s} \\sum^{N_{w}-1}_{n=0}w^{2}[n]})$\n",
  "\n",
  "We get the power of the signal by squaring the absolute values of the FFT output $y[n]$, and normalizing by the sampling rate $F_{s}$ and the sum of our window weights $w$, where $N_{w}$ is the length of our window. Don't forget to add a factor of 2 since we are dealing with a one-sided spectrum. The PSD is measured in decibels per hertz (dB/Hz)."
  ]