New answers tagged power-spectral-density
5
No. The aliased component will interfere with the non-aliased components and the interference can constructive or destructive.
Trivial example:
$$x[n] = \sin\left(\frac\pi2n\right)$$
If you down sample this to $y[n] = x[2n]$, you get all zeros.
0
The factor of "2" comes from the contribution of the negative frequencies, which doesn't apply to DC.
A better way to plot this is to NOT multiply with 2 but plot the entire FFT range from -400Hz to +400Hz. There you will see three components: 1 W at DC and 0.25W each at -50Hz and +50Hz which is exactly what's happening here.
If you want to plot ...
1
If the system described by the transfer function $H(s)$ is stable, you can obtain its frequency response by substituting $s=j\omega$, and use the relation that you found:
$$S_Y(\omega)=S_X(\omega)\big|H(j\omega)\big|^2\tag{1}$$
where $S_X(\omega)$ and $S_Y(\omega)$ denote the power spectra of the system's input and its output, respectively.
Top 50 recent answers are included
Related Tags
power-spectral-density × 588fft × 125
fourier-transform × 79
frequency-spectrum × 74
matlab × 73
noise × 69
signal-analysis × 65
autocorrelation × 62
discrete-signals × 37
python × 28
random-process × 27
signal-power × 22
filters × 20
digital-communications × 20
dft × 19
cross-correlation × 16
spectrogram × 16
stochastic × 15
window-functions × 14
snr × 14
gaussian × 13
spectrum-estimation × 13
sampling × 11
bandwidth × 11
continuous-signals × 10