New answers tagged power-spectral-density
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I think it may be an optional parameter, 'spectrumtype', see below.
https://www.mathworks.com/help/signal/ref/pwelch.html
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Why everyone displays (dB) in the unit in the graph?
dB is a relative logarithmic measure which is a reasonably first order approximation for human perception. It always needs a reference. For many acoustic measurement, it's actually dBSPL (Sound Pressure Level) where the reference pressure is $20\mu Pa$.
$dB/Hz$ or $dB/\sqrt{Hz}$ doesn't make sense for ...
2
pwelch() can return a one sided (default) or two sided spectrum. For one sided, the energy of negative frequency is added to the symmetric positive ones.
pwelch() returns a spectral density in something like $W/Hz$ which is actually dependent on the sample rate. By default pwelch() assumes a sample rate of $2\pi$.
Try
pp = pwelch(x, ones(n,1), n-1, n,1,'...
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A standard continuous wavelet transformation (the one that produce a 2D scale/shift map) is a linear operator. It produces real or complex coefficients that are related to the amplitude on "how a given wavelet at specific shift and scale matches the signal". These coefficients are (most generally) homogeneous with the signal's amplitude.
This being ...
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Its absolute value is amplitude. Squared is power. But if it's a plot you've come across, it's not possible to tell without units, as it could be log-transformed (decibels), which nullifies the distinction between amplitude and power (amp: $\log(x)$ -- pow: $\log(x^2) = 2 \log(x)$, all intensities double and colors don't change if autoscaled). However, for ...
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How does that make a difference? Intensity and Power are linked by a strictly monotonous function (the very complicated p(i)=i²); since colors aren't "linear" by any means, the only difference between plotting the power and the amplitude would be a relabeling of the color bar.
In fact, that's why we often use decibel, so that the scale is identical ...
1
Typically a transfer function is described as a function of the complex variable $s$ as given by the Laplace Transform of the systems impulse response:
$$H(s)= \frac{N(s)}{Q(s)}$$
By expressing the transfer function of a linear system as a ratio of two such polynomials, we are able to describe the linear system uniquely in terms of the roots of those ...
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I don't think they get a special name -just the numerator and denominator function.
Notice that the frequency response is defined as the ratio of output spectrum to input spectrum, but since the input signal is called X and the output Y, I don't think N and Q have a direct relationship with them (lest you're omitting some context from the material where you ...
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Proper STFT isn't simply putting a window on data and taking its FFT; I wouldn't recommend reinventing it unless knowing exactly what you're doing. There's open source implementations: librosa, ssqueezepy.
For matching against pre-computed values, it's important to account for any pre- or post-processing steps, such as baseline normalization or the log ...
1
Power of a 1D signal is defined as time-average of energy:
$$
P_x = \frac{1}{N}\sum_{n=0}^{N-1} |x[n]|^2
$$
This can be applied on each channel independently.
However, there are many other measures of "power of brain signals" - depending on the exact physical source we seek to describe. In particular, EEG describes electrical sources, and MEG ...
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