24 votes
Accepted

Power spectral density vs. FFT bin magnitude

The fast Fourier transform ($\textrm{FFT}$) algorithms are fast algorithms for computing the discrete Fourier transform ($\textrm{DFT}$). This is achieved by successive decomposition of the $N$-point $...
user avatar
  • 3,272
13 votes
Accepted

What should be the correct scaling for PSD calculation using $\tt fft$

There is only one correct way of scaling DFT when calculating PSD with RMS values. Given input signal $x$ and its DFT $X$, the exact formula is: $$\mathrm{PSD}=\frac{2\cdot \hat{X}}{f_s\cdot S} $$ ...
user avatar
  • 10.5k
12 votes
Accepted

What is the difference between the PSD and the Power Spectrum?

The power spectrum is a general term that describes the distribution of power contained in a signal as a function of frequency. From this perspective, we can have a power spectrum that is defined over ...
user avatar
  • 1,372
8 votes
Accepted

Understanding the Windowing Method in PSD Calculation

I don't really understand what do you mean by multiply them in the time domain and multiply them with window function. I think that you are trying to implement the Welch's PSD calculation. If so, ...
user avatar
  • 10.5k
7 votes
Accepted

Is it only me or matlab's periodogram's function is confusing?

As the documentation states, periodogram provides a power spectral density estimate pxx: ...
user avatar
  • 405
7 votes
Accepted

How to interpret spectrogram correctly?

The problem is not the spectrogram parameters, these are correct since they only depend on what resolution you want in time and frequency domain. Also, the spectrogram interpretation is correct, there ...
user avatar
  • 186
6 votes

What is cross-spectral density- CSD?

To add to the above well stated explanation, in the case of wavelets, which are finite in time, it is more correct not to use the term 'power' but 'energy'. For Fourier who has as basis functions the ...
user avatar
6 votes
Accepted

Interpretation of Clarke's Doppler power spectral density

A simple, "non-technical" way of thinking of it is the fact that the Doppler frequency is proportional to $\cos\theta$. The amplitudes of cosine, however, are not uniformly distributed, but are ...
user avatar
  • 2,142
6 votes
Accepted

signal of $\frac{1}{f}$ Noise

Power-law behaviors in frequency can be found in several unrelated observations and systems. This is apparently the case for $1/f$ or flicker noise. Note that an exact $\alpha=1$ exponent might be too ...
user avatar
5 votes
Accepted

How Exactly Does MATLAB Zero Pad Signal?

Lets say you have a vector $ x = {\left[ 1, 2, 3, 4 \right]}^{T} $. You want to have a look on its DFT transform then you apply DFT on it and have the 4 points DFT transform of the data. In MATLAB it ...
user avatar
  • 40.4k
5 votes
Accepted

What is the relationship between the PSD of a continuous signal and the PSD of its periodically sampled one?

If you sample a finite-power continuous-time random process $x(t)$ you get a discrete-time random process $y_k$. If $x(t)$ is wide-sense stationary (WSS) you get for the autocorrelation function of $...
user avatar
  • 80.2k
5 votes
Accepted

Is the periodogram squared-magnitude DFT or squared-average DFT?

The periodogram is simply the squared magnitude of the DFT. Since the periodogram is a rather poor estimate of the power density spectrum of a random process there are methods which use averaging of ...
user avatar
  • 80.2k
5 votes
Accepted

WSS Ergodic Process with Power Spectrum

You can compute the power of the process from its power spectrum as well as from its PDF. Equating the two gives you a relation between the constants $A$ and $B$. More specifically you get $$\int_{-B}...
user avatar
  • 80.2k
5 votes

Averaging multiple FFTs in matlab

Welch’s method is a scheme to reduce the fluctuations (noise) in spectral power estimations when you have only a single time sequence with which to work. Because you have multiple time sequences, I’m ...
user avatar
5 votes
Accepted

Power spectrum estimate from FFT

The difference is in the scaling of the power spectrum. I suppose you will find that the difference in scaling always equals $L/F_s$, which for the numbers in your question is indeed $8000/500=16$. ...
user avatar
  • 80.2k
5 votes
Accepted

Numerically generating noise time series from spectral density

As mentioned by @MBaz in comments, you could use the fact that filtering white noise with unitary power spectral density (for example from independent Gaussian samples zero mean and unitary standard ...
user avatar
  • 1,732
5 votes
Accepted

Decorrelating Stationary Colored Gaussian Noise -- Effect On The Desired Signal

Yes, the "Whitening" is basically filtering the signal using an LTI System. The Result would be the signal $ \mathbf{s} $ filtered by the system which whitens the noise. In the framework of Matched ...
user avatar
  • 40.4k
5 votes
Accepted

Power spectral density of $\left(x(t)\right)^2$?

Since the question has been raised as to whether the hint that I had given to the OP in a comment on the original question was appropriate for a newcomer to signal processing, here goes. Stripped of ...
user avatar
5 votes

When to use cross spectral density versus cross correlation?

The cross-spectral density is in the frequency domain while the cross-correlation function is in the time domain. The two are Fourier Transform pairs, the FT of the cross correlation function is the ...
user avatar
  • 37.1k
5 votes
Accepted

Calculating the Spectral Centroid of a Signal

The function you wrote is basically like calculating the center of mass of a body or for that matter the Mean Value of a Distribution. If you remember from Probability, the Mean is given by: $$ E \...
user avatar
  • 40.4k
5 votes

Interpretation of Clarke's Doppler power spectral density

In addition to Carlos answer, I want to correct your general understanding: What I understand of Doppler spread is that the relative motion between Transmitter (TX) and Receiver (RX) change the ...
user avatar
5 votes

Cross Power Spectrum

Whenever talking about Cross Correlation of signals it is important to well define it. If you mean Cross Correlation in most common sense (Signal Processing): $$ \left( x \star y \right) \left[ n \...
user avatar
  • 40.4k
5 votes

PSDs and Parseval's theorem

That equation is indeed simple, but it's also wrong. So your doubts are completely justified. What is probably meant is something like $$S_X(f)=\lim_{T\rightarrow\infty}\frac{1}{T}\left|X_T(f)\right|^...
user avatar
  • 80.2k
5 votes
Accepted

Show That the Power Spectrum Density Matrix Is Positive Semi Definite (PSD) Matrix

Pay attention that for a Scalar Random Process the Power Spectrum Density is non negative. Namely, let $ y \left[ n \right] \in \mathbb{R} $ be a WSS Random process with its Auto Correlation function ...
user avatar
  • 40.4k
5 votes

$|X(e^{jω})|^2$ - Power or Energy Density?

do you see anywhere in your book where this "DTFT" is defined for your w.s.s. process, $x[n]$? the DTFT is normally defined as $$ X(e^{j \omega}) \triangleq \sum\limits_{n=-\infty}^{+\infty} x[n] e^{...
user avatar
5 votes
Accepted

Power Spectral Density From Variance

The power spectral density is NOT the Fourier transform of the variance. For wide-sense-stationary (WSS) signals, the power spectral density is the Fourier transform of the Autocorrelation function, ...
user avatar
  • 37.1k
5 votes
Accepted

Filter before or after multiplication of two signals?

A personal rule: in general, it can be better to perform non-linear operations before linear ones. One reason behind that is that a lot of practical concerns are related to outliers or suspect ...
user avatar
5 votes
Accepted

Is spectral density conserved after aliasing?

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 ...
user avatar
  • 31.4k
5 votes
Accepted

Allan Variance vs Autocorrelation - Advantages

My current work involves the design details of atomic clocks where we use the Allan Variance and Allan Deviation (ADEV) extensively. The primary point is that it can be used for non-stationary ...
user avatar
  • 37.1k
5 votes
Accepted

Conversion of dBm/Hz into watt

First, multiply (-174dBm/Hz) by 180000, then convert the result into watt? Because the decibel is a logarithmic unit, you need to be careful here. $-174\mathrm{dBm}$ means $10^{-17.4} \mathrm{mW}$. ...
user avatar
  • 8,240

Only top scored, non community-wiki answers of a minimum length are eligible