# Questions tagged [power-spectral-density]

The Power Spectral Density (PSD) is the distribution of signal power over frequencies.

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### Variance of White Gaussian Noise

It could seem an easy question and without any doubts it is but I'm trying to calculate the variance of white Gaussian noise without any result. The power spectral density (PSD) of additive white ...
28k views

### Why so many methods of computing PSD?

Welch's method has been my go-to algorithm for computing power spectral density (PSD) of evenly-sampled timeseries. I noticed that there are many other methods for computing PSD. For example, in ...
370 views

### Power Spectrum: Definition

I am new to the study of time series. Recently I have asked a question about the covariance of real and imaginary part of a real(in time domain) stochastic time series and I have received an answer ...
26k views

### What is the difference between PSD and squared magnitude of frequency spectrum?

The power spectrum of a signal can be calculated by taking the magnitude squared of its Fourier transform. Being an audio person, the signal of interest for me would be a time series. How does this ...
9k views

### How do you calculate spectral flatness from an FFT?

Ok, the spectral flatness (also called Wiener entropy) is defined as the ratio of the geometric mean of a spectrum to its arithmetic mean. Wikipedia and other references say the power spectrum. Isn'...
13k views

### Difference between Power spectral density, spectral power and power ratios?

What 'exactly' is power spectral density for discrete signal? I was always under the assumption that taking the Fourier transform of the signal, and then the ratio of desired freq range magnitude over ...
4k views

### Understanding the Windowing Method in PSD Calculation

I have some issues understanding the use of a window (it doesn't matter which one) to calculate the Power Spectral Density of a signal. For example say I want to use the hann window, with $N = 1024$,...
5k views

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

I would to calculate the PSD of a signal using FFT however the result do not match with periodogram command. What did was as follow : ...
47k views

### Power spectral density vs. FFT bin magnitude

What's the difference between these? Both are measurements of some form of signal power, but surely there's some difference between the power they are measuring?
29k views

### PSD (Power spectral density) explanation

I'm trying to understand how the PSD is calculated. I've looked in a few of my Communication Engineering textbooks but to no avail. I've also looked online. Wikipedia seems to have the best ...
31k views

### What is cross-spectral density- CSD?

I asked a question earlier but I didn't get any answer for it. So now I am simplifying it: what are Cross-Spectral Density (CSD) and Power-Spectral Sensity (PSD)? What is their application? How can I ...
20k views

### Power spectral density vs Energy spectral density

I read the following on Wikipedia: Power spectral density: The above definition of energy spectral density is most suitable for transients, i.e., pulse-like signals, for which the Fourier ...
353 views

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

If $x(n)$ is an aperiodic signal and $X(e^{jω})$ its DTFT, then, what is $|X(e^{jω})|^2$? Power or Energy Spectral Density? My understanging of Fourier transforms so far tells me that its energy ...
964 views

### Dividing Audio signals into Barks Bands

I want to apply the following steps in matlab 1) Read the audio data 2) Apply window function on that data 3) Apply fft on the result of window function 4) Make power spectrum of fft 5) divide ...
748 views

### How do I modulate complex time domain signal to a carrier frequency?

I want to modulate a complex time domain signal to a carrier frequency 1880MHz but the sampling frequency is 30M which is smaller than Fs. I did upconversion using ...
135 views

### Spectral density of modulated noise process

Suppose we have a noise process $F(t)$. Suppose $F$ is stationary and we know its autocorrelation function $$\rho_F(\tau) \equiv \langle F(0)F(\tau) \rangle$$ where the average is over realizations of ...
7k views

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

I am really confused with matlab's periodogram. First of all, it says in the documentation that its unit is "dB per unit frequency". What does that really mean? I just don't quite get it. Second of ...
13k views

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

Can any one explain the difference in the amplitude between the two and what does each one represents? For example, when using the pwelch algorithm in MATLAB how ...
5k views

### variance in the time domain versus variance in frequency domain

Hi All: I'm trying to better understand the connection between variance of a time series and the integral of the spectral density over all frequencies. Rather than going through all of the relations, ...
7k views

### Working backwards from PSD to possible signal

I have been trying to reconstruct a random signal from its PSD and am running into trouble. I know that many different signals in the time or spatial domains can result in the same PSD-- I am ...
9k views

### Is autospectrum the same as power spectrum density?

In my slides about signal processing, there is one that mentions the same thing as the beginning of this and this answer, namely that the Fourier transform of a signal, squared is the power spectrum ...
878 views

### Properties of Up- and Downsampling

Given a gaussian white noise with mean 0 and $\sigma = 1$. I'm interested in the PSD (power spectral density), when the signal is plain up- or downsampled. No interpolation, no filtering nothing. ...
3k views

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

In Oppenheim's "discrete time signal processing", it says, How is the equation (10.65) derived? PS: you may try to derive it with Fourier transform of the original and the sampled signals. But i ...
556 views

### Frequency magnitude distribution of noise

By the Wiener-Khinchin theorem, we have a straightforward way to calculate the power spectral density for stationary noise. If we know the bandwidth of a system, we can further calculate the variance ...
177 views

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### Implementing Welch's method for Power Spectral Density

I want to implement Welch's method for PSD calculation in MATLAB. I do not want to use built in MATLAB cpsd function, such that I can change the FFT implementation ...
137 views
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### Help with obatining power spectral density of a simple continuous cosine (using both forms of the definition for PSD)

I am trying to go through a simple example to teach myself about Parseval's theorem and calculating power spectral density (PSD) in practice, and would be very grateful if someone could check my ...
321 views

### Oversampling while maintaining noise PSD

I'm designing a digital PID for control and stabilization of laser amplitude. The noise PSD of the laser intensity is around -140dB/Hz, and I want to servo that between DC and 100kHz. I think I've ...