Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [power-spectral-density]

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

0
votes
1answer
196 views

Autocorrelation and PSD

Let $X(t)$ and $Y(t)$ be two orthogonal processes with power spectral densities $$S_{xx}(f) = S_{yy}(f)=\begin{cases} 1-\lvert f\rvert, & \lvert f\rvert<1 \\[1ex] 0,& \text{otherwise} \end{...
1
vote
1answer
393 views

Question on the definition of one-sided PSD in AWGN channel

I am currently simulating the following in a telecommunications exercise in Python: Consider a binary sequence $m[n]$ that is being modulated with QPSK (Gray-mapped) that is being transmitted via ...
3
votes
2answers
123 views

Filter away sinusoidal noise properly

I have a stereo music signal corrupted by strong sinusoidal noise that varies over time. Here is the spectrogram of Left channel I plotted with Matlab. As you can see there are 3 or 4 strong ...
4
votes
1answer
503 views

Power Spectral Density of Digital Modulations

I want to simulate the power spectral densities of different modulations in MATLAB (without Simulink). Unfortunately I have only very basic understanding of signal processing, hence I struggle with ...
0
votes
1answer
103 views

Spectral density interpolation: Applications?

Let $\Phi_1$ and $\Phi_2$ be two matrix-valued power spectral densities. I wonder whether the problem of interpolating $\Phi_1$ and $\Phi_2$ has been studied in the literature and/or applied in ...
0
votes
1answer
381 views

What is the difference between the PSD of a deterministic and stochastic signal?

I am learning about stochastic processes and I don't get one thing: What is the advantage of calculating the PSD of a signal using the Wiener-Khinchin theorem $\Phi(\omega) =\mathcal{F}\{R_{xx}\}$ ...
1
vote
1answer
432 views

Trying to implement MATLAB $\tt pwelch$ in Python

I'm implementing an existing MATLAB script in Python and noticing some differences in the behaviour of MATLAB's pwelch function compared to ...
0
votes
1answer
186 views

MATLAB's $\tt cpsd$ and $\tt pwelch$ - different results for cross spectral power density

I am wondering why the following code does not yield the same results for Sxy1 and Sxy2, where ...
3
votes
0answers
651 views

Power Spectral Density of Brownian Motion despite non-stationary

Note: I originally asked this on Physics Stack Exchange but haven't attracted any interest there so I'm asking here where it may be more relevant. A white noise process, $\xi(t)$ with delta ...
0
votes
1answer
53 views

Welch's overlapped method for amplitude by frequency estimation

pwelch is a useful matlab function for computing real/magnitudes for power using WOSA method, but I'd like to apply the same thinking in order to output complex pairs for amplitude (not power) ...
0
votes
1answer
258 views

How to Estimate a Normalized PSD Using the Burg’s Method in MATLAB?

I'll try to be most sintetic as I can. I'm using an EEG system and I want perform an frequency analisys of the brain waves. I found this interesting article which describe how is possible to discern ...
1
vote
0answers
41 views

Is power density invariant to Fourier Transform? Does it hold through derivation?

Assumptions We have a finite discrete measurement. Introduction I had some troubles determining a power spectral densities needed for Wiener deconvolution. Looking through the continuous equations ...
0
votes
1answer
293 views

“Noise Spectral Density” a.k.a “Power Spectral Density” in datasheets

In the case of statistics, there are two terms: "Variance" and "Standard Deviation" to - for in the latter case - have one to note the case in which the units are without squares. Am I correct to ...
1
vote
1answer
115 views

Why MATLAB only allows cpsd and mscohere between vectors with the same length?

I am studying the applications of finding coherence in the frequency spectrum between two signals for pattern recognition. I have a recording that is way longer than the sampled signal that I want to ...
3
votes
2answers
222 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 ...
2
votes
1answer
412 views

Estimating the PSD (Periodogram): How do you find the Expected Value

The periodogram $\widehat{P_x}(e^{jω})$ is an estimate of PSD $P_x(e^{jω})$ and for mean-square convergence - $\lim_{N \rightarrow \infty}E\left\{\widehat{P_x}(e^{jω})\right\}=P_x(e^{jω})$ My ...
0
votes
0answers
48 views

How do I improve the SNR of my signal given a noise profile (additive noise)?

From an iPhone microphone, I have a background recording of 5s(fs = 44.1 Khz), and immediately after that, I have a voice recording of a person saying 'aaa...' for 10s(fs = 44.1 Khz). How can I use ...
0
votes
1answer
143 views

Methods of scaling FFT power

I wanted to know what are the well-known methods of scaling the FFT power of a signal? I am referring to EEG signal but this should apply to all signals I guess. I need to plot the powerspectrum/PSD ...
0
votes
1answer
481 views

Blackman-Tukey periodogram?

I have been reading about the non-parametric estimation of the spectral density, and I'm particularly interested in the Blackman-Tukey method. If we take the rectangular window we will have the ...
1
vote
0answers
144 views

What is the power spectral density after filtering?

Consider a signal $x(t)$, which is input to a pulse shaping filter with transfer function $g_t(t)$: $$x(t) = \sum_n d_n \delta(t-nT_s)$$ with $n$ an index from negative to positive infinity and $...
1
vote
1answer
371 views

Why does increasing FFT length (narrowing bandwidth) not decrease Noise Power per bin?

I was under the impression that zero-mean white guassian noise had a constant Power Spectral Density which means that smaller bandwidths should decrease the power in that band. I'm getting surprising ...
0
votes
1answer
344 views

DOA estimation; Music (Multiple Signal Classification) algorithm

Why do we say that signal subspace and noise subspace are orthogonal in e.g. MUSIC algorithm? precisely, Suppose we have 2 sources (signals) which are WSS, in WGN in a uniform linear array. After ...
0
votes
1answer
746 views

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

Given a Wide Sense Stationary Multi Variate (Vector) Random Process $ \boldsymbol{x} \left[ n \right] $ it Auto Covariance Matrix Function is given by: $$ {R}_{x, x} \left[ m \right] = \mathbb{E} \...
1
vote
0answers
259 views

Power Spectral Density of a WSS Random Process with 2D Discrete Fourier Transform

I'm trying to understand how the random process (RP) signal in discrete time domain is related to its power spectral density (PSD) in frequency domain if the signal is wide sense stationary (WSS). If ...
1
vote
1answer
95 views

Energy Detection Algorithm Uncertainty

I'm currently working on a project to perform energy detection of an IEEE 802.15.4 using the block diagram illustrated below. However, I do have a little uncertainty about the algorithm. I'm wondering ...
0
votes
1answer
326 views

PSDs and Parseval's theorem

OK, I have been banging my head for quite a while trying to make sense of this simple equation: The $1/T$ is what is causing me all the grief. I assume that the square of the Fourier transform of ...
1
vote
1answer
110 views

Response of Linear System to Stochastic Process

Somehow I am getting the variance{u(n)} equal to '0' !! This is the case when I take the coefficient 'a' as real. As it is not mentioned in the question I need to find the solution to this question ...
1
vote
2answers
900 views

Pa^2/Hz to dB/Hz conversion

I have PSD data from an computational aeroacoustics analysis, which is in the units of Pa^2/Hz. I want to convert this to dB/hz; would it be correct if I use PSD[in dB/Hz] = 10log10(PSD[in Pa^2/Hz]) ...
0
votes
1answer
8k views

dB/hz to dB Conversion

I'm have a PSD graph of dB/hz vs. frequency in hz. I want to convert the dB/hz unit to dB, but I can't find any way of doing it. Help would be much appreciated!
2
votes
2answers
452 views

Clarification concerning power spectral density

Many books in signal processing, e.g. Papoulis [1], define power spectral density (PSD) as: $$S(\omega)=\sum_{k=-\infty}^{\infty}R_{xx}(k)e^{-j\omega k}$$ Which is the fourier transform of the ...
2
votes
1answer
269 views

Vibration Analysis by using FFT

I have 6 column vectors $(\mathbf A_x,\mathbf A_y, \mathbf A_z, \mathbf G_x, \mathbf G_y, \mathbf G_z)$ taken by accelerometer to analyze the vibration of a construction. Each column is a $64998\times ...
0
votes
2answers
634 views

Calculating power in frequency band using power spectral density

In a text I am using it states: The fourier transform $F(\omega)$ has both positive and negative frequencies and $F(\omega) = F^*(-\omega)$. The power spectral density $S(\omega)$ is similarly ...
1
vote
0answers
37 views

Interpretation of steady state sensor signal

I try to understand some measurement results of an accelerometer MEMS sensor. I used a mikrocontroller which is sampling an accelerometer's analog signal with the built in analog-digital-converter. ...
-1
votes
1answer
175 views

Reason for decrease in the PSD gain with increase in the number of FFT points

what is the reason for that? The gain should increase ideally I guess. This is the code I tried. As I increase the length of F by zero padding,the gain of PSD reduces. ...
3
votes
1answer
514 views

Average Power Spectral Density of PAM signals

I am reading through the PAM transmission scheme and about the power spectral density of the signals. Given that the Average Power Spectral Density of PAM Signals is: $$ \Phi_{ss}(f)=\Phi_{aa}\left(e^...
1
vote
0answers
149 views

AWGN Build vs Randn noise do not match

I am generating noise in two different cases with the same SNR once using AWGN command which is a built in command and second time using randn function with the correct scaling however I am getting ...
0
votes
1answer
216 views

Compute Power Delay Profile (PDP) from Delay Spread

I have data pertaining to channel obtained from measurements. In order to make use of this data, I need to convert it into a form as follows: ...
0
votes
2answers
321 views

Why use cross-spectral density to calculate frequency response?

I am taking a class about system identification and currently learning about cross-spectral density. My textbook says that the frequency response, G, of a system can be determined as $$G=\frac{S_{uy}}...
0
votes
1answer
44 views

How to transform flat-field corrected spectra to those under Standard illuminant E (ideal equal energy illuminant)

My ultimate goal is to convert a flat-field corrected hyperspectral image of reflectance (360nm-780nm) to corresponding CIEXYZ image and thus device-independent color image. By flat-field correction, ...
2
votes
2answers
454 views

Cross Power Spectrum

Is it necessary that cross power spectrum (CPSD) should always be between power spectrum (PSD) of individual signals, irrespective of the method we compute it? The images are shown below.
1
vote
2answers
166 views

Is there an equivalent time-domain operation to the spectrum averaging in Welch's method?

In Welch's method a time-series is segmented and then the subsequent FFTs of the segments are averaged. Is there an equivalent time-domain operation? I guess doing the the Welch estimate and ...
1
vote
1answer
509 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 ...
0
votes
1answer
329 views

Determining power spectral density from a sample

To start, I have absolutely no background in electrical engineering, I am a computer scientist by trade. I'm currently working on a project where I am attempting to code a function that uses the ...
0
votes
1answer
584 views

How to evaluate Spectral Density of DC component vs. AC component during computing PSD?

When computing the PSD, how to manipulate the DC component?  PSD integral is the total signal power, does it include the power of DC component? In other words, if there is one signal with DC value ...
0
votes
2answers
258 views

Calculate the harmonics in the power supply of $50\textrm{ Hz}$ using FFT

I need to calculate the harmonics in the power supply of $50\textrm{ Hz}$. If suppose I need to calculate up to 20 harmonics. Then my sampling frequency by Nyquist criteria should be : $$f_s \ge 2 ...
1
vote
1answer
206 views

Do I need to bandpass filter the signal before applying the Zoom FFT algorithm?

Let's say I have an acoustic signal that I want to make a spectrogram of filled with broadband noise and tonals, sampled at oh, $44100\textrm{ kHz}$, and I want to zoom in on the band between $2600\...
0
votes
1answer
332 views

Creation of Brownian noise as random walk

I am trying to create brown noise by integration of white noise (random walk). I created Gaussian white noise. The histogram shows Gaussian distribution and Welch (and also FFT) shows flat spectrum. ...
0
votes
0answers
28 views

How are phases dealt with when using FFT with blocks

An FFT of a signal returns a complex number, with a phase angle related to the starting location of each frequency within the signal. If I have break my signal into blocks, and FFT them individually, ...
0
votes
1answer
248 views

A query on Power spectral density (PSD)

Say a narrow band signal $n(t)$ has Power Spectral Density (PSD) $S(f)$. If the signal $n(t)$ got multiplied by $\cos(2\pi Ft)$, then what will the PSD of resulting signal in terms of $S(f)$ be? Will ...
1
vote
1answer
328 views

FFT processing gain

I am working on radar received signal which is $15000\times 2008$ matrix. Here each row corresponds to one chirp or one signal, this way there are 15000 signals. The difference among them is just the ...