Power spectral density. PSD shows the signal power distribution over the frequency.

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21 views

Difference between PSD estimate and variance of DFT

In Bartlett's PSD estimate one averages over L segments of the squared DFT coefficients. From wikipedia I found this formula $$ \textrm{PSD}(k) = \frac{1}{L}\sum_{l=1}^{L} \frac{1}{M} \lvert X^{[l]}(...
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35 views

PSD looks to clean/continuous

I generated an signal with a base frequency of $50\textrm{ Hz}$ and its harmonics and quantization noise in it (as an array in MATLAB). It's sampled fast enough to make sure there is no aliasing etc. ...
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70 views

PSD of sine wave

I'm learning some basic signal processing to use in my research. So I'm trying to understand the pwelch function in MATLAB to calculate the PSD. My understanding ...
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29 views

Power autocorrelation function calculation

Calculate the power autocorrelation function $\phi^p_{ff} (\tau)$ and power spectral density $\Phi^p_{ff} (\nu)$ for the signal$$f(t)=A \cos(2 \pi \nu_m t) \cos(2\pi v_c t).$$ Attempt: According to ...
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26 views

Autocorrelation function and energy spectral density

Find the energy autocorrelation function $\phi^e_{ff}(\tau)$ and the energy spectral density $\Phi^e_{ff}(\nu)$ of the signal $f(t) = e^{-\gamma |t|},$ where $\gamma>0$ is a real constant. ...
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46 views

How to find PSD (Power spectral density) of spatial data

I have profiled a surface, measuring the height of peaks and troughs at 0.02mm intervals. I have 1501 data points, the below listed as an example: $$\begin{align} x &= 0\,\mu\text m & y &...
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26 views

How do we find the Power Spectrum Density (PSD) and which data type is valid for that?

I want a simple explanation on how to find PSD and which type of data (in which units, I mean) can be used for doing so. If found similar interesting questions 1 & 2 and some on Mathworks, like ...
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52 views

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 ...
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35 views

Measuring amplitude of a spectral component

I'm trying to measure the amplitude of a spectral component in a signal. The component's frequency is always known beforehand. I take a given number of samples, apply the flattop window to reduce ...
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42 views

What could be causing these humps every 10 Hz on my PSD estimate data?

I am working with EEG recordings about 1,000,000 data pts long, recorded at 4,000 Hz. I'm generating PSD estimates for these recordings using the matlab "periodogram" function like so: ...
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31 views

Translating Bessel filter from python to C - odd behavior past the cutoff frequency

I recently translated the code from scipy.signal.bessel to C in order to implement a bessel filter in a piece of analysis ...
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15 views

How can i plot the power spectrum in terms of time history representation of a signal?

I have a signal and How to plot the power spectrum in terms of time history representation as shown in the below figure in MATLAB. and also i would like to plot the spectrogram as shown in the ...
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83 views

Finding the Amplitude of a Sinusoid in Noise

I'm trying to solve for the amplitude and frequency of a sinusoid embedded in zero-mean gaussian white noise. I am supplied a sample file of a 40000 element array. I first took the autocorrelation ...
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16 views

Power Spectral Density Via Rank 1 Update

I know that I can find the autocorrelation matrix of a series of finite length sequences via rank-1 updates using the relation: $\mathbf{R}[k] = \frac{1}{k}\mathbf{R}[k-1] + \frac{1}{k+1}\mathbf{r}[k]...
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64 views

How to convert fft plot into PSD(Normalized) vs Freqeuncy (Hz)

I am trying to convert my fft signal into PSD(Normalized) vs Freqeuncy (Hz) but can't get it right. I want to get some thing like shown in the figure. I found these figures in the literature. How to ...
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37 views

How do I perform a spectral averaging? Amplitude spectral density

I haven't been doing much signal processing over the years and I'm wondering if my logic is sound. I'd appreciate any input. So, I have a data set with independent variable ($A$) in Frequency ($1\...
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2answers
84 views

Why Fourier Transform doesn't show obvious periodicity?

I have a clearly 4Hz periodic signal (see image below). However when I apply a fourier transform, there is no peak at 4Hz. Also, when I do a power spectrum density (using Matlab's pwelch algorithm), ...
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39 views

Calculating the SNR from the power spectrum

I have a signal that is sampled at 20 Hz. It has almost stationary behavior, with a main frequency around 1.0-1.5 Hz. This frequency range is to be expected and is of interest for further processing. ...
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55 views

How to calculate the discrete power of a discrete signal?

If I have a time series defined by a series like $$ x = [a_1, a_2, a_3, ..., a_n] $$ for time from $t = 1$ to $t = n$ How can I get to the power of the signal in this form: $$ P_x = [p_1, p_2, p_3, ...
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1answer
86 views

Apply band pass filter (BPF) before calculating the power of a signal (PSD)?

From my understanding PSD tries to give a good estimation on the power each frequency attributes to the overall signal power. If I am only interested in a frequency range $(\omega_0 \leq \omega \leq ...
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3answers
62 views

Logaritmic amplitude squarewave

This morning i was experimenting with GNU Octave. I created several signals(Sine, Saw tooth, square wave and noise). After this i used the periodogram. in the periodogram the square wave weren't ...
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35 views

Correlation in DSBSC modulation

Suppose we have a DSBSC signal given by : $$s(t) = 10 \cos (2\pi f t + \phi ) \cdot m(t) $$ where carrier is random signal with phase ($\phi$) uniformly distributed in $[0,2\pi]$. If ...
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55 views

Obtaining power spectral density without having knowledge about frequency bandwidth or sampling frequency of the signal in Matlab?

Is there a way to plot PSD of a signal which show true frequency amounts ( not normalized one) without having knowledge about frequency bandwidth or sampling frequency of the signal in matlab ?
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175 views

How do we calculate Power Spectrum Density (PSD) which is given in dB/Hz and not just dB?

I found many definitions for this quantity, PSD. In a document on signal analysis by National Instruments say that it is the amount of power in a unit bandwidth. Let's say P(f) is the power of the ...
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59 views

How to calculate the noise power for a non-stationary noise?

With stationary noise we have constant mean and variance (let's assume it is Gaussian noise). My first question is, how is the noise power calculated and how it is related to the variance? Now, I ...
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142 views

PSD scaling due to the windowing

I am struggling with the following problem for a while: If I have signal of duration N and I apply window (assume rectangular window) of size M < N how will this influence PSD of that signal after ...
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1answer
158 views

Conversion of FFT to PSD

I would like to convert FFT data which is set of 396 values for 396 frequencies (from 4Hz to 399Hz by 1Hz) in unit of g's (gravitational akcceleration) to PSD in unit of (g^2)/Hz, is it possible? ...
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642 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?
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57 views

Coherence vs. Magnitude Squared Coherence

currently I am writing my masther thesis. The theory part is about the turbulent wind field generation, where the coherence (not magnitude squared) is used: $$\text{coh}(f) = \frac{|P_{xy}|}{\sqrt{P_{...
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355 views

Generate time-domain random signal from PSD

Given an analytical description of the PSD, for example (MATLAB "pseudocode"): ...
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2answers
129 views

Can I see from the PSD if a system is a LTI system?

I am studying the meaning of the power spectral density (PSD) and I am wondering whether I can see from the PSD of the input signal and output signal if a system is a LTI system?
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158 views

What is the best Algorithm to estimate the frequency for Almost-Periodic Data or complex periodic data?

I’ve got what it looks like a periodic signal but the periods seem not equally repeated, I want to estimate the PSD, particularly I need to obtain the dominant frequency of this data. I’ve estimated ...
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148 views

Welch's Overlapped Method

I am measuring wind speed using a number of different anemometers. These anemometers are placed on a structure which exhibits sinusoidal motion. Thus, the signal of the anemometers contains both the ...
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350 views

What is the best method to estimate the frequency(PSD) for noise signal

I’ve been trying to estimate the frequency of a signal I obtained at 1000Hz sampling frequency. The dominant frequency is expected to be not more than 4 or 5 Hz. I’ve estimated the PSD using ...
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44 views

Can uneven sampled points generate valid PSD and spectrogram?

My recording device samples signal at 100 Hz. At each sampling point, it generates 512 values (I assume due to non-ideal impulse in practice, so each impulse is actually a window with certain width ...
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1answer
98 views

Effect of number of data segments in Periodogram-based PSD

In Welch or Bartlett method, original signal is divided into L segments, of D overlapping (D=0 in Bartlett method). Then FFT is done for each segment, and the result is the average of all segments' ...
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221 views

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

How is the periodogram defined? I have been searching the internet a lot, and I find two different definitions: periodogram is the squared magnitude of the DFT periodogram is the squared average of ...
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189 views

What's the number of data points in a Welch-based PSD?

In Welch periodogram Power Spectral Density estimate, we devide the N-long signal into K segments, each of length L with overlapping D, such that N=L+(K-1)*D. In this paper, just above eqn (7), the ...
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1answer
499 views

Calculating the Power spectral density

I've already asked this question on SO, but didn't get an answer, I tqake a shot here. I am trying to get the PSD of a real data set by making use of fftw3 ...
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1answer
159 views

Will using window in Welch's method introduce artificial peak in estimated PSD?

I'd like to estimate the power spectral density of the signal attached here, the sampling rate is 100 Hz. If I don't do windowing (i.e., use boxcar window), the result seems to be a simple $1/f^2$ ...
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2answers
3k views

PSD estimate using FFT - scaling and units

I know that similar questions have already been asked – I have read the answers, yet I am still not sure if I understand the topic properly at some points. I want to use FFT to calculate PSD ...
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51 views

Importance of phase of time-series for PSD

I have $m$ complex-valued time-series $z_m(t_n)$, which I am currently analyzing. I started by calculating their PSDs and CSDs. These exhibit an unexpected peak at a given frequency, which is present ...
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113 views

Only random signal has PSD?

I heard from someone online who said: "Only random signal has PSD, determinate signal does not have. For example, period signal does not have PSD." I am very astonishing about this statement, but it ...
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2answers
270 views

What can we deduce about variance when we are given the noise spectral density?

Given the noise spectral density ${N_0\over 2} = a$, what can be deduced about the variance? In the case of a two-symbol canal(/cable), and when $T_0 = 1$. Is it that, $\sigma_X^2 = {N_0 \over 2} *...
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77 views

PSD of a 100 1kB packets with equally probable 1s and 0s

SO i have to calculate the PSD of mentioned input. here is my code. (every little thing written wholly and solely by myself) ...
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567 views

PSD - Is this formula correct?

Trying to understand whether or not I am calculating the PSD correctly. Below is the equation that I am using: $$ PSD_{rms}(f_{m} = m \cdot f_{res}) = \frac{PS_{rms} }{ENBW} = \frac{2 \cdot \left | ...
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1answer
170 views

PSD - Correct Formula for removing Noise

Ok, so finally some things are making sense. I'm trying to scale the results, which I have done by the following equation: $$ PS_{rms} = \frac{2 \cdot \left |y _{...
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1answer
318 views

PSD - Spectrum analysis

Could someone tell me where it is that I might be going wrong with the following problem? Ok, so I'm computing a spectrogram, and, trying to return the PDS of the signal (to show where the signal ...
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1answer
3k views

Power Spectral Density estimate (PSD)

I'm trying to understand PSD, and, it's functions. So far I have carried out the following: Segmented a signal with NFFT = 256 and ...
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103 views

How to properly express periodogram over analog frequency?

Assume a signal $x[n]$ with $N$ samples and its $N$-point FFT $X[k]$. Assume also the simplest power spectral density estimator: $$ S_x[k] = \frac{\left| X[k] \right|^2}{N} $$ With this estimator, ...