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Questions tagged [power-spectral-density]

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

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287 views

Find highest frequency of a very manky signal

I'm trying to compute the highest frequency (as can be sampled) in some pretty manky looking discrete time-dependent signals. My current method - a discrete fourier analysis - fails for some pretty ...
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1answer
144 views

Some subtleties in the PSD of digitally generated noise with $S_X(f) = A(f)$

I understand that the title is not the most descriptive, but I didn't know how to describe my problem in a more literal way. The situation is as follows: I wanted to digitally generate noise with an ...
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1answer
633 views

Classifying a time series with a Lorentzian power spectral density

I was wondering if there is a general classification for time-varying signal with a Lorentzian shaped power spectral density, specifically with some nonzero center frequency. In terms of equations, ...
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2answers
205 views

Can one generate a signal with an asymmetric power spectral density?

My question is as follows. I know that classically speaking, if you have some time varying signal $X(t)$ its power spectral density $S_X(f)$ will be symmetric around $f=0$ as the signal is real. This ...
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1answer
852 views

Power spectral density of a PAM signal

Say I have a PAM signal as $x(t) = \sum_n a_n h(t-nT)$ where $\{a_n\} \in \{\pm 1\}$ are equiprobable random binary bits and $h(t)$ is bandlimited to $[-1/(2T),1/(2T)]$. ($x(t)$ is random process and ...
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2answers
198 views

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

The relation between $x(t)$ and output $y(t)$ of a non-linear device is expressed as $$y(t) = (x(t))^2$$ Let $x(t)$ be zero-mean stationary Gaussian random process with auto-correlation $$R_x(...
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0answers
60 views

How to preprocess such signals?

I am interested in denoising accerelation measurements, recorded in ambient vibration tests. Such tests consist in recording the vibrations of a mechanical structure, say a table for example. So say I ...
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1answer
596 views

What does PSD represent in the spatial domain?

People use FFT methods to analyze topographic features in the spatial domain, such that the signal varies over (x) rather than (t). If a PSD curve characterizes amplitude versus frequency of an ...
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2answers
94 views

Can white Gaussian noise improve signal level in non-linear device?

In the system shown below, can white Gaussian noise amplify or attenuate the input signal? Most of the time we check signal level proportional to noise level (such as noise figure) not singly. I ...
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2answers
8k 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 ...
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2answers
688 views

Power spectral density of sinusoidal signal in noise

In a literature I face with this input and power spectral density (PSD) $$x(t)=s(t)+n(t)=A\cos\left(\omega_c t +\phi\right) + n(t)$$ first I want to know How can we find PSD of $\cos\left(\omega_c t ...
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119 views

Power spectrum and filtering with only signal squared

I have a time-series signal $E(t)$, which unfortunately, I only have easy access to the quantity $|E(t)^2|$ -- that is, I don't have easy access to the phase information. What I want to do is (high-...
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1answer
233 views

Power spectrual density of white Gaussian noise

I know that power spectral density of white Gaussian noise is $\frac{N_0}{2}$. In a simulation I want to plot a system output and its very important to define the value of $N_0$,I want to know what ...
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1answer
487 views

Does the Wiener–Khinchin-Einstein theorem hold for non-Gaussian processes? If so are there any assumptions?

The Wiener–Khinchin-Einstein theorem states that the auto-correlation $(r_{xx}(\tau))$ and spectral density $(S(f))$ are Fourier duals, i.e. $$r_{xx}(\tau) = \int^{+\infty}_{-\infty} S(f) \exp\left( ...
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2answers
3k views

Root mean square bandwidth of a signal with flat spectrum

I am trying to derive a simple expression for root-mean-square bandwidth $B_{\rm rms}$ for a signal that has flat spectral density over its entire bandwidth $B$. The expression for the $B_{\rm rms}$ ...
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1answer
175 views

how to create a DFT with scalloping/spectal leakage

I had some problems with scalloping and spectral leakage. I think I solved that. I wrote an algorithm in C++ using FFTW3. It works. But now I want to show when you get scalloping. It took me some ...
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1answer
323 views

What is the computational complexity of Spectrum Estimation Algorthms and What they depend upon?

There are lots of spectrum estimation techniques, each with some pros and cons. Algorithms like: Music Welch's method Yule-Walker AR method Periodogram modified covariance method multitaper method (...
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1answer
752 views

PSD using MATLAB's $\tt pwelch$ algorithm window length and measure units

When using pwelch algorithm in MATLAB for a signal with $N$ samples, Is there a good rule of thumb for determining the length $L$ of the sections (second variable ...
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1answer
243 views

A few questions about the output value of dsp.SpectrumAnalyzer

I am testing the output values of dsp.SpectrumAnalyzer for a sine wave mixed with white noise. The $\sigma^2$ of the white noise is 1e-4, so I use 0.01*randn(1024,1)...
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2answers
229 views

Calculating spatial width from power spectrum HWHM

Say I have a 1D (spatial) signal (resolution = $1000$) which is zero everywhere except from $x = 250$ to $750$, where it equals one. I ultimately want to calculate the spatial width of this signal ...
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1answer
271 views

What does the frequency axis of a Power Spectral Density mean?

I have never really understood what the frequency axis meant when we plot the Power Spectral Density(PSD). Does it correspond to frequency as we get after we take the Fourier Transform of a time ...
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1answer
804 views

Smoothing a power spectrum

My question is regarding how one could/should smooth a rather noisy power spectrum obtained from measurements. There are various methods one can use (a moving average, binning, etc) and I am not sure ...
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1answer
57 views

SNR problem with different sampling rates using innerproduct

I'm trying to measure the amplitude of a sinusoidal component in a noisy signal. Since the signal frequency is known beforehand, I'm calculating scalar product with a sine and cosine base function ...
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0answers
61 views

can I compensate for hann-window preceding fft? [duplicate]

To reduce spectral leakage, I have created a hann window going from almost 0 to 1 to almost 0 across 128 time points. I multiply that with my 128-point time series data, then feed the result to FFT. ...
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2answers
3k 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 : ...
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2answers
512 views

Zero-padding the middle of a signal

I sample a signal at a certain frequency for a finite amount of time to get a sequence $$(x_n)_{n=1}^N = (x_1, x_2, ... , x_N)$$ with the intention of analyzing its power spectral density by ...
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2answers
229 views

RTL-SDR units, $\textrm{dBm}$

I am using the Python rtlsdr library to get complex samples from my RTL-SDR USB stick. I am getting power by squaring the real and imaginary components of these ...
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2answers
113 views

Should I filter before calculating power, if I'm looking for relative changes in power?

I am building a "scanner" sort of program, which reads IQ samples from an rtl-sdr stick, and keeps track of the power on certain frequencies, in certain bands. I am interested in detecting activity ...
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5answers
8k views

Where does the delta function come from if we derive autocorrelation directly?

I am reading a book "Creating Noise" written by Hollos & Hollos and have a question about the autocorrelation function of the Gaussain white noise when reading the following passage: From the ...
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1answer
720 views

PSD of a sum of two stationary real signals

I have 4 signals ($w_1(t),w_2(t),u_1(t),u_2(t)$ of which I know the power spectral densities (PSDs) $S_{w_1,w_1}(\omega),S_{w_2,w_2}(\omega),S_{u_1,u_1}(\omega),S_{u_2,u_2}(\omega)$ and the cross PSD $...
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1answer
355 views

Finding the deterministic autocorrelation function (ACF) from its power spectrum

The power spectrum of a stationary discrete-time random signal is $$\Phi_{xx}(e^{j\omega})=\begin{cases} 1 & |\omega|<\pi/2 \\ 0 & \pi/2 <|\omega| \le\pi \end{cases} $$ (a) ...
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273 views

Flattening out a power spectral density

The situation is as follows. I am generating a white noise voltage signal with a certain power spectral density amplitude of choice, from 0 to some cutoff frequency, for example 200 MHz. This proceeds ...
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1answer
373 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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1answer
191 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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2answers
131 views

If noise is your signal, what is your noise?

Consider the following contrived situation. Imagine a Gaussian white noise process $x[t]$, with bandwidth $Δf$, with PSD equal to some quantity $A$ which you would like to measure. So the way to ...
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2answers
3k 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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0answers
926 views

Epilepsy seizure detection in EEG

I want to develop a method to detect the occurrence of epilepsy seizure in an EEG signal. I am using a large data set for number of patients so the algorithm has to detect the seizure in any of the ...
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155 views

Why the SNR is very high?

In a cellular network, let us say that I have these parameters: Transmit power = 30dBm Noise spectral density = -174dBm/Hz (AWGN) Bandwidth = 10MHz Let us say ...
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208 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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930 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. Attempt:...
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425 views

How to calculate Power spectral density of windowed signal

To compute the (absolute) spectral powers in the above eight frequency bands, PSD of the input signal needs to be estimated. The PSD of a signal describes the distribution of the signal’s total ...
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1answer
676 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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1answer
210 views

Decorrelating Stationary Colored Gaussian Noise — Effect On The Desired Signal

So given stationary colored gaussian noise $\mathbf{n}$, I know that I can decorrelate it by first finding it's autocorrelation $R_{nn}$ and performing $R^{-\frac{1}{2}}_{nn} \mathbf{n}$. In ...
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1answer
2k 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 ...