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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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2answers
9k 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
780 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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1answer
267 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
551 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
181 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
345 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
771 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
258 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
244 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
301 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
928 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
63 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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2answers
4k 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
540 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
250 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
840 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
390 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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0answers
306 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
394 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
204 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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1answer
723 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
232 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 ...
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2answers
281 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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1answer
80 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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0answers
120 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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1answer
1k views

Plotting Power Spectrum (Matlab)

I want to make a plot of the power spectrum for a .wav sound file, over the frequency range from -2000 to 2000 Hz. Attempt: I used the following code, but the resulting plot is one sided. It doesn't ...
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1answer
129 views

Evaluating the spectral density of generated noise through the autocovariance

I'm working on generating noise signals $X(t)$ (with $t \in \left[0,T\right]$ with step size $\delta t$) with a prescribed power spectral density $S_{XX}(f)$ and I'm figuring out how well I am ...
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1answer
336 views

Periodogram frequencies not matching with signals

I am new to signal processing world. I am working on a project where we have to find change points using spectral densities. I am running some simulations where in I created a wave which is a linear ...
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4answers
1k 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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0answers
21 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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1answer
458 views

Evaluation of Autocorrelation and Power Spectral Density of white noise through a filter

So say there's a filter with an impulse response of $h(t) = (0.8)^t u(t)$. I'd like to pass white noise through this and figure out the autocorrelation and power spectral density of the output. I'm ...
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0answers
1k views

1/f noise parameter characterization

I would like to characterize 1/f noise in some time series data. I would like to estimate the 1/f noise corner, and the standard deviation of the 1/f noise component and white noise component. The ...
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0answers
35 views

Generating 3-dimension $1/f^\alpha$ noise

I'm stumped trying to find a way to generate a 3-dimensional $1/f^\alpha$ noise time series. Basically I want simulate a forcing that is $1/f^\alpha$ in the 2 space dimensions and $1/f^\beta$ in time, ...
2
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1answer
865 views

Calculating energy spectral density function of half-cosine function

I have the following function: $$ g(t) = A\cdot \textrm{rect}\left(\frac{t}{T}\right)\cos\left(\frac{\pi t}{T}\right)$$ How do I find the energy spectral density function? I think? it is defined as ...
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0answers
218 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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0answers
61 views

Quantifying how good I'm producing a spectral density

I recently asked a question here on how to create noise with a specific spectral density $S_{xx}(f)$. The helpful people of this stack exchange told me one way to do it was filtering white noise with ...
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2answers
690 views

Numerically generating noise time series from spectral density

I'm trying to figure out a way to construct (numerically) time series of random variables given some spectral density $S_{xx}(f)$. I'm interested in various types of spectral densities (flat, ...
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3answers
2k views

How to interpret spectrogram correctly?

I have a pressure transducer signal from a reacting mixture available here, which has a sampling frequency of 50kHZ. I have also obtained the spectrogram of the signal with NFFT=256, noverlap=4 as ...