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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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### Generate a Time Series from Power Spectral Density Python

I am trying to generate a time series from a defined PSD function, however i tried to do this in python , with the following steps: Define the Power Spectral Density Define the time parameters Define ...
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### Energy and Power: Power Spectral Density is units of Energy

To help focus answers: The following is specific to “Energy” and “Power” as used for signal processing, not physical units of energy and power (then to ask can units of “Watts” and “Joules” be used, ...
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### Two meanings for "innovation" in Wiener filter are the same?

This is related question to A question about Wiener filter based on Linear Estimation by Kailath, based on the textbook Linear Estimation by Kailath. In that link I talk about how I first learned what ...
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### Implementing a non-causal Wiener filter

I'm attempting to implement a non-causal Wiener filter for removing additive white noise from a measured signal. I've had some trouble and I have reduced my problem to a demonstration on simulated ...
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I need help! I'm trying to calculate the Power Spectral Density of a quantum operator ($\delta \hat{n}(t)$) given by: $$\delta \hat{n}(t) = A(t)\delta\hat{a}(t)+A^{*}(t)\delta\hat{a}^{\dagger}(t)$$ ...
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### PSD of real and imaginary parts of complex envelope of a bandpass signal

I know that we can write a real bandpass signal x(t) as: $x(t)=x_c(t)\cos\omega_ct + x_s(t)\sin\omega_ct$ $x_c(t) = 2x(t)\cos\omega_ct$ for $|f|<W$ $x_s(t) = 2x(t)\sin\omega_ct$ for ...
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### Find the spectral density of the square of white noise with a limited bandwidth

I tried the following order of operations: Let's consider the spectral density of the square of white noise with with a limited frequency band. If $S_{x} \! \left( f \right)$ is the spectral density ...
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### Derive PSD of an MA(1) process

Suppose there is a moving average process of order 1 that also includes a zeroth term thus: $$Y_t=\theta\left(B\right)X_t = \left(\theta_0+\theta_1B\right)X_t$$ where $X_t$ ...
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### What happens to the 0 and Nyquist frequency when using Welch's method?

Welch's method is a way to get better power spectral density (PSD) estimations than simple, naive periodograms. It has two main components: Cutting the input into many segments and average their ...
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### The power of a sinusoidal component in noisy PSD

I am very new to signal processing and I have been doing a lot of reading on it but I don't seem to understand everything. I'm hoping you can help my confusion a little. I am simulating a lidar signal ...
1 vote
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### Calculation of the discrete cosine transform

I am wanting to use the discrete cosine transform to relate the autocovariance function of a process to its periodogram. Following Chris Chatfield's book (Time Series Analysis, p129), I am wanting to ...
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### Modelling MEMS accelerometer noise

I am trying to compare two MEMS accelerometers in terms of their noise for ground motion monitoring applications. I would like to take some "clean" data (recorded by good quality ...
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### Deriving Power Spectral Density of $a \cdot x(t)+b$ if PSD of $x(t)$ is known

I want to derive the PSD of $a \cdot x(t)+b$ if the PSD of $x(t)$ is known. Here $a$ and $b$ are constant. The signal $x(t)$ is a zero mean stationary random variable. Thanks in advance.
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### Why is the FFT of an even real valued vector not real?

I am trying to find the PSD of a signal by taking the DFT of its auto-covariance sequence. My code is as follows ...
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### What's the exact definition of the power spectral density function?

I learned from my signal processing course that PSD is the Fourier transform of the autocorrelation function. $$\mathscr{F}\Big\{\mathrm{E}\big[x(t)x(t+\tau)\big]\Big\}$$ Today I took my statistic ...
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### PSD of the sum of two zero-mean white noise signals

I am trying to solve the following exercise, where $y(t)$ is the sum of two signals $x_1(t)$ and $x_2(t)$ with each of them being the product of the convolution of $e_i(t)$ with $h_i(t)$. So far I ...
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### How to calculate The Signal-to-Noise Ratio (SNR) in dB (different units)?

Recently, I've ventured into a new domain that I intend to incorporate into my work. After thorough research and consultation, I've found this model to calculate the data transmission rate (Capacity). ...
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### Why a windowed signal is considered to evaluate the Power Spectral Density?

Let's consider a real function of time $x(t)$ being a Fourier-transformable signal. The synthesis equation states that: $$x(t)=∫_{-∞}^{+∞}X(f)⋅e^{2πjft} df$$ Meaning: $x(t)$ can be seen as the sum of ...
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I'd like to model the behavior of photodiodes, the input is like data bits (0 & 1) where each bit is represented maybe with 100 samples / bit and the bit rate is $B$ bits/sec with period \$T_{bit}=\...