Questions tagged [sampling]
In signal processing, sampling is the reduction of a continuous-domain signal to a discrete-domain signal.
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Amplitude modulation vs sampling rate?
As a sampled tone's frequency nears $f_s / 2$, amplitude modulation grows apparent:
("Actual" curve in grey; blue is what we get if taking samples (dots) "at face value"). This is ...
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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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"Complex sampling" can break Nyquist?
I have heard anecdotaly that sampling complex signals need not follow Nyquist sampling rates but can actually be gotten away with half Nyquist sampling rates. I am wondering if there is any truth to ...
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Is there a condition for bandpass sampling?
Consider a signal that has lowest frequency component $F_l$ and highest frequency component $F_h$.
According to the theory of bandpass sampling, this signal can be sampled and succesfully recoverd if ...
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Subsampling in frequency domain? Effect of sampling rate on spectrum?
Given a sequence
$$
x[n] = [0, 1, 2, 3, 4, 5, 6, 7]
$$
and its subsampling (by e.g. factor of 2)
$$
x_\text{sub}[n] = [0, 2, 4, 6]
$$
are $x_\text{sub}$ and $x$ related in spectrum? That is, given $X =...
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Absolute convergence of periodic sinc interpolation
An $N$-periodic complex discrete-time sequence $[x_0, \dots, x_{N-1}]$ can be resampled to an $M$-periodic sequence $[y_0, \dots, y_{M-1}]$ with $M>N$, using sinc interpolation:
$$\begin{align}y_m ...
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Aliasing after downsampling [duplicate]
Let me start with time domain representation of the original signal
\begin{equation}
x_n=\sum_{k=0}^{2N-1}X_ke^{j\frac{2\pi nk}{2N}}
\end{equation}
where $2N$ is number of time/frequency samples ...
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How to Extrapolate a 1D Signal?
I have a signal of some length, say 1000 samples. I would like to extend this signal to 5000 samples, sampled at the same rate as the original (i.e., I want to predict what the signal would be if I ...
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How Do I Measure the Time Duration of a Finite Length Discrete Sequence?
Assume I have a five-sample time-domain sequence (none of the five samples are zero valued) and the time period between each pair of samples is one second. Measured in seconds, what is the time ...
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Relation between the DTFT and the spectrum of a sampled signal
In the $\rm DTFT$ (Discrete Time Fourier Transform) the spectrum is periodic with a period of $2\pi$ . A continuous signal when sampled has a spectrum which is a repeated version of its original ...
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Random sampling vs uniform sampling
In this paper of Lustig, he speaks about a something which appears unintuitive: sampling at random may exhibit better performance than sampling uniformly. I tried to understand this starting from page ...
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Nyquist Frequency Phase Shift
The figure below shows in dashed lines sinusoidal signals of the same frequency at three different phase shifts. The signals are then sampled such that the sinusoidal frequency is exactly a half of ...
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implication of sampling and reconstruction theorem
I am asking this question sorta as a surrogate for a friend at comp.dsp who posted a similar one.
Even though I did it for a quarter century, laying out math (using "ASCII-math") is crappy, ...
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What is Faster Than Nyquist signaling?
Faster than Nyquist signaling is used to improve the spectral efficiency by reducing the time spacing (relaxing the orthogonality constraint) to pack more data in the same channel while tolerating a ...
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What is meant by *sampling* in terms of the *sampling theorem*?
Let $y:\left(-\frac T2,\frac T2\right)\to\mathbb{C}$ be a square integrable function. The Fourier coefficients of $y$ are $$\underline{Y}(k):=\frac 1T\int_{-T/2}^{T/2}y(t)e^{-i\omega_kt}\;dt\;\;\;\...
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What can be meant by "bandlimited"?
This question was a source of disagreement on whether "amplitude aliasing" can occur for a signal bandlimited to below half the sampling frequency. The question was closed before the ...
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Is there such a thing as band-limited non-linear distortion?
So if you generate a square wave by just switching a signal between two values, at sample boundaries, it produces an infinite series of harmonics, which alias and produce tones below your fundamental, ...
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What is the frequency representation of nonuniform sampling?
Uniform sampling can be thought of as multiplication of a function $x(t)$ with a Dirac comb function: $$\text{III}_T(t) = \sum_{k=-\infty}^{\infty}\delta(t-kT)$$
Multiplication of $x(t)$ with $\text{...
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Exponential moving average cut-off frequency
I am trying to implement a low pass filter from this example.
What is the cut-off frequency for this type of filter? Is it $$F_s \left(\frac{1-\alpha}{2\pi\alpha}\right)$$ where $F_s$ is sampling ...
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How replicas are formed in Frequency domain when a signal is sampled in Time Domain?
I know that sampling in one domian (time or frequency) gives raise to replicas in another domain (frequency / time).
How replicas are formed?
What is this Time domain periodicity and frequency domain ...
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Sampling Theorem and Dirac Comb
I am reading "The Scientist and Engineer's Guide to Digital Signal Processing" and trying to understand Figure 3.5 below which is about the sampling theorem and aliasing.
I do not understand the ...
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Question About Sampling White Noise
Assuming that we have a continuous signal $v(t)$
$$v(t) = \int_0^t g(u)\, \mathrm du\tag1$$
where $g(t)$ is white noise.Then take the derivative of it.
$$\frac{\mathrm d}{\,\mathrm dt} v(t) = g(t)\...
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Fourier Like Spectral Analysis with Uneven Intervals and Redesigned DFT Matrix
I intended to use a discrete Fourier transform (DFT) on a time series sampled at uneven intervals. What I did was to calculate a DFT matrix where the elements are the values at the uneven locations ...
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Phase difference between signals sampled at different frequencies
I want to know that if it is possible to measure the relative phase difference between a signal that has been sampled at two different locations with different sampling frequencies? Also can that ...
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Is downsampling LTI for bandlimited inputs?
This question stems from the discussion we had on a previous question of mine.
The point of contention is whether the downsampling operator is time invariant or not. Which gives us a new condition to ...
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Choosing right cut-off frequency for a LP filter in upsampler
I'm implementing a upsample function in Matlab but it's not perfect right now,for reasons I'm not sure. Here is my code:
...
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How to be sure that we chose the correct sampling rate in practice?
Let say I perform an experiment and I record data at a given frequency sampling $F_s$ and then I perform FFT analysis on these results.
As I do not know the characteristics of the perturbation that I ...
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Nyquist Theorem - Why unique frequencies upto Fs/2 and not Fs? f+Fs is start of Aliasing
If any frequency, f, displays an alias at f + Fs, This shows that unique frequencies have a range of Fs. Why does Nyquist theorem say that actually there is only half of this with unique frequencies ...
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Having Nyquist bin = aliasing?
Here I motivate the question by deriving FFT upsampling for $N \rightarrow 2N$ with even $N$.
One might naively try xup = 2*ifft([xf[:N//2], zeros(N), xf[-N//2:]]), ...
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Upsampling and comb function
Could somebody explain how upsampling works with comb function. How comb function looks for upsampling process?
(if it possible I would appreciate if answer would be related to DFT)
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What is meant by "stochastic sampling"?
What exactly is meant by "stochastic sampling" and is it profoundly different from the regular Nyquist-Shannon sampling theorem? Is it related to sampling a stochastic process?
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When is aliasing a good thing?
In Hamming's book, The Art of Doing Science and Engineering, he relates the following story:
A group at Naval Postgraduate School was modulating a very high
frequency signal down to where they ...
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Converting frequency from $\textrm{Hz}$ to radians-per-sample
In MATLAB I have to pass cut-off frequency for designing a filter. But this Cut-off frequency is in radians-per-sample. How do I convert my analog Cut off frequency in $\textrm{Hz}$, into the required ...
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Can we have a Digital Anti Aliasing filter?
I am working on a board that has no antialisaing filter at the input of the ADC. I have option to I implement my own filter using RC + Opamp circuit. But is it also possible to implement Anti ...
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Difference between Nyquist rate and Nyquist frequency?
So I've been searched online and can't seem to find a clear cut answer to this question.
From my understanding, the Nyquist rate is double of the maximum frequency of a signal which Nyquist frequency ...
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Quantization Noise for Coherent Sampling - Phase Noise?
Update: See added thoughts at bottom of this post.
Under general sampling conditions not constrained by what is described below (signal uncorrelated to sampling clock), quantization noise is often ...
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How to determine where to sample for demodulation of BPSK signals?
I have a simple BPSK demodulator. Very simply, the signal comes in and is split into two branches, one for I and one for Q.
The I branch is mixed with a sin wave of the carrier, and the Q branch ...
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Proving Nyquist Sampling Theorem for Strictly Band Limited Signals (Whittaker Shannon Interpolation Formula)
I understand that the Nyquist sampling theorem dictates that the minimum sampling frequency, $f_s$, be s.t. $f_s > 2B$, where $ B $, is the bandwidth of the signal. I have read the explanation for ...
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Demonstrating the effect of aliasing
How does the signal look when we don't use the Nyquist rate to remove aliasing from a signal during sampling?
Let's suppose the signal is sinusoidal, with a frequency of 500 Hz and an amplitude ...
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How to pick coefficients for Fractional Delay Filters?
I have a Virtex 6 FPGA running at 200MHz with ADC/DACs on it. I have been converting a WiFi signal (2462MHz) down to a more reasonable IF of 25MHz, sampling, running the signal through taps, tweaking ...
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Digital to analog aliasing or mirror query... DAC can output negative frequency?
Using a clock Fs = 1 MHz.
The Digital to Analog (DAC) can make frequencies upto 500 KHz.
500 kHz to 1 MHz is an alias? Or is it called a mirror?? Is aliasing a concept only on the ADC and sampling ...
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Nonnegative or positive band-limited interpolation
Given samples of an everywhere non-negative or positive-valued continuous-time signal band-limited to half the sampling frequency, is there some practically applicable way to interpolate it so that ...
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What is the underlying concept behind Bandpass sampling?
Can you suggest me some books/webpages on Bandpass sampling?
I undestand that if the signal is restricted between $f_L$ and $f_H$, then the minimum bandwidth required is $2(f_H - f_L)$. But say the ...
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Confusion regarding Nyquist Sampling Theorem
The first time Nyquist Theorem was mentioned in class. It stated that we should sample at twice the highest frequency content of the signal. Example: If we wanted to sample $\cos(2 \pi f_0 t)$, the ...
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Passband vs Baseband Bandwidth
Bandwidth is the difference between the upper and lower frequencies in
a continuous band of frequencies. A key characteristic of bandwidth is
that any band of a given width can carry the same ...
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OFDM sampling frequency offset
how the 4G LTE Or 5G NR OFDM measures and corrects the sampling frequency offset? if there is an algorithm using matlab please help
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Sampling at non-uniform intervals
I measure noise in different systems by looking at voltage fluctuations. I wanted to use a Keithley SMU for that purpose, by storing the data in the buffer and then reading them out. However, I found ...
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Upsampling with time offsets
Suppose I have done 4x oversampling for a continuous time signal, but the successive sampling times have a linearly increasing offset. Specifically, the samples with indices {4k; k=0, 1, 2,...} are ...
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Why does my sinusoid look "AM" in shape?
My code is :
Fs=200e6;
Ts=1/Fs;
NFFT=2^14;
Runtime=(NFFT-1)*Ts;
t=0:Ts:Runtime;
f_in=90*1e6;
y_in=sin(2*pi *f_in *t);
plot(t,y_in)
ylim([-1.5 1.5])
Then why does ...
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Nyquist frequency Plotting Distortions
I'm trying to plot some sinusoidal signals in Matlab.
But while frequency is getting higher (closing to fs/2), results are getting distorted.
I guess it's lack of my knowledge but distortion is ...
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