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Questions tagged [sampling]

In signal processing, sampling is the reduction of a continuous-domain signal to a discrete-domain signal.

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What is advantage of Logarithmic Sampling?

Logarithmic Fourier Transformation This paper starts off in the abstract saying that the given audio signal is sampled logarithmically. We also know that the human ear has a sort of a filter bank ...
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138 views

Logarithmic Spacing

What is the meaning of sampling logarithmically? How do you space the samples logarithmically? Or to rephrase the second question, How to sample an audio signal logarithmically? It would be ...
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834 views

Why is aliasing inherently non-linear?

E.g. when having 2 signals $x(t)$ and $y(t)$ and transforming each one with adding their spectra, the operation is linear, as the result would be the same as the transformation of $(x + y)(t)$. Even ...
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1answer
6k views

Exponential moving average cut-off frequency

I am trying to implement low pass filter from this example. What is the cut-off frequency for this type of filter? Is it $F_s \frac{1-\alpha}{2\pi\alpha}$, where $F_s$ is sampling frequency?
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2k views

Laplace transform of product of signal and impulse train

I'm reading 'Discrete Time Control Systems' book by Ogata and came across a few statements (specifically, (3-1) and (3-2)) which I have not been able to understand. It is said that any continuous ...
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1answer
245 views

Uniform sample rate

I have some sensors connected to an Arduino Due. The Arduino sends the buffer of data over the its SerialUSB connection. The last element of this buffer defines when are passed 1 seconds (it is 0 "...
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1answer
652 views

Sampling rate vs ADC noise tradeoff

I have a digital sensor that can output at two frequencies (250Hz, 1000Hz), but with different RMS AWGN noise (.35 units RMS, .5 units RMS respectively). The signal of interest has a single frequency ...
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1answer
117 views

Which window function to use for QPSK signal?

I am trying to Receive a QPSK signal and for Sampling I need to recover clock. Now QPSK Signal is generated at 2.4GBaud. It is than sampled at 80GHz.Than further it is downsampled to 10GS/s (Symbols ...
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262 views

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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1answer
548 views

Spatial sampling frequency equation

Upon reading this microphone array tutorial, I'm stuck in the following piece: The spatial sampling frequency along the x-axis is given by $f_{x_s} = \frac{\sin \theta \cos \phi}{\lambda}$ ...
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1answer
90 views

First-Order Hold Filter Gain

I want to know the amplitude of the first-order hold filter at the Nyquist frequency (the roll-off amplitude/gain). I know that the Fourier transform of the reconstruction is given by: $$\sum^\...
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1answer
678 views

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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2answers
83 views

How do you compute for fc and t in modulating an I and Q component

I know that in a $2^b$-ary QAM system you need to modulate the $I$ and $Q$ components through the mixer and are separated by 90° through a local oscillator (by applying a $\cos$ and $\sin$). By ...
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156 views

Signal Processing for Discrete Events

This is less a specific question, and more... "what is this called" and "where can I read more about it"? Several times in my career, I've had to work with datasets with "discrete events". Lets say ...
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1answer
62 views

Hybrid Sampling Scheme Idea?

I am facing a problem which I could not find any robust solution for . Assume we have a signal, $x$, composed of sum of a few sinusoidal. e.g. $$x=A_1\sin(\omega_1t+\phi_1)+A_2\sin(\omega_2t+\phi_2)+...
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111 views

Discrete Time Processing of Continuous Time Signals LTI Concept

I wonder if the input signal (CT) violates Shannon-Nyquist Theorem for a given sampling rate, is there any chance for the overall system not to be LTI although discrete time system is LTI? Thanks.
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78 views

2-D sampling and reciprocal lattice

I got this problem wrong, but I'm not sure why. I know that the FT of a signal is fully determined within 1 unit cell of a reciprocal lattice and outside this range are replicas. Here's the problem: ...
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2answers
107 views

Undesirable zeros in sampled signal using train of impulses

I'm trying to analyze a signal like the example below, but it contains undesirable zero value samples, is there any way to eliminate them? I'm using Matlab. Actually, the problem is this: in a ...
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212 views

Is this signal perfect reconstructable?

The question is as follow: Let me do the analysis: The downroad first: \begin{align} X_1(z) &= z^{-1}X(z)\\ X_2(z) &= \frac{1}{2}\left\{X_1\left(z^\frac{1}{2}\right)+X_1\left(-z^\frac{1}{2}\...
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2k views

Is sampling at double the desired reproduction frequency accurate?

This is probably a general principles question, though I'm thinking specifically in relation to sound, which is commonly sampled at a rate of 44.1 kHz in part because the maximum frequency the average ...
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0answers
695 views

Sinc interpolation formula for signal reconstruction in frequency domain from bipolar samples

As per the title, I was wondering if there was a $\operatorname{sinc}$ based interoplation formula for reconstructing a signal in the frequency domain which has been sampled with respect the bipolar ...
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1answer
559 views

How to find Sampling frequency of a video signal

i took the Digital Image processing subject in college and i am a little confused that how i can find out sampling frequency of a video signal given its bandwidth. For example what will be the ...
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If humans can only hear up to 20 kHz frequency sound, why is music audio sampled at 44.1 kHz?

I read in some places that music is mostly sampled at 44.1 kHz whereas we can only hear up to 20 kHz. Why is it?
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133 views

Effect of sampling

I have this continuos-time system $$\dot{x}=Ax+Bu$$ where \begin{equation}A=\begin{bmatrix}0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & \phantom{0}2.8040 & -\phantom{0}5....
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1answer
72 views

Fitting discrete curve to cosinus

I have a curve which the asymptotic behavior is the one of a cosinus. I look at this curve on all integers. I know that the asymptotic curve has this behavior : $$ cos(a*x+b) $$ My question is : how ...
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33 views

Rectangular window to insulate two sinusoids

We have two sinusoids with the same amplitude and two different frequencies: $15 \ \mathrm{kHz}$ and $18 \ \mathrm{kHz}$. Sampling frequency is $100 \ \mathrm{kHz}$. What is the minimum length of the ...
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1answer
336 views

Sampling and the creation of multiple images at integer multiples of the sampling frequency

From what I thought I learned about sampling is that when you draw a sampled signal in the frequency domain, you can show copies or "images" of that signal at integer multiples of the sampling ...
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2answers
293 views

what is the best way of sampling an exponential decay?

Some signal is decribed by a formula $$S(t)=S_0 e^{-tC}\text.$$ I have given $t_\text{min},t_\text{max}$ and number of points. What is the optimal way of sampling such a signal? How to choose the ...
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1answer
582 views

How to calculate FFT of a non-uniformly sampled signal?

Is it possible to calculate the FFT of a signal that was not sampled uniformly? I have an MPU6050 connected to an Arduino uno. I write the samples at the default frequency, approximately 20 ...
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2answers
2k views

preprocessing raw ECG data

I need to preprocess raw ecg data in R, here is a sample already standardized. I'm not an expert in signal processing nor experienced in working with medical data, so I need concrete answers ideally ...
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1answer
91 views

How to choose an interpolation method for seismic ground motion signals

I am working with seismic ground motion records from the PEER database. They are acceleration measurements that are band limited to 50 Hz and sampled at 200 Hz. I use these records to drive an ...
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2answers
226 views

Interpretation of a sampled signal in the frequency domain

Suppose we have a signal $y(t)$. For sampling we use a Dirac $\delta$ function. The sampled function is $\widetilde{y}(t)$. So $$\widetilde{y}(t) = y(t)\cdot\sum_{n=-\infty}^{\infty}\delta(t-nT).$$ ...
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1answer
212 views

Reconstruct under sampled signal

I have a signal from a PWM inverter that was sampled at 3,84 kHz. The PWM has a switching frequency of 5 kHz. The pwm signal is feeding an induction motor. If I low-pass filter the PWM signal it ...
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1answer
127 views

DFT for different data lengths

I have a sinusoidal signal that is sampled at $f_s=10$ Hz. I am asked to find the absolute value of the DFT for different data lengths (1 sec., 2 sec. etc.) I do not understand where will I use the ...
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1answer
106 views

Beam Former linear array antenna

How can I design a beam former (with weigth vector $w$) that protects a signal coming from an angle of arrival $\theta_0$ and completely suppresses signals coming from $\theta_1,\theta_2,...,\theta_k$?...
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1answer
29 views

How to sample $f:=f_{1}\cdot f_{2}\cdot…\cdot f_{K}$?

Let $f_{k}$ be $\sigma_{k}$-bandlimited, $k=1,2,...,K$ and define $f:=f_{1}\cdot f_{2}\cdot...\cdot f_{K}$; then how should I choose $T>0$ such that we can recover $f$ from samples $f(nT)$? ...
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1answer
120 views

How to accurately model wideband RF reflections?

I would like to model a transmitter and received pair, both sampling at the same bandwidth (not clock synchronized), where there are a number of reflectors. The time delay due to the reflectors can be ...
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1answer
196 views

Spurious When $F_s/F$ is not an integer

We are using a 16-bit DAC for a waveform generation between to $500\textrm{ MHz}$ with the sampling frequency of $1200\textrm{ MHz}$. The specification for the waveform generation is $10\textrm{ Hz}$ ...
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90 views

Can picking an inappropriate roll-off frequency for a digital filter just alias the roll-off value?

I believe a related question is asked here, but my question deals more with what filter is realized if one fails to consider design parameters relative to sampling rate. In designing an IIR filter we ...
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1answer
127 views

What is the best approach for studying the information within frequencies of an unknown signal

If we have a signal and we do not know anything about this signal. We do not know which frequencies contain specific information, and which frequencies does not contain information. Which is the ...
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1answer
256 views

what is difference between Alias vs. down sampling? [closed]

could someone help me explain downsampling in the context of Nyquist–Shannon sampling theorem and tell the difference between Aliasing and downsampling.Also is downsampling and undersampling the same ?...
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2answers
109 views

Simplification after sampling an analog signal [closed]

$80\textrm{ Hz}$ Sampling rate produces the $x[n] = 3\cos(5\pi n/4)$ signal, the original analog signal is $x(t) = 3\ cos(100\ π t)$. This is a solved problem used as an example. In the solution ...
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1answer
88 views

On number of samples needed

Suppose we get $m+1$-bit signed noise samples $n_i$ with magnitude of noise as high as $m$ bits. Does averaging say $m\log m$ samples suffice to get average of $n_i$ to magnitude within few LSBs? ...
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1answer
141 views

upsampling and downsampling operator

I am trying to prove that for all $x,y \in l^{2}(\mathbb{R})$, it holds that $$\left\langle\left(\downarrow M\right)\left[x\right],y \right\rangle = \left\langle x,\left(\uparrow M\right)\left[y\right]...
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1answer
98 views

Deciding on the FFT length for water waves in flume (wave facility)

Soon I'll be conducting experiments in a wave facility (flume) for my MSc thesis. And I would like to analyse wave spectra (amplitude and energy density). The time step (or 'accuracy') of the wave ...
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2answers
704 views

Coherent Sampling And The Distribution Of Quantization Noise

I have a question concerning the distribution of noise in the frequency domain in case of Coherent Sampling. I read up about Coherent Sampling and understood that in order for a frequency $f_{in}$ to ...
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1answer
241 views

DTFT reconstruction

I have a sampled DTFT. If we assume that there isn't aliasing in time domain, what is the best way to reconstruct DTFT from its equidistant samples? I though about Dirichlet interpolation. Do you know ...
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1answer
1k views

Relationship Between Sampled Continuous and Discrete Time Signals

Consider the sketched system below. $x_c(t)$ is an arbitrary, continuous-time signal at the input and $s(t)$ is an impulse train, defined as $s(t)=\sum_{n=-\infty}^{\infty} \delta(t-nT)$, where T is ...
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1answer
38 views

How to calculate a significant value of a definite curve/shaded region in a graph?

The attached graph below consists of $4.5$ seconds of pattern which I have recorded via a hardware device. The $x$-axis is the timestamp value in seconds and the $y$-axis is the hardware value. The ...
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0answers
38 views

Number of trials to judge performance of Compressive Sensing recovery algorithms

I'm trying to get a conclusive numerical value for Mean Squared Error (MSE) as the performance metric of a few CS sparse recovery algorithms. To do this, I vary the number of measurements ($M$) taken ...