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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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1answer
207 views

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, which is ...
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149 views

Is sampling a Fourier transformed signal and fourier transforming a sampled signal the same?

I'm having a hard time understanding an assignment that states: Draw the complex spectrum of the sampled signal $f(t)$ (periodic and continuous). Do this, by first calculating the Fourier ...
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173 views

How do you deconvolve irregularly sampled points?

$f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a signal and $g:\mathbb{R}^n\rightarrow\mathbb{R}$ is a known point-spread function (say, a Gaussian). A system samples $f\star g$ at a known sequence of ...
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124 views

Model-based Kalman filtering a noisy signal

In a healthcare application, I need to calculate urine flow by differentiating the mass of urine emitted by a person over time. The measuring instrument consists of a load-cell under a fluid container,...
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270 views

How does Delta-Sigma Modulation convert a 1-bit signal to higher resolution signal?

I've looked at various resources about Delta-Sigma modulators, and I find them fascinating. However, I'm confused on a particular point and and am looking for an explanation. In my understanding, ...
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170 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
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Is Fourier series a sampled version of Fourier transform?

I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
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746 views

Regarding the Nyquist Criterion

I recently read that with compressive Sensing it possible to sample the signal at a rate lesser than that suggested by Nyquist Criterion. However, I am still not getting how this is possible. Can ...
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535 views

Precise 5th and 7th harmonics of a sampled sine wave

Does anyone know in decibels (to 1/100th of a dB) what the theoretical 3rd, 5th and 7th harmonic of a 0dB fs 24-bit (i.e. full-level; 0dB = -8,388,607 to 8,388,607) sampled sine wave without dither ...
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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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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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What Does 'Zero Order Hold' and 'First Order Hold' Mean?

While studying the Image Magnification in spatial domain, I have come across this definition of Image Magnification by Replication: Replication is a zero order hold where each pixel along a scan ...
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984 views

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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1k views

Suitable sampling rate for triangle wave

I know this is a fairly simple question but I can't convince myself of the right answer. For a 5KHz triangle wave, being sample at Fs sampl/second, what's a suitable choice for Fs such that an ...
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1answer
976 views

Why can't DFT be used when samples are not equally spaced in time?

I found the following comment here The DTFT can be used when the samples are not equally spaced in time, the DFT cannot My initial thought was that this had to do with periodicity of the basis ...
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3k views

Why is oversampling helpful to an anti-alias filter?

Why does oversampling make the job of an anti-alias filter easier? I don't understand the intuition on why it becomes helpful. Isn't it economical to just keep the sampling rate at the minimal level,...
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121 views

What will be the filtered output?

I tried to solve this question from basic Here is my work Image 1 Image 2 But the correct answer is Option $(B)$.What is the mistake i am doing?
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1answer
286 views

Bandwidth confusion

Let's imagine that I took a Fourier analysis of a random voice signal that I want to sample and plotted it's frequency components in frequency domain (frequency vs amplitude). Now I want to sample it. ...
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423 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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Determine maximum frequency of input signal to make system LTI

This is question 4.26 from the third edition of Alan Oppenheim's textbook "Discrete-time Signal Processing". It is stated as follows: Firstly, the answer is the input signal should be bandlimited to ...
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1answer
266 views

Given a continuous time signal, does the minimum Nyquist sampling rate depend on the choice of the set of basis functions?

This is my first question on a StackExchange. When the basis functions to represent a signal are chosen as $e^{j\omega t}$ such as in a continuous-time Fourier transform then the sample rate $f_\...
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1answer
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What is “Equivalent Time Sampling” and what is it good/used for?

The literature on this method seems scarce, but I know that it has been used on radar systems to 'get away with' not having to sample nearly as fast as Nyquist would otherwise dictate, (at the cost of ...
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Reconstructing/interpolating small regions of a bandlimited signal by taking the fewest possible samples

I have a signal which is bandlimited and can be sampled at arbitrary continuous positions. The value at any position is given by an expensive computation. I need to do some further computation on ...
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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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Does oversampling improve processing gain?

I am used to Time-Bandwidth product describing the processing gain or improvement in SNR for a spread spectrum signal using a matched filter. One could view the bandwidth $B$ as the sample rate (...
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With regards to multirate processing, what are the benefits of having a 'slower' sampled signal?

With regards to multirate processing, what are the benefits of having a 'slower' sampled signal? Let's say I have a continuous signal $$x(t) = \cos(2\pi\cdot3t) + \cos(2\pi\cdot 7t)$$ and it is ...
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846 views

How do I resample an image to a rotated grid?

I have an image, I, sampled on a uniform grid: $\ x_i = i*\Delta x, y_j = j*\Delta y, $ I need to resample this image to a grid rotated counterclockwise by an angle $\ \theta$ around $\ (x_0,y_0)$: ...
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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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157 views

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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491 views

Should I sample at twice the bandwidth or twice the highest frequency?

I am confused about what rate I should sample at. I've heard 2 different ways: 1) Sample at twice the highest frequency 2) Sample at twice the bandwidth If I have a signal composed of just cosine, ...
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1answer
537 views

Bridging CTFT and DTFT for a cosine

I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT. For example if I take a basic example: $$\begin{aligned} x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \...
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Minimum period of a signal

What is the minimum period P (in samples) of the signal $e^{j(\frac{M}{N} )*2πn}$ for the following values of M and N? M=1,N=3 M=5,N=7 M=35,N=15 I have got the answer for the first pair of values, ...
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136 views

What is the difference between the Point Spread Function and Sampling Aperture?

I've been told that the point spread function of a pixel is its distribution of intensity, while the sampling aperture of a pixel is its distribution of sensitivity. I'm a little unsure of what the ...
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1answer
611 views

Reference for Supersampling

I want to downsample images to arbitrary sizes using supersampling to avoid aliasing effect. The only two good explanations I found were on Wikipedia and everything2.com, but there are still gaps. ...
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485 views

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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1answer
3k views

Correlation of two signals at different sample rate

I have a signal $X$ and I want to find signal $Y$ in $X$, I can achieve this by cross-correlation. Signal $X$ is sampled at $8000\textrm{ Hz}$, and $Y$ signal is sampled at $44100\textrm{ Hz}$. My ...
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1answer
2k 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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90 views

oversampled coefficient for existing exponential smoothing

Say I have an exponential smoothing for certain $\Delta t$, $t_{i+1} = t_i + \Delta t$. In this sampling, I choose a particular $\alpha$ to filter signal $z_i$ like $$ v_1 = z_0 \\ v_{i+1} = \alpha\:...
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1answer
267 views

Explanation of LidarBoost Algorithm?

I am trying to understand the LidarBoost algorithm as explained in this paper (PDF warning). I don't understand how they take the original depth-images $Y_k$ and transform them into the up-sampled ...
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1answer
47 views

Can the Nyquist sample rate be extended to stochastic sampling?

It appears there are lots of questions here about Nyquist, and a few questions about stochastic sampling here. But I haven't found any that address quite what I'm after. This is the closest I've ...
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1answer
355 views

Smoothing 3D Data for the Second Derivative

I am not a signal processing expert and my feeble attempts at solving this problem have come up short. I have a C++ application which is being fed regularly-spaced (in time) 3D position samples. The ...
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1answer
5k views

Sampling of band-limited white noise

The context is communication where we have a front-end that samples a signal and a noise (but here we focus only on the noise). My goal is to determine the noise power that I should use to simulate (...
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1answer
1k views

How to apply a Butterworth filter to data of varying sample rate?

I am trying to apply a Butterworth bandpass filter to accelerometer data of my smartphone. However, the accelerometer samples I receive do not come at regular intervals. Sample frequency varies ...
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1answer
160 views

Getting error in fit

I was wondering if anyone had run into the problem of trying to estimate errors in their signal processing on spectroscopic data. I know that many people use spectroscopic techniques to estimate ...
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1answer
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Dynamically changing cut-off and sampling frequency of a digital filter

I have designed a low pass filter that smooths the output coming from an accelerometer attached to a vibrating machine. I designed this assuming cut-off frequency $f_{c1}$, and sampling frequency $f_s$...
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Compensating for measurement errors

I have a system where I sample some data periodically (every 10usec). The shape of the data is triangle, in other words it linearly increases and decreases in time. (Both theory and practice are in ...
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A question about sampling rate of cosine signal

Given $$c(t) = \cos(2\pi\cdot 30 \cdot t) $$ If we sample this signal at the Nyquist rate 60 Hz and at a higher rate of 80 Hz, we get the following: There is no aliasing as $f$ = 30 Hz is less than ...
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What is the difference between cubic interpolation and cubic “Spline” interpolation?. How to use it for upsampling purpose?

After considering a couple of advices and suggestions for upsampling techniques here, I finally converged to use the cubic interpolation technique to estimate the voltage values corresponding to ...
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2answers
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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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2answers
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Why is a square wave aliased?

I understand an ideal analog square wave contains sine-wave-components above Nyquist frequency (and towards infinity) and is thus subject to aliasing. So obviously we need an anti-aliasing-filter. Or ...

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