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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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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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“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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How do I 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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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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1answer
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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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Why would I leave a signal oversampled?

I can't think of a better way for asking this question so I will start with an example. Suppose that I have an input signal with a max frequency of 50Hz (sampled at 100Hz). Now the signals of interest ...
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Why do we choose 44.1 kHz as recording sampling rate?

Peoples' ears can hear sound whose frequencies range from 20 Hz to 20 kHz. Based on the Nyquist theorem, the recording rate should be at least 40 kHz. Is it the reason for choosing 44.1 ...
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What are the advantages, if any, of derivative sampling?

In Five short stories about the cardinal series $[1]$, the author makes the following comment: Interestingly enough, Shannon goes on to mention that other sets of data can also be used to ...
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Downsampling an image by an integer factor

When downsampling an image by an integer factor $n$, the obvious method is to set the pixels of the output image to the average of the corresponding $n \times n$ blocks in the input image. I remember ...
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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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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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1answer
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Sampling of a continuous function: Kronecker's or Dirac's delta?

I've been reading some papers in signal proccesing and I'm very confused about the issue in the title of my question. Consider a continuous function of time $t$, $f(t)$, that I sample at uneven times $...
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How does the quantization error generate noise?

I'm learning about sampling and DSP on my own. I have a hard time to understand how the quantization error results in noise. I think I miss a fundamental understanding but can't tell what it is. So ...
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What is anti-alias pre-filter for preventing aliasing after under-sampling?

We know that the under-sampling results in aliasing and frequencies higher than half of the Nyquist rate is not distinguishable. I've a base band signal that I want to use the higher frequencies which ...
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3answers
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Alias frequency Formula

I'm taking a multimedia systems class in my MSc Computer Science, and I'm having some trouble understanding the formula for the alias frequency - this could stem from my misunderstanding of the alias ...
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2answers
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The current state of the art in audio signal interpolation

Three questions: What are all the metrics one can use to measure audio interpolation quality, objectively? (but also in terms of psychoacoustics if possible) By those metrics, what is the current ...
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1answer
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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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1answer
639 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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Practical wideband digital beamforming for large arrays in radar applications

I do understand the mathematics behind digital beamforming but I am not sure how such systems are practically implemented. For example, in a typical wideband FMCW radar operating in S-band, the (...
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700 views

How to measure the agreement between to curves?

I have values (plotted below) of expected RSSI values over time that I would like to compare with my measured RSSI values. What I was looking for was a way to quantify it so I can change parameters ...
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687 views

Sampling the Dirac function

I would like to ask a theoretical question concerning the Dirac function. The Fourier Transform of the Dirac function is the value 1 (DC) for every frequency. If we consider the Sampling Theorem, we ...
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Signal values we will 'miss' between sampling instances during sampling of band limited signals

According to the Nyquist–Shannon sampling theorem, any continuous time signal with a bandwidth $B$ smaller than Nyquist frequency $f_N=f_s/2$ (with $f_s$ the sampling frequency), which is sampled at ...
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3answers
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Zero, First, Second … nth-order Hold

The rectangular function is defined as: $$\mathrm{rect}(t) = \begin{cases} 0 & \mbox{if } |t| > \frac{1}{2} \\ \frac{1}{2} & \mbox{if } |t| = \frac{1}{2} \\ 1 & \mbox{if } |t| < \...
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Directly compare subpixel shifts between two spectra — and get believable errors

I have two spectra of the same astronomical object. The essential question is this: How can I calculate the relative shift between these spectra and get an accurate error on that shift? Some more ...
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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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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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Why is telephone audio sampled at 8 kHz?

When did we decide to sample telephone at $8$ kHz? Has this always been the case? Why did we do that? Is it because higher bit rates can't be transferred as quick? And do these reasons still count? ...
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1answer
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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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3answers
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What is the effect of aliasing on the magnitude of the autocorrelation?

I've a question about the effect of aliasing on the magnitude of autocorrelations. From a simulation in MATLAB, I don't see any effect of aliasing or any need to anti-alias filter when I take the ...
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1answer
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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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143 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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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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2answers
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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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Compressive sensing vs. Sparse coding

There apparently are different terminologies used to refer to the same field called "compressive sensing" such as (see this wiki page): compressed sensing, compressive sampling, or sparse sampling. I ...
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649 views

determine two signals with a scale factor

Suppose I have 2 signals from function $f_1(x)$ and $f_2(x)$, respectively, and assume the sampling rate is above Nyquist frequency, so we can restore the underlying functions $f_1(x)$ and $f_2(x)$. ...
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BandPass Signal Vs PassBand Signal

Am reading Rick Lyons - Understanding DSP book about Sampling. I have few doubts related to this chapter. what is the difference between Bandpass Signal and a Passband Signal ? Can somebody give an ...
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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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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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2answers
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why total energy of a finite duration continuous signal becomes infinite after sampling

If I have a continuous-time energy signal and multiply it with an impulse train, the frequency domain representation has infinite replicas. The total energy if we sum them up becomes infinite. What ...
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258 views

Is there any way to make a sampling rate reduction in the frequency domain?

Is there any way to take advantage of the frequency domain to make a clean/nice sampling rate reduction effect ? and how ? Basically, deducted from my tests: if I set to 0 the magnitude uppon a ...
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1answer
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Dealing with Random Errors in Sampling Rates?

I wonder what generalization I can make about what happens when I introduce some error in my sampler spacing. For example, If I sample once every second I would want my sampler to take a signal at ...
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3answers
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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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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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Sampling Theorem illustration

Can someone please explain the illustration (figure 1.19) at the bottom of this image? It looks like there are four sampling points but I don't understand what the different curves represent. Actually ...
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1answer
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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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1answer
175 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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1answer
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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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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

Determining the mean of of a sampled signal (improvements to time averaging method)

I am sampling a signal at 1kHz, which is essentially a single-frequency sinusoid with a DC offset (and a small amount of noise). I don't know the precise frequency of the sinusoid (it is at most 10Hz),...
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1answer
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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 ...