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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?
Soham De's user avatar
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5 answers
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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 ...
Spacey's user avatar
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30 votes
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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 ...
new_comer_forever's user avatar
29 votes
1 answer
11k views

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 ...
datageist's user avatar
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26 votes
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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 ...
PearsonArtPhoto's user avatar
22 votes
5 answers
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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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What sampling frequency should I use if Nyquist is not available?

I have the following homework question that confuses me: We have an audio emitter that can emit two signals: It either emits a sine wave at 23 kHz or it emits a sine wave at 25 kHz. The receiver has ...
NN amateur's user avatar
18 votes
2 answers
20k views

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 ...
Styg Oldenbaum's user avatar
18 votes
3 answers
2k views

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 ...
datageist's user avatar
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16 votes
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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 ...
gpuguy's user avatar
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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, ...
endolith's user avatar
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15 votes
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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? ...
Lewistrick's user avatar
13 votes
5 answers
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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{...
Gillespie's user avatar
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13 votes
2 answers
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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 ...
Bent Rasmussen's user avatar
12 votes
3 answers
14k views

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 ...
gpuguy's user avatar
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Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?

I have been studying signals and systems lately and I have came across the following claim: The uniform sampling of a periodic continuous-time signal may not be periodic! Can someone please ...
a4w's user avatar
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4 answers
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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 ...
Jan Deinhard's user avatar
12 votes
1 answer
5k views

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 $...
Néstor's user avatar
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11 votes
2 answers
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Does the Nyquist frequency of the cochlear nerve impose the fundamental limit on human hearing?

The bandwidth of human hearing by empirical data is $20 \; Hz$ to $20 \; kHz$. A cochlear implant stimulates the auditory or acoustic or Cochlear nerve directly so that the hearing can be improved in ...
kbakshi314's user avatar
11 votes
3 answers
1k 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 ...
toozie21's user avatar
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10 votes
2 answers
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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 ...
QQStack's user avatar
  • 101
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2 answers
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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 ...
jurij's user avatar
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4 answers
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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 ...
user1058210's user avatar
10 votes
4 answers
12k views

What is Frequency Resolution?

Im trying to tackle the following problem while still not having a firm idea on what "frequency resolution" means : Suppose we sample a continuous time signal with sampling period Ts = 1/2000, and ...
Αποστολης Καρασμανογλου's user avatar
10 votes
3 answers
2k views

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 ...
Hossein's user avatar
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3 answers
491 views

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 (...
user4673's user avatar
  • 325
9 votes
4 answers
12k views

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| < \...
Mark's user avatar
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9 votes
3 answers
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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 ...
George Tseres's user avatar
9 votes
3 answers
6k views

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 ...
Hossein's user avatar
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9 votes
3 answers
732 views

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 ...
Retinite's user avatar
9 votes
2 answers
2k views

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 ...
Learn_and_Share's user avatar
9 votes
1 answer
1k 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 ...
Dan Boschen's user avatar
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9 votes
1 answer
2k views

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 ...
JBWhitmore's user avatar
8 votes
3 answers
16k views

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 : ...
justin's user avatar
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8 votes
8 answers
12k views

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 ...
Kenneide's user avatar
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8 votes
2 answers
11k views

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 ...
bikalpa's user avatar
  • 211
8 votes
2 answers
1k 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 $f_2(x)$. ...
chaohuang's user avatar
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8 votes
3 answers
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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 ...
aroth's user avatar
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8 votes
1 answer
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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 ...
Spacey's user avatar
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8 votes
1 answer
7k views

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 ...
Arrow's user avatar
  • 243
8 votes
1 answer
722 views

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 ...
RJ_DSP's user avatar
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7 votes
4 answers
2k views

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 ...
Kartik Hegde's user avatar
7 votes
2 answers
4k views

Increasing SNR and Dynamic Range using Oversampling

How much gain in dynamic range and SNR can be expected if we are to oversample a signal with fixed analog input bandwidth. For Example if I have a analog filter at the input which limits the bandwidth ...
malik12's user avatar
  • 488
7 votes
3 answers
3k views

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 ...
srk_cb's user avatar
  • 415
7 votes
3 answers
6k views

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 ...
rajez79's user avatar
  • 357
7 votes
3 answers
9k views

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 ...
Sufiyan Ghori's user avatar
7 votes
2 answers
8k views

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 ...
user782220's user avatar
7 votes
2 answers
330 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}\...
stander Qiu's user avatar
7 votes
2 answers
1k 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 ...
MisterFilter's user avatar

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