What is Sampling: Definition and 207 Discussions

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt for the samples to represent the population in question. Two advantages of sampling are lower cost and faster data collection than measuring the entire population.
Each observation measures one or more properties (such as weight, location, colour) of observable bodies distinguished as independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine if a production lot of material meets the governing specifications.

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  1. P

    Nyquist frequency and sampling frequency

    Homework Statement ##N= \frac{2 f_s}{f_{lowest}}####\frac{f_s}{2} - \frac{f_s}{N}## Homework Equations - The Attempt at a Solution I have these equations listed on a formula sheet but I do not know what they are used for. It is from a chapter titled "Discrete Sampling and Analysis of Time...
  2. T

    Sampling Distribution of Mean for Discrete Uniform Distribution with Replacement

    Homework Statement suppose that 50 random samples of size n = 10 are to be taken from a population having the discrete uniform distribution f(x) = 1/10 for x = 0,1,2,...,9 0 elsewhere sampling is with replacement so that we are sampling from an infinite population. we get 50 random...
  3. I

    Band-limited function, Shannon-Nyquist sampling distance

    Homework Statement If ##\delta## and ##\Omega## are two numbers with ##0 < \frac{\pi}{\Omega} < \delta## find a function ##f\in L^2(\mathbf R )## such that ##\hat f(\omega)=0## for ##|\omega|> \Omega## and ##f(n\delta) = 0## for ##n \in \mathbf Z##, but ##f\ne 0## as an element of ##L^2(\mathbf...
  4. S

    One question on the sampling theorem in Fourier transform

    Hello everyone, The question that I have may not be fully relevant to the title, but I thought that could be the best point to start the main question! I'm working on 2-D data which are images. For some reason, I have converted my data to a 1-D vector, and then transformed them to the...
  5. T

    Estimate noise improvement as a funtion of sampling rate

    Hi all, I would like to estimate from my experimental data what would be the noise of the signal if I could sample at a higher rate. It is possible to do that? Do you have any references to good books that explain this topic? Thank you!
  6. D

    MHB Sampling distribution of a statistic

    Looking at another textbook problem, hope someone can let me know if I'm on the right track: Let $X_1, X_2, ... X_{25}$ be a random sample from some distribution and let $W = T(X_1, X_2, ... X_{25})$ be a statistic. Suppose the sampling distribution of W has a pdf given by $f(x) =...
  7. C

    MATLAB Transforming Complex Exponential to Discrete Vector Form

    Hi, I want to transform a complex exponential with quadratic phase to discrete form, in other words to a vector form. can anyone help me with that? Thanks
  8. xaratustra

    Understanding quadrature sampling

    Hey everyone! Can anyone explain, why quadrature sampling works the way it does? i.e. taking 2 samples for the I and 2 samples for the Q. I mean I can understand if one tries to sample one mono frequency signal, say 40 Hz sine wave, on 0, 90, 180, 270 degrees, that is a sampling frequency of...
  9. J

    Sampling Time Calculation for Bode Plots: Plant Comparison & ZOH Preceding

    Homework Statement In the figure, the Bode plots of a continuous-time plant (thin line) and of its discrete-time counterpart, representing the discrete-time operation of the plant preceded by a Zero Order Hold (ZOH) (bold line), are displayed. What is the Sampling time used? Homework...
  10. Ackbach

    MHB How to Compute Standard Deviation in a Mixed Sampling Problem

    This is problem AP3.7 on page 669 of The Practice of Statistics, 5th AP Ed., by Starnes, Tabor, Yates, and Moore. A certain candy has different wrappers for various holidays. During Holiday 1, the candy wrappers are 30% silver, 30% red, and 40% pink. During Holiday 2, the wrappers are 50%...
  11. M

    Beginner's Guide to Compressed Sensing in Signal Processing

    I hope this is the right place for this post. I'm originally a physics student but my thesis supervisor assigned me a work in which the concept of compressed sensing (CS) becomes the underlying aspect. I have searched some sources online but, no good. I guess this is because this CS thing is...
  12. M

    Sampling Continuous-Time Signal

    This my homework: Input signal to system is: where H(exp(jw)) is transfer function of ideal low pass filter with cutoff frequency wg=3*pi/4 and zero phase characteristic. Sampling in A/D converter is done with period T=(1/125) seconds. a) Calculate output signal ya(t) b) Calculate...
  13. C

    MHB How Is the Sampling Distribution of a Sample Mean Determined?

    1. On this question I really have no idea how they got these answers so I just need someone to walk me through it step by step please 2. Part B on this question I don't know how to get the correct answer either
  14. anubodh

    Effective Methods for Microbial Sampling from Student's Feet

    Can anyone tell on how to take microbial sample from the feet of students (13-14 year olds).I have searched about many methods like williamson and kligman method but do not know the best method to carry out the sampling.I intend to give separate kits to the children (around 50) so that they can...
  15. V

    Question about the Nyquist sampling rate

    I'm trying to look up sources on the nyquist sampling rate, but I keep finding this small subtle difference between sources, and I am not sure if it is laziness or some subtle point I am missing. Sometimes I see the nyquist rate as Fs>2Fm and sometimes I see it as Fs>=2Fm. So is it the sampling...
  16. M

    Sampling from normalized and un-normalized posterior

    Help me understand something. I get that the posterior ##p(\theta|y) \propto p(y|\theta)p(\theta)## should be normalized by ##\frac{1}{p(y)}## for the probability to sum to 1, but what about the mean and variance? Am I not right understanding that sampling from the un-normalized posterior...
  17. A

    Sampling for hypothesis testing

    Hi guys. I'm not a statistician although I use it enough that I'm surprised something is bothering me. I'm doing hypothesis testing on a population >100,000. What I'm wondering is whether there is any difference whatsoever between performing multiple tests on several samples or just doing one...
  18. electronic engineer

    Sampling Frequencies: f1, f2, f3 with fs=1000Hz

    Homework Statement We have the following signal frequencies: f1=18 Hz, f2=510 Hz, f3=1100 Hz when using the sampling frequency fs=1000 Hz. how would these signals be like? my question is if I could use the same formula stated below for all the frequencies f1,f2,f3.. because the second and...
  19. S

    How to fit plane onto sampling data?

    For example I have the variables x, y and a probability distribution p(x,y). I want to approximate p(x,y) as a linear function, a plane in this case, at least somewhere in the domain. However I only have samples from the distribution. In case of big amount of data the it is easy to collect them...
  20. R

    How calculate a single frequency of a multifrequency signal?

    I'm just coding a program where I've to calculate the individual frequencies inside an audio file *.wav file. The modulation is pcm and the information I've is a lots of points, like this: http://www.renesas.com/media/support/faqs/faq_results/Q1000000-Q9999999/samp_1.gif To be exact, I've...
  21. S

    MHB Proving Parseval's Theorem for Schwartz Functions with Compact Support

    How to prove the following: Suppose f is in the Schwartz Space ( smooth function with very fast decay). Its Fourier transform is smooth and has compact support contained in the interval (1/2,-1/2) Show, ∫ (|f(x)|^2) dx = ∑ (|f(n)|^2) (where integral over R and sum up over n for all intergers)
  22. B

    Calculating Sampling Rate of Sinc Signals - Nyquist Rate

    I have tried calculating sampling rates for signals like sinc(200pi t). It was simple and I thought I understood until I cam across signals like sinc(200πt)*sinc2(400πt). I need help with finding sampling rate of these kind of signals and get a clear concept on the topic. Thanks in advance.
  23. V

    What is the Best Way to Determine Sampling Accuracy in Large Populations?

    Good afternoon! Suppose I have a box with N marbles of different color and I want to know the ratio of the number of green ones to N (number X). The number of marbles (N) is so huge that there`s absolutely no way to get them all out of the box and count. What I do instead is I take a sample of...
  24. W

    Why Is the Value '2' Used in Calculating Coin Variance?

    Homework Statement A bag contains a large number of coins comprises of 1 cent and 5 cents coins in the ration of 1:3 find the man and variance of the values of coins.. i have attached the sample ans here. i don't understand why the value of '2' is used?? why not '5' ...for me '5' represent 5...
  25. S

    Solve Sampling Problems: 95% Interval for Mean of X

    Homework Statement If X is distributed normally with mean = 7 and the variance of X is 4 , calculate a 95% interval for mean of X . size interval is 10 Homework Equations The Attempt at a Solution here's my working : ( 4- 1.960 x (surd(4/10)) , 4+1.960 x (surd(4/10)) ) my ans is incorrect...
  26. D

    MATLAB Sampling with replacement in Matlab

    I am trying to simulate the probability of rejecting a good batch for a probability of \(0.94\) using the Binomial Probability Law. My two cases are \[ P[k\geq 95] = \sum_{k = 95}^{100}\binom{100}{k}p^k(1 - p)^{100 - k} \] and \[ P[k\geq 98] = \sum_{k = 98}^{100}\binom{100}{k}p^k(1 - p)^{100 -...
  27. R

    Exersize related to sampling frequency of 2D signal

    For an image, higher the dimensions of image ,more is the resolution of the image.But is there any relation present between sampling frequency and dimensions of image? Also, Whether the Number of samples presents in an image is equal to product of dimensions of image?
  28. R

    Calculation of sampling rate and its effect on an Image?

    I know that for a given signal, the sampling frequency Fs must be twice or more than maximum frequency of the signal Fm. It is easy to understand the concept for a 1D signal. But I don't know how to calculate sampling frequency or Nyquist rate for a 2D image. Also what is effect of...
  29. W

    Sampling a signal and do the discrete Fourier transform

    When I sample a certain digital signal with increasing sampling frequency, the fast Fourier transform of the sampled signal becomes finer and finer. (the image follows) Previously I thought higher sampling frequency makes the sampled signal more similar to the original one, so the Fourier...
  30. C

    Frequency measurement -- how to choose sampling ?

    Hi, let's say I want to measure the frequency f of a periodic signal. I may take N data points with an arbitrary timestep of T. The question is how shall I choose T for a fixed N to have the best accuracy? In principle the frequency resolution is 1/(N*T) when taking the Fourier transform...
  31. K

    Discrete fourier transform data of 2 different sampling frequencies

    Hi All, I have a problem I've been thinking about for a while, but I haven't come up with a really satisfactory solution: I want to do a discrete Fourier transform on data that has been sampled at 2 different sampling frequencies. I've attached a picture of what my data will look like...
  32. N

    MHB Log-concave posterior density function adaptive rejection sampling

    Let $x_1,x_2,\ldots,x_n$ be binary observations which have independent and identical Bernoulli distributions with parameter $\theta$, so that $f(x_i | \theta) = \theta^{x_i} (1 - \theta)^{1-x_i}$. Suppose that the prior density for $\theta$ is \begin{equation*} f(\theta) \propto...
  33. U

    How Do You Calculate the Probability of a Sample Mean in Normal Distribution?

    The scores X1 and X2 in papers 1 and 2 of an examination are normally distributed with means 24.3 and 31.2 respectively and standard deviations 3.5 and 3.1 respectively The final mark for each candidate is found by calculating 2X1+1.5X2. Find the probability that a random sample of 8candiates...
  34. N

    How Much Rope is Needed for Towing a Plankton Net at a Specific Depth?

    Homework Statement I have a boat moving at 2.3 mph towing a plankton net in water weighting 8.5lbs. I want the net to be towed at a depth of 10m from the surface. How much rope do I need to let out from the boat? Homework Equations basic trig sin=cos=tan The Attempt at a...
  35. dexterdev

    Sampling low pass filtered white noise

    Homework Statement If we filter out ideal white noise using an ideal LPF of cutoff frequency W Hz and then sample it at F Hz , What are the conditions for different F so that the resulting discrete signal is correlated, uncorrelated , statistically independent and orthogonal etc? I would...
  36. Jameson

    MHB Estimate \theta with Importance Sampling: Plot Convergence vs Sample Size

    Problem: Use importance sampling to estimate the quantity: \theta = \int_{0}^{\infty}x \frac{e^{-(y-x)^2/2}e^{-3x}}{Z}dx, where Z=\int_{0}^{\infty}e^{-(y-x)^2/2}e^{-3x}dx and $y=0.5$. Plot the converge of the estimator versus sample size. Note: You may consider $3e^{-3x}$ as the density for...
  37. S

    Sampling from a stochastic process

    Homework Statement Given X(t) = cos(2\pi50t + ω), where the stochastic variable ω is uniformly distributed between 0 and 2\pi. Suppose the sampling frequency fs is 30 Hz. What frequency interval is covered after the sampling? Homework Equations Normalized frequency when sampling can be...
  38. F

    Galaxy - random sampling issue

    I need to generate initial conditions for modeling galactic spiral arms. I start with the following polar equation: rho = a. / (log (b * tanh (theta / (2 * n))) with a, b ​​and n are parameters to choose from. to give a thickness along the curve for the generated points, I did the...
  39. E

    Easy-to-compute posteriors / closure under noisy sampling

    I have a question on (I think?) Bayesian statistics. Consider the following situation: -P is a class of probability measures on some subset A of the real line -q is a probability measure on some subset B of the real line -f is a function on AxB -My prior distribution on the random...
  40. J

    How to Design a Gas Sampling Probe for Varying Exhaust Gas in a Brick Catalyst?

    I want to sample exhaust gas just behind a Catalyst. The problem being the gas varies across the area of the brick so a normal sample probe could read high or low. The general idea is to use a tube with holes in across the area of the brick, however I'm not sure what size to make the holes as...
  41. C

    Sampling with multidimensional transformations

    I am not sure if I have the title right, but here is my problem: I have a ray which 'should be' shot vertically from a point p, but depending on the situation it can: 1) either be shot in any direction in the hemisphere above p 2) shot with an angle of no more than σ off the vertical 3) shot...
  42. J

    Finding sampling frequency for analog to digital conversion

    The input signal to an analog to digital converter is x(t) = 5.4 cos (134.5πt + 0.1π). The output from the converter is y(n) = 5.4 cos (0.47πn - 0.1π). Compute the sampling frequency (samples per second) of the analog to digital converter. Hint: the continuous-time input signal is...
  43. J

    Finding original signal, given signal obtained by sampling

    Let, x(n) = 3.9 cos(0.80πn + 0.2π) be the discrete-time signal obtained by sampling a continuous-time signal x(t) at a sampling rate of 578.4 samples/sec. Find possible expressions for x(t). Hey all, I am quiet unfamiliar with this type of question, and haven't been able to put anything...
  44. H

    Question on sampling frequency/low pass filter

    Hi all, I have a question relating to sample rates and data filtering. I have a (relatively) high sampling rate of 100Hz, there is some high frequency "noise" present that acts over the range of 1-15Hz. My question is, given that I am interested in much lower frequencies (slow movement...
  45. H

    Stat HW: Xbar and sampling infinite populations

    Homework Statement Two problems: 1) We're given a probability distribution function with possible values and their probabilities of occurring: X=1, P = .67 X=2, P = .19 X=3, P = .05 X=4, P = .04 X=5, P = .03 X=6, P = .02 And we need to find P(XBAR >=6) and P(XBAR >=5). I don't...
  46. G

    Arguments in favour of the fair sampling assumption

    Hi all, I'm no expert in quantum mechanics by any means, but I've been quite interested in, and done quite some research on, Bell's theorem and related inequalities such as CH and CHSH. The theories all look perfectly sound, except that they all contain the "no enhancement assumption", some...
  47. K

    Writing a script to repeat a C program (Umbrella Sampling Script)

    I have a C code that creates a small histogram, but I need it to rerun many many times by changing one variable that the user can input. I've NEVER used C until this week so if someone could given me an idea of how to write a script to repeat a code and save a bunch of data from it that would be...
  48. dexterdev

    A signal sampling related doubt

    Hi PF, I have a signal which is sum of 2 sinusoids having frequencies 6KHz and 12KHz. Now if I sample it at a rate of 16KHz and pass it through a ideal Low pass filter having 16KHz cutoff frequency, what is the signal I obtain. What frequency contents does it have. Please help me...
  49. P

    Accurate phase measurement with relativly low sampling frequency

    Hello. To give some more information on what I am to use this for: I have two signals. Both are periodic sine waves with the same frequency, but with a constant phase difference. Let's call one of the signals for ref (reference) and the other sig (signal). They can look like this: ref(t)...
  50. E

    Calculating Nyquist sampling rate and interval

    Homework Statement Determine the Nyquist sampling rate and the Nyquist sampling interval for this signal. sinc(2100\pit) Homework Equations N/A The Attempt at a Solution Ok I know that the Nyquist sampling rate is double or 2 times the bandwidth of a bandlimited signal. So I...
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