Questions tagged [sampling]

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

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Does a 20 kHz sine wave sampled at 44.1 kHz need to be reconstituted before playback?

I am interested in building a synthesizer but I am confused about the Nyquist-Shannon Theorem and sampling rates. If I sample a 20 kHz sine wave at 200 kHz and plot the data points, the plot looks ...
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280 views

Sound quality with really high sampling rate, but really low bit depth with dithering?

This question is probably more for fun and theory, but how will the sound quality be, if you create a sound with really high sampling rate (like 192kHz) and really low bit depth (e.g. 3bit)? Can you ...
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12 bit ADC to 8 bit DAC

A bit of background information: I plan to start experimenting with digital signal processing on microcontrollers. The particular microcontroller I plan to use (TI Stellaris LM4F230H5QR, from the ...
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311 views

Phase difference between signals sampled at different frequencies

I want to know that if it is possible to measure the relative phase difference between a signal that has been sampled at two different locations with different sampling frequencies? Also can that ...
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How would you interpret the pattern in this picture? (generated by re-sorting pixels based on their RGB value)

Was playing with some pictures and ran the ruby code below. The code reads an input image using the ImageMagick library, gets an array of pixels, re-sorts the pixels and then writes out an image with ...
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Periodicity of sum of discrete signals

In my lecture slides for school and from this website here "The sum $z[n] = x[n] + y[n]$ of periodic signals $x[n]$ with fundamental period $N1$, and $y[n]$ with fundamental period $N2$ is periodic ...
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Sampling frequency of modulated signal

A very naive question... A signal with bandwidth of 20 MHz is modulated using a carrier of 1 GHz. What will be the sampling frequency? I was asked this question during an interview. I answered 2 GHz ...
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How can I generate a sine and cosine function using an exponential function?

I have been trying to generate sine and cosine sampled graphs by a given sampling frequency. ...
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How do MATLAB and/or Python treat $2^n$ samples rule in FFT

As far as I have read, an FFT requires that the number of original data points must be a power of 2. I'm wondering whether the tools like MATLAB or Python which have FFT functions take care of this ...
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Philosophy of perfect inter-sample interpolation

How would you define perfect (inter-sample) interpolation, and is it possible? To quote Armifinn's prior answer: "I guess the most important result is that for signals with bandwidth limitation, ...
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Relation between the DTFT and the spectrum of a sampled signal

In the $\rm DTFT$ (Discrete Time Fourier Transform) the spectrum is periodic with period of $2\pi$ . A continuous signal when sampled has a spectrum which is a repeated version of its original ...
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Unexpected Result When Using Sinc Interpolation

blue is how I tried to sinc interpolate. why would something like this happen?
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Sampling Theorem and Signals Explained to a Mathematician

Let $f:\left(-\frac T2,\frac T2\right)\to\mathbb{R}$ for some $T>0$. The Fourier coefficients of $f$ are $$\left\{\begin{matrix}a_0&=&\displaystyle\frac 1T\int_{-T/2}^{T/2}g(t)\;dt\\a_k&...
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Does audio upsampling create noise/artifacts or degrade the signal?

I've read that upsampling performed in digital music playback can color the sound, produce artifacts, etc. For example, an audio file ripped from a CD might be 44.1Khz/16-bit, and then upconverted to ...
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611 views

minimum sampling rate for very short duration signals

I understand that sampling rate should be twice the signal bandwidth for successful reconstruction. But what I don't get is how this translates in the time domain. For example, I have a sine wave ...
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Spectrum of a Signal Going Through a Zero Order Hold Sampling System

What does the spectrum of a sampled signal look like if one uses a zero-order-hold? There is some information in: Sampling theorem and Dirac comb, but I am wondering, how to apply this in practice. ...
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How to predict the spectrum of an aliased/folded signal without looking at the FFT?

This seems like a trivial concept but I just can't get the hold of it. I have a signal with two complex sinusoids having frequencies -25MHz and 17MHz. Currently it is being sampled at 64MHz so I get ...
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Convolution : Anechoic Speech signal and Impulse response

I am trying to perform convolution in MATLAB of an anechoic speech signal (2.1 s) and a impulse response (20 s) using the following code: ...
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Contradictory results from power spectral densities and autocorrelation in shot noise

I have a white noise generator circuit which involves a Zener diode meant to undergo breakdown across a resistor $R1$, and am trying to compare power spectral densities and autocorrelation of the ...
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In the Sampling Theorem, why are the image frequencies at n*fc not a problem?

In this example I have been working through, we first look at the situation when fs > 2fc and then the situation when it isn't: In the example, the frequency responses of a sampled sinusoid at fc = 5 ...
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Estimate sampling frequency given an array of values

Given an array x of size 2000, is there any way to calculate (or estimate) the sampling frequency using Matlab? The values are the only information I have about the signal. I know the signal has been ...
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Why analog anti aliasing filter is used before analog to digital converter when there is already a digital filter after ADC?

Normal data acquisition consist of: Analog anti aliasing filter( Sampling frequency : $5\textrm{ kHz}$) ADC - Digital Filter - (Sampling : 200K samples /sec) Digital low pass filters Filters DAC ...
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Sample Rate: How to determine sample rate [closed]

I have this ADC and I have this 169p micro-controller. The system oscillator clock frequency (FOSC) is 8 MHz. According to the ADC documentation the conversion process takes 16 cycles. So if I have ...
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Define comb function in terms of exponential function

I have one signal with $N$ samples and I want to downsample it by factor of $M$. Essentially my downsampler is comb function which takes every M$^{th}$ sample while others are set to zero, i.e., $$ \...
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Downsampling and Then Upsampling

Given this system: I need to show the $\mathcal Z$-transform of $y[n]$ as a function of the $\mathcal Z$-transform of $x[n]$. Now I know that for downsampling alone: $$Y(z) = \frac1M\sum_{m=0}^{M-1}...
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510 views

Cut-off frequencies for fractional sample rate adjustment

We have a signal sampled att 22 kHz that we want to interpolate to 40 kHz. So we can do this by upsampling by a factor 20, then downsampling by a factor 11. My question regards the choice of cut-off ...
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Interpreting the cross correlation results

I am new to this forum. I am just trying to understand how to calculate delay (in terms of samples) between two signals using cross-correlation function. I wrote a small Matlab code in order to ...
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Sampling of bandpass signal with bandpass filter

Trying to solve the following problem about bandpass signal sampling. I have a signal whose Fourier transform is such that $X(w)= 0$ if $w>w_h$ or $w<w_l$. The reconstruction is done using a ...
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Cross Domain Equivalent to Nyquist Sampling Theorem?

In attempting to answer this question by @Oliver here: What characterizies 'causality' for a finite FFT? I have considered the minimum requirement to avoid time domain aliasing in the Discrete ...
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Variance of a signal

How to calculate the variance of noise samples modeled as follows: $n_a(t)$ is a Gaussian zero-mean white noise process with (two-sided) power spectral density $\frac{N_0}{2}$. $n_a(t)$ is passed ...
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Understanding Pitch Detection with Autocorrelation Methods

I've been reading through A Smarter Way to Find Pitch, describing its pitch detection algorithm using autocorrelation. I've been having trouble understanding the accuracy claims. It says: MPM runs ...
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When Two Sampled Sinusoidal Are Orthogonal?

If two analog sinusoidal are orthogonal with duration T, their minimum frequency difference should be 1/2T in case of no phase offset between them. And if there is phase offset, the difference is 1/...
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703 views

About phase unwrapping

I am not too familiar with phase-related problems so I need some suggestions or corrections in a problem that might be an old but easy one. Here is my problem: given a complex signal: $$y(t) = e^{j\...
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Plotting the discrete time signal

Consider the following analog signal $$x(t) = 2 \sin(100\pi t)$$ The signal $x(t)$ is sampled with a sampling rate $F_s=50\textrm{Hz}$. Determine the discrete time signal. Plot the discrete time ...
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Upsampling and Downsampling using IFFT and FFT

Assume in OFDM , there are N=64 subcarriers. I would like to upsample my signal by Factor 8 after IFFT and pass it through channel then downsample it by factor 8 before FFT. I can use upsample, ...
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115 views

What do I with the sampling period when I inverse $\mathcal Z$-transform?

Given the input $$e(kT_s) = {0.4, 0.8,1.2, - 0.9}, \quad k = 0,1,2,3$$ and transfer function $$T\left(z^{-1}\right)=\frac {z^{-1}-0.8z^{-2}}{1-1.1z^{-1}+0.3}$$ Find the output $Y(kT_s),\...
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Why do we use discrete-time sampling?

I have been reading Signals and Systems (2nd ed.) recently. Chapter 7 is about sampling. Oppenheim uses discrete-time signals and continuous-time signals to explain sampling. But why do we need ...
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313 views

Making a low pass filter for irregular samples

We are interested in reconstructing the red channel of a scene. The red channel is slowly varying. Unfortunately the camera does not have a Bayer sensor, and the red samples are irregularly spaced ...
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521 views

Calculating an incoherence property from sub-optimal sampling patterns

EDIT (after comments and subject matter review) CS is based on a choice of a sensing basis $\Phi$ relative to a representation basis $\Psi$. Using an "Incoherence Property" $\mu$ that measures the ...
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Expression to represent alternating pulse train?

I have a question regarding an alternating pulse train signal, $p(t)$, and a system which looks like this: Immediately, I'm supposed to be able to extrapolate that $$ P_t = P_1(t)-P_1(t-\Delta) $$ ...
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1answer
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FFT and aliasing

I have got a txt file which contains voltage and time data. When I did fourier transform using fft function in matlab I got complex numbers. I understand that the real part is the magnitude and the ...
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Adding echo to audio sample

I have recorded my own voice in Matlab and I intend to add some echo to it.I came up with one solution for getting the desired echo effect: Delay the sampled audio in the time domain and adding it to ...
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FFT of white noise with different sampling rate

I have a question on how I should interpret the white noise power level (noise floor) obtain from FFT for different hardware sampling rates. I realized if I sample the same noise at different rates (...
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DFT: a function of $n$?

I‘m a high school student and I haven’t studied physics or anything. Why does the DFT depend on an integer, say $k$ or $n$ (it’s usually expressed like $F(n)=...$ or $F(k)$ or $F_k$, etc.) if it is ...
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variance of the product of two samples with awgn

problem solved itself, sorry for your inconvenience. I'll try to post better questions next time.
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How to delay an audio signal by 1 microsecond? [duplicate]

I have an audio signal sampled at 44100Hz. I want to delay this signal by 1 microsecond (and maybe even less) for a steganographic purpose. Now if I delay it one sample, the corresponding time delay ...
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648 views

Relation between the DTFT and CTFT in sampling- sample period isn't as the impulse train period

I will quote an answer of Matt L. from this post (I didn't comment there because I can't) If you have a continuous-time signal $x(t)$, then the two signals you're talking about are $$\begin{...
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Why is one of the modulated frequency spikes smaller?

This is a simple amplitude modulation experiment. Both waves are sinusoids of the type cos(2 x pi x f x t). The base signal has a frequency 100Hz, and the ...
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110 views

Effect of nonlinear transformation on digital signal

Currently, I know that by passing a band-limited baseband digital signal through a nonlinear system results in the expansion of the original signal's bandwidth and creates harmonics. Therefore, I ...
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322 views

Denoising short, non-uniformly spaced, bandlmited sequences

Consider a bandlimited signal $x(t)$ with bandwidth $BW$. Samples of this signal are observed at non-uniformly spaced sample points in the presence of noise: $y(t_i)=x(t_i) + n_i \qquad i\in\{0,1,\...

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