Questions tagged [sampling]

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

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Simulating Effects of Sampling after Butterworth Filter

Is there anyway to simulate the effects of sampling an analog signal with Python/MATLAB? I am trying to show what happens to the frequency domain (magnitude and phase) of the analog signal after it ...
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102 views

Minimum sampling frequency, quantization, and bitrate calculation

An analogue sensor has a bandwidth which extends from very low frequencies up to a maximum of 14.5 kHz. Using the Sampling Theorem what is the minimum sampling rate (number of samples per second) ...
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58 views

What is the Uncertainty or error due to sampling frequency?

If I want to detect the distance between two peaks in a signal sampled at 100 Hz. Then is it right to say that the first and second peaks occurred within 0.01 seconds of uncertainty? Therefore, the ...
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15 views

Dynamic sampling points based on the first order derivative of signal amplitude

Problem: I need to measure an arbitrary experimental data set $x(t)$ where t = linspace(min,max,N). However, the experiment is extremely time consuming and I don't ...
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1answer
34 views

Relation between continuous time transfer function and sampled approximation

Suppose I have some continuous time system and associated transfer function: $$ y(n)=x(n)+x(n-1)$$ $$ H(j \omega) = 1+e^{j \omega (-T_s)} $$ Now suppose I create a discrete-time approximation of this ...
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61 views

I/Q sampling with just one ADC

Usually I/Q sampling is performed on two signals with a 90° phase shift using separate ADCs. Suppose I have only a single (fast) ADC available to perform I/Q sampling, which approaches do exist? Is ...
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45 views

What should be IQ sample rate at least?

As i read, IQ sample doesn't need nyquist criteria. What is the mathematical representation of this result? Why IQ sample doesn't need nyquist frequency? I know that can be set to nyquist frequency ...
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3answers
128 views

Under what conditions is there a one-to-one mapping between continuous-time and discrete-time signals?

As the sampling theorem dictates that the uniform sampling frequency must be at least twice the maximum frequency present in the bandlimited signal (Nyquist rate), a question arises about the ...
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44 views

How to measure correlation between 1 bit samples and theoretical original waveform?

I'm investigating quantization error. I have an analogue waveform that looks like this and is of theoretically infinite resolution:- I've sampled it as (8 bit oscilloscope readings & 0b1) to ...
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1answer
109 views

Recovering a signal after nonuniform sampling

Let $x(t)$ be a bandlimited signal such that $X(j\omega) =0 $ when $|\omega|>M$. Also $p(t) = p_1(t) - p_1(t-\Delta)$ is a nonuniformly spaced periodic pulse train where $$p_1(t) = \sum_{k = -\...
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65 views

Condition for aliasing

Which one of the following is the condition of aliasing? (a) Tails of the replicas enter into the Nyquist interval (b) The tails of the replicas enter into the Nyquist interval and add to the ...
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68 views

Question about aliasing

As far as I understand, you can have two different continuous-time signals with the same discrete-time frequency spectrum after they are sampled and it may be possible these shifted replicas in the ...
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204 views

Using oversampling to increase resolution of a DC-signal as input

Currently I'm working on a project which uses oversampling to increase the resolution of a 12 bit ADC to a maximum of 16 bits. My goal is to fully understand the theory behind oversampling and why it ...
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40 views

Sampling interval $T$ as a multiplier in digital processing of a continuous-time signals

[from: Discrete-Time Signal Processing, Oppenheim and Schafer, p.224] Q: Why do we have $T$ as multiplier in $TY_a(j\Omega)$ in Eq.155?
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Multiple choice on sampling and aliasing

I found some multiple choices in a well known book . The problem is that I don't get the answers in some and I want to do so. Question 1: The signal x(t) with Fourier transform $X(j\omega) = u(\omega)-...
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150 views

Is this an error in Oppenheim and Schafer's Discrete-Time Signal Processing?

In Discrete-Time Signal Processing by Alan V. Oppenheim and Ronald W. Schafer (3rd Ed.), in Figure 4.47 the input of D/A converter is $\hat{y}[n]$ but later in Figure 4.64 the input of D/A converter ...
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51 views

What happens to the phase spectrum when I resample?

[An update is added at the end of the post after receiving first response] I have an algorithm which is very sensitive to phase shifts. It works with signal sampled at 40MHz (it's a neural network so ...
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61 views

Optimal sampling rate for the HMM forward-algorithm

I have a system with a binary-state. The system state is estimated by an HMM forward-algorithm. Also, the system allows a varying sampling rate. Considering that the system state transition takes a ...
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63 views

Sampling pure tone sine waves [closed]

What would happen if I am using the maximum frequency as the sample rate for sampling a pure tone sine wave? For example, a $10\ \rm kHz$ sampling frequency for a $10\ \rm kHz$ monotone sine wave. ...
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1answer
83 views

Difference in information between IQ Sampling vs. Real Sampling at $2F_s$

As per my current understanding we use IQ sampling as way to increase the useful bandwidth to Fs rather than $F_s/2$ when viewing the FFT because the IQ sampling removes the negative frequencies and ...
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40 views

First order hold from zero order hold filter

I'm stuck in this question for more than 4 hours. (h is the sampling period) I simplified the block diagram but it just seems impossible to get the FOH transfer function from the reduced block ...
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1answer
90 views

Difference between sampling rate and baud rate and their relation to channel capacity

The sampling rate says that one Hz can carry at least 2 samples, and the bit rate is obtained by multiplying the sampling rate by the number of bits per sample. Thus, many samples and many bits can ...
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28 views

decomposition of a function to piecewise functions

Is the next answer correct: $$a\left(z\right)=\sum _{\left\{k\right\}U\left\{k'\right\}:f_k\le \:z,\:z\:\in R,\:f_{k'}\ge z\:;\:z\ge 0}1-\frac{f_k}{z},\:b\left(z\right)=\sum _{\left\{k\right\}:f_k>...
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54 views

Is Sum of Absolute Value / $ {L}_{1} $ Norm of Differences Convex?

I'm not sure how to approach this exercise. One idea is to derive it w.r.t z, show that there is a min-extremum at $z=f_k$ and then show that for each value from the right and the left of the loss ...
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sampling using L1 optimization

As much as I understand the F should be the interval medians (correct me if I wrong), according to the next slide, where is also the Loss function defined: What I don't understand is the next note in ...
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Why Is the Total Time Equal to $ N \cdot {T}_{s} $ and Not $ \left( N - 1 \right) \cdot {T}_{s} $ In the Context of DFT?

In the definitions of the DFT DFT $$ X(j)=\sum_{k=0}^{N-1} x(k) \exp \left(-i 2 \pi\left(\frac{j}{N}\right) k\right) $$ Let us say, if we have $10$ points, $N=10$, each sampled at $0.2$ seconds, why ...
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39 views

Quantization and Sampling - putting it all together

So after I learned this two topic: quantization and sampling, I'm learning the way to look at both of them and try to optimize the split of a given amount of bit B to N and k, where N is the amount of ...
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39 views

NUFFT of non-uniformly sampled signal

I am trying to understand how to use nufft from the Matlab doc. My goal is to compute a FFT of an image (2D) which has missing points (not sampled). I have a list x and y of coordinates of the points ...
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46 views

The peak in frequency spectrum from sampled data is higher than the true amplitude

I am given a task to do sampling on the function $$f(t) = 1.3 \sin(2\pi \cdot 10 \cdot t)$$ with sampling frequency 4 Hz and start at time t_start = 0.0877s, so ...
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1answer
51 views

Relationship between amplitude and sampling rate

I'm loading a signal with librosa in python. With the original sample rate of 22050 Hz, i get the following waveplot: When i choose to resample my signal with the sample rate of 512 Hz, i get the ...
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270 views

How Do I Measure the Time Duration of a Finite Length Discrete Sequence?

Assume I have a five-sample time-domain sequence (none of the five samples are zero valued) and the time period between each pair of samples is one second. Measured in seconds, what is the time ...
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22 views

Response time of residual current device and sampling times

The table below is from this document: Schneider RCD When the maximum response of the device is 40 mS, does it measure current doing RMS or peak detection? The document does not explicitly say it. ...
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26 views

Impulse invariance vs. DT representation of a CT system: Where is the inconsistency?

Suppose you have a continuous-time (CT) system $h_c(t)$, bandlimited to $B$. Your goal is to represent the system as a discrete-time (DT) system $h[n]$, sampled at $f_s \leq 2 B$. Clearly $h[n]$ won't ...
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251 views

What can be meant by “bandlimited”?

This question was a source of disagreement on whether "amplitude aliasing" can occur for a signal bandlimited to below half the sampling frequency. The question was closed before the ...
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420 views

Amplitude modulation vs sampling rate? [closed]

As a sampled tone's frequency nears $f_s / 2$, amplitude modulation grows apparent: ("Actual" curve in grey; blue is what we get if taking samples (dots) "at face value"). This is ...
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54 views

Coherent Sampling vs Windowing for 50/60 applications

Let's say I need to sample 50/60 Hz signals to find RMS. I can use for example 1kHz sampling frequency. That means 100ms sampling is 5 cycles of 50Hz and 6 cycles for 60 Hz. That's coherent sampling. ...
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579 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 ...
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1answer
101 views

Aliasing at $f_0 + kf_s$

In this question, it has been proved that $x(t) = \sin(2\pi f_0 t)$ and $x_k(t) = \sin(2\pi (f_0 + k f_s) t)$ have the same sample points. So sinusoids with frequencies $f_0$ and $f_0 + kf_s$ will ...
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Sampling frequency error in OFDM [duplicate]

If the sampling rates at receiver and at transmitter are different, there will be ICI. However I don't find any practical technique to estimate and compensate this kind of error. Is it true that we ...
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1answer
64 views

Inverting a sampled system

I'm doing some self-study for an upcoming exam and came across the following question: My first idea to solve it was using the bilinear transform to get some approximation of $H(Z)$ (or just using ...
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fo we need RMS in SNDR of harmonic distortion

In my system we have the following. $$V_{in}=1+\cos(2\pi 900,000)$$ $$V_{sample}=V_{in}-0.01V_{in}^2$$ $$V_{noise}=200 \times 10^{-6}V$$ After the input i get in $V_{sample}$ the following ...
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50 views

why we do multiple aliasing of high order harmonics

the general rule for aliasing. If my sampling frequency is Fs=800Mhz signal frequency =120Mhz. for the 4th harmonics 480MHz its 80MHz above nyquist frequency(400Mhz) thus its mirrored 80MhZ back to ...
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30 views

Goertzel filter for non-equidistant sampling

We have a sensor that reports a new value asynchronously only when the value changes. Therefore, we receive samples at arbitrary time stamps. We basically receive value + timestamp of the measurement ...
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48 views

Why negative harmonics copies in sampling

i have a signal of 120Mhz and sampling at 800Mhz. we look at the region of fs/2=400MHz so obvios we have harmonics of the fundamental which is 240 360. But in the document i see that there is another ...
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90 views

Multiplying signals in discrete-time vs continuous-time

Given two discrete-time signals $a[n]$, $b[n]$ and its product $c[n]=a[n] b[n]$. The ideally interpolated, continuous-time version of $c[n]$ is \begin{align} c_1(t)&=\sum_{n=-\infty}^{\infty} a[n] ...
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73 views

Sampling Dirac function and a DC signal

Can we sample the Dirac function? $$ x(t) = \delta(t) $$ Can we sample a DC signal? $$ x(t) = 1$$ I think that we can't sample $x(t) = 1$ because the Fourier Transform of $x(t) = 1$ is $2\pi \delta(...
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3answers
128 views

Downsampling vs. ADC with lower Sample-Rate

I would like to know in general where the advantages and disadvantages are: Downsampling of a high sampled continuous analog signal in FPGA or µC and Direct use of a lower sampling rate, i.e. using ...
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64 views

What is the multiplication rate in FIR filter

Consider a system implementing a rational sampling rate change by 5/7: for this, we cascade upsampler by 5, a lowpass filter with cutoff frequency pi/7 and a downsampler by 7. The lowpass filter is a ...
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2answers
128 views

OFDM sampling frequency offset

how the 4G LTE Or 5G NR OFDM measures and corrects the sampling frequency offset? if there is an algorithm using matlab please help
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Showing that filtering a signal with bandwidth B with a brickwall filter of bandwidth W>B has no effect in time domain

The time-domain representation of $G(f) H(f)$, where $H(f)$ is an ideal brickwall filter of bandwidth $1/(2T)$ is: $$ \int g(\tau) \operatorname{sinc}\left(\frac{t-\tau}{T}\right) d\tau $$ I want to ...

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