Questions tagged [nyquist]
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Nyquist Frequency and Window Length
The Nyquist theorem states that the sampling rate must be twice the highest frequency to be observed. How does the length of the interval play into this relationship?
The main resource that I found ...
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987 views
Does the Shannon theorem not apply when the amplitude of a wave is changed faster than half the time period of the wave?
Shannon's version of the sampling theorem states that if a function contains frequencies all strictly less than $B$ hertz, then it is completely determined by giving its ordinates at a series of ...
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33 views
Selecting the Nyquist rate for a combination of signals
If several sine waves were combined but each had a separate frequency, for example 10 Hz, 20 Hz and and 30 Hz, what would the required Nyquist rate be for analysis?
From my research, it suggests that ...
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48 views
How to deal with “weird” phase plots in bode diagram when designing a controller
I am trying to design a balance controller for a robot. With MATLAB simulink I arrived at the transfer function between the input and the pitch angle for the robot. I have plotted the bode and Nyquist ...
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Reconstruction of a signal based on non-uniform samples and a well below nyquist sampling rate
I have a set of non-uniform samples that are the following set of data over the course of 1 second:
The rightmost column is in milliseconds, and the first three leftmost columns are each different ...
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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 ...
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37 views
Wavetable and Nyquist: which size do I need?
I was reading this tutorial by the master earlevel, while trying to build some sort of wavetable.
He says First, let’s back up and figure out how long our tables need to be. Recalling that we need to ...
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89 views
Restore real signal from its complex representation if sampled under Nyquist frequency
Assume we have:
real signal: $s(t)$
its analytic representation: $s^+(t) = s(t) + j*H(t)$,
where $H(t)$ - Hilbert transform of $s(t)$
Spectrum of $s^+(t)$ has only positive part, so may be sampled ...
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28 views
What is the between spatial frequency of an image and pixel size of the sensor?
In my lecture notes about the sampling of an image I've written that:
Since pixels have a finite dimension the spatial frequency response is attenuated before the "ideal" Nyquist frequency
...
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1answer
58 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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1answer
119 views
Aliasing below $f_s/2$
phi = exp(linspace(0, log(511), 1024)) - 1
x = cos(2 * pi * phi)
Above will alias, despite peak instantaneous frequency evaluating to ...
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21 views
Interpreting Nyquist Plot for Phase and Gain Margins
I have an open-loop system transfer function given by $G(s) = \frac{K(ABs^2+As+1)(Cs+1)}{s^2A(s(C+D)+1)}$ so I'd expect two poles at the origin and one at $s=\frac{-1}{C+D}$. After using Matlab to ...
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40 views
A basic question regarding frequency analysis of an EEG signal
Assume that an EEG signal is sampled at $f_s = 300$ Hz then a 10000-point segment of it is selected, called $x[n]$. The corresponding 10000-point DFT is then computed and called $X[k]$.
Assume further ...
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1answer
68 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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180 views
Confused on Pulse Filter Bandwidth and Symbol Rate Relation
***Still need help in 2021 - not fully clear still on Jan 20th ***
I am confused about the relation between Sinc and Rectangle transform pair and how that relates the Bandwidth of Pulses, Bandwidth of ...
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2answers
499 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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1answer
75 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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1answer
113 views
Use of the harris-Moerder Nyquist Pulse Shaping Filter
I became aware today through fred harris' excellent presentation at the DSP Online Conference (https://www.dsponlineconference.com/) of the harris-Moerder pulse shaping filter which was published 15 ...
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1answer
339 views
Generating digitized white noise: uniform vs normal sampling
Consider the following two ways of generating noise in the time domain for audio applications:
Generate samples from a uniform distribution [-amplitude, +amplitude]...
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2answers
108 views
Can I sample at Nyquist rate if I know that my samples are taken only at the signal's maxima or minima?
I know that in general the sampling rate, $f_s$, must be greater than twice the highest frequency of the signal, $f$.
If I sample at the Nyquist rate, it can lead to the following:
However, if the ...
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1answer
39 views
SDR Dongle, 2MHz Bandwidth related to Fs but bandwidth range 50-2000 MHz
Having a conceptional issue.
If a SDR dongle has a 2MHz signal bandwidth, but that can be anywhere within the range of 50-2000 MHz, why is the bandwidth only 2 MHz.
The clock must be double the ...
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2answers
171 views
Determine stability of feedback system from open loop transfer function and Nyquist stability criterion gives different results
I'm confused due to the fact that the Nyquist stability criterion and looking at the transfer function doesn't give the same results whether a feedback system is stable or not. When I have the system ...
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40 views
I need help in understanding “Nyquist Criterion” definition
I am researching the split-step parabolic equation and its split step solution as in:
Ozgun, Ozlem & Apaydin, Gokhan & Kuzuoglu, Mustafa & Sevgi, Levent. (2011). PETOOL: MATLAB-based one-...
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Why the Nyquist frequency is 0.5 of Fs, why not 0.55 or 0.65?, brief explanation [duplicate]
This my elaboration of the aliasing issue:
a continuous signal can be represented by factors of :
$e^{(i2{\pi}ft)}$ if we sample this signal then I will get:
$e^{(i2{\pi}fk/N)}$ where $k=0,1,2.., N-1$
...
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3answers
214 views
aliasing in image processing
I know that aliasing occurs when a signal is subsampled. If the sampling rate is lower than twice the max frequency in a signal, aliasing occurs.
How is it in pictures? as far as I know, a sinc-filter ...
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1answer
389 views
Sample rates, Samples per Symbol, and Digital Pulse Shaping
Having some confusion about digital pulse shaping for complex baseband (passband) signals. The complex baseband linear modulation equation is
$$s(t)=\sum_{m=-\infty}^{\infty}\text{Re}\{a_m\}h(t-mT)+j\...
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2answers
75 views
When do we divide by $2\pi$ while solving Nyquist problems?
I slightly lost the tempo in the course for a couple of days, so I apologies for the noob question if seemed so.
Why do we divide by $2\pi$ in Nyquist problems sometimes and sometimes not? I saw there ...
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5answers
344 views
Positive and negative frequencies in DFT due to frequency folding, or due to negatively indexed frequencies?
When I look for the cause of the mirroring of frequencies in DFT output, I get two types of explanations:
The first one which says the frequencies are mirrored because of the complex exponential ...
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1answer
39 views
What is an example of using aliasing to your advantage when recovering an input signal?
Suppose you have an arbitrary analog input signal $x_a(t)$ guaranteed to have frequencies within a bandwidth $[f_1,f_2]$ Hz.
Suppose your sampling frequency $F_s$Hz, and sample $x_a(t)$ to produce $...
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42 views
Multichannel sampling with aliasing
if i have 2 sensors, sensor1 and sensor2, that sample a signal on complementary points so that sensor2 samples always between sensor1s sampling points. can I achieve the doubled sampling rate with the ...
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1answer
56 views
Cross Domain Equivalent to Nyquist Sampling Theorem?
In attempting to answer this question by @Oliver here: What characterizies 'causality' for a finite FFT? I have considered the minimum requirement to avoid time domain aliasing in the Discrete ...
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3answers
98 views
Nyquist Rate of cosine modulated function
Here's my understanding:
$$y(t) = x(t)~ \cos(\Omega_0 t)$$
I take the Fourier transform of y(t) and I get this result:
$$Y(\Omega) = \frac{1}{2}X(\Omega - \Omega_0) + \frac{1}{2}X(\Omega + \...
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2answers
315 views
Sampling and Reconstruction of digital signal in Matlab
I'm trying to write a program in Matlab that samples (using Nyquist theorem) and recovers signal. However, I cannot write sampling part for sum of 2 signal.
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72 views
Whats the difference between spatial and temporal resolution?
Iam trying to understand how super-resolution works. But i think i have not understood correctly the difference between the optical resolution (spatial resolution?) and the resolution i know from a ...
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65 views
creating this famous basic nyquist theory photo
Hello i ha built this code
which create a only one replica of the data,
how can i create the whole photo shown bellow of many cycles as shown bellow?
i read in the internet that zero padding could ...
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3answers
89 views
Upsampling with time offsets
Suppose I have done 4x oversampling for a continuous time signal, but the successive sampling times have a linearly increasing offset. Specifically, the samples with indices {4k; k=0, 1, 2,...} are ...
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93 views
Nyquist-Shannon sampling theorem: implications on matching data records?
I have two data records $R_1$ and $R_2$ with sampling periods $T_1$ and $T_2$, where $T_1$ < $T_2$. These records arise from sampling and filtering two signals to remove any noise (including ...
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70 views
does aliasing occur always if i sample a vibration in real world applications?
I was reading about the aliasing effect and nyquist. I understand that aliasing effect occurs if the sampling rate is lower than twice the maximum frequency in the signal I want to sample.
So I was ...
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1answer
105 views
Nyquist theorem vs sampling theorem vs shannon sampling theorem?
Is there any difference between these three?or these are just three names of same theorem?
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226 views
Reconstructing/interpolating small regions of a bandlimited signal by taking the fewest possible samples
I have a signal which is bandlimited and can be sampled at arbitrary continuous positions. The value at any position is given by an expensive computation. I need to do some further computation on ...
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5answers
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A question about sampling rate of cosine signal
Given $$c(t) = \cos(2\pi\cdot 30 \cdot t) $$
If we sample this signal at the Nyquist rate 60 Hz and at a higher rate of 80 Hz, we get the following:
There is no aliasing as $f$ = 30 Hz is less than ...
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2answers
137 views
anti-alias filter of square pulses
I'm trying to determine whether or not an anti-alias filter is needed for sampling square waves. The goal is to sample square wave pulses from a video detector with an ADC, do some time-domain digital ...
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1answer
253 views
Bandwidth computation for NRZ baseband transmission scheme
In Andrew Tanenbaum's book on Computer Networks, while explaining about bandwidth of a NRZ (Non Return to Zero) baseband transmission scheme, he says the following:
With NRZ, the signal may cycle ...
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1answer
124 views
How do I apply the Nyquist criterion on the following spectrum to see if it satisfies the criterion or not?
I am trying to find out if the pulse in the figure satisfies the Nyquist criterion for a modulation interval T. I'm used to the Nyqusit frequency, but I cannot grasp what the Nyquist criterion is ...
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2answers
204 views
What is the right way to downsample using Fourier method?
I want to know what is the right way to downsample a sampled signal using Fourier transform as the implementation in scipy.signal.resample confuses me.
Reading ...
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1answer
101 views
How to determine sampling frequency for an x(t) signal avoiding aliasing?
The antitransform of the function is given:
$ \hat{x}(f) = \frac{123 + i246\pi f}{246 - 24600 \pi^2 f^2 + i4920\pi f} $
I'm asked to determine which frequency can I sample using the function x(t) ...
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1answer
101 views
Do you really have to always satisfy Nyquist with all signals if your purpose is to reconstruct a signal?
If not, when can you not comply with it?
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84 views
Nyquist sampling theorem / Nyquist - Shannon theorem evaluation over M-PSK
I am trying to simulate an M-PSK Tx-Rx System on Simulink and analyse what the effect of sampling rate reduction would have on it. More, particular I am trying to prove what Nyquist sampling theorem ...
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213 views
Spherical equivalent of Nyquist frequency
Let $\phi$ be a scalar function defined on the surface of a sphere. I have samples of $\phi$ at various locations on the sphere. I want to apply a spherical harmonic transform. I know that $\phi$ is '...
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Nyquist zero ISI criterion for rectanguar pulses in the frequency domain
Nyquist criterion for zero ISI states that in the frequency domain, the replicas of the frequency characteristic of combined:
TX pulse shaping filter - channel - RX pulse shaping filter
must add ...
