Questions tagged [nyquist]
The nyquist tag has no usage guidance.
202
questions
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1answer
48 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 ...
0
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1answer
26 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 ...
1
vote
2answers
53 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 ...
0
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0answers
33 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-...
0
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2answers
72 views
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 $k=0,1,2.., N-1$
...
1
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3answers
56 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 ...
3
votes
1answer
102 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
$$s(t)=\sum_{m=-\infty}^{\infty}\text{Re}\{a_m\}h(t-mT)+j\...
0
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2answers
61 views
When do we divide by $2\pi$ while solving Nyquist problems?
I slightly lost the tempo in the course for a couple of days, so I apologies for the noob question if seemed so.
Why do we divide by $2\pi$ in Nyquist problems sometimes and sometimes not? I saw there ...
0
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5answers
134 views
Positive and negative frequencies in DFT due to frequency folding, or due to negatively indexed frequencies?
When I look for the cause of the mirroring of frequencies in DFT output, I get two types of explanations:
The first one which says the frequencies are mirrored because of the complex exponential ...
0
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1answer
17 views
What is an example of using aliasing to your advantage when recovering an input signal?
Suppose you have an arbitrary analog input signal $x_a(t)$ guaranteed to have frequencies within a bandwidth $[f_1,f_2]$ Hz.
Suppose your sampling frequency $F_s$Hz, and sample $x_a(t)$ to produce $...
0
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1answer
37 views
Multichannel sampling with aliasing
if i have 2 sensors, sensor1 and sensor2, that sample a signal on complementary points so that sensor2 samples always between sensor1s sampling points. can I achieve the doubled sampling rate with the ...
2
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1answer
45 views
Cross Domain Equivalent to Nyquist Sampling Theorem?
In attempting to answer this question by @Oliver here: What characterizies 'causality' for a finite FFT? I have considered the minimum requirement to avoid time domain aliasing in the Discrete ...
1
vote
3answers
72 views
Nyquist Rate of cosine modulated function
Here's my understanding:
$$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 + \...
1
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2answers
112 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.
...
0
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1answer
44 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 ...
-1
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1answer
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 ...
1
vote
3answers
77 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 ...
1
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0answers
76 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 ...
0
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3answers
44 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 ...
0
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1answer
57 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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23 views
How to estimate the frequency of a feature in an image?
I have a background in the 1-D signal analysis but I am totally new to image analysis. I would appreciate any help.
Given the following original image and the downsampled image, as you could see, ...
4
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5answers
205 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 ...
3
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5answers
2k views
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 ...
1
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2answers
100 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 ...
1
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1answer
83 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 ...
0
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1answer
60 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 ...
2
votes
2answers
98 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 ...
0
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1answer
82 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) ...
2
votes
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?
0
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0answers
54 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 ...
9
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3answers
178 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 '...
2
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0answers
78 views
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 ...
1
vote
1answer
39 views
Sampling a signal with varying frequency
Question
I'm trying to figure out the sampling rate for my ADC to sample essentially signal essentially of the form:
$$y(t) = \sin(\max(t, \omega_{max})\times t) + n$$
where $n$ is noise.
Context
This ...
0
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1answer
37 views
Perform frequency analysis on grouped pulses
I have a system which consists of individual pulses grouped in trains.
The trains have a frequency of 10 Hz, with a timing precision of sub ns.
The pulses have a frequency of 2.2 MHz with a timing ...
0
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2answers
58 views
Passing a sampled signal through a filter
I was wondering why is it wrong to use a band-pass filter on a sampled signal?
If the signal we want to sample has frequencies up to fmax, we sample it with frequency fs = 2fmax (so that Nyquist ...
0
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2answers
459 views
Derivation of Nyquist Frequency and Sampling Theorem [closed]
I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
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2answers
427 views
Nyquist noiseless channel capacity; how can bit-rate be two times the bandwidth?
I'm confused by the Nyquist channel capacity formula. How can channel maximum capacity approach double the bandwidth.
$C = 2\times BW \times log_{2}(L)$ bits/sec
The way it was explained to me ...
1
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1answer
288 views
Conclusions of sampling around Nyquist Rate
I'm trying to understand some results of playing around with sampling around a signal's Nyquist sampling rate. For my example, I'm sampling a $B=5\mathrm{Hz}$ wave over a 1 second period.
In the ...
0
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2answers
483 views
Minimum sample frequency of IMU accelerometer and gyroscope
I was wondering how I would justify a sampling rate of 125 Hz for accelerometer and gyroscope data from wearable sensors. This is a rate used in a lot of biomechanics literature, but I can't seem to ...
9
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4answers
2k views
reconstruction filter - How does it actually work?
I'm trying to form my own understanding on the religious war around using 192kHz as a sampling rate for playback (the Internet seems to have a wealth of material on both sides). I'm struggling to ...
0
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1answer
170 views
One sided frequency spectrum (Matlab vs. Origin)
There are a lot of queries on fft frequency all over the web. I guess the following point not discussed anywhere explicitly. Hope someone can provide an insight here.
If we have and even number of ...
4
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3answers
472 views
Absolute convergence of periodic sinc interpolation
An $N$-periodic complex discrete-time sequence $[x_0, \dots, x_{N-1}]$ can be resampled to an $M$-periodic sequence $[y_0, \dots, y_{M-1}]$ with $M>N$, using sinc interpolation:
$$\begin{align}y_m ...
2
votes
1answer
546 views
Shannon-Nyquist theorem reconstruct 1Hz sine wave from 2 samples
Lets say I want to set the minimal sampling rate to reconstruct a 1Hz sine wave, according to the Nyquist-Shannon theorem that states that the maximum recoverable frequency is Fs/2 i.e. we must sample ...
1
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3answers
922 views
Why is the high-pass filter result in a discrete wavelet transform (DWT) downsampled?
From Wikipedia's description of the Discrete Wavelet Transform, a signal yields a set of:
approximation coefficients (low-pass: by averaging + downsampling)
detail coefficients (high-pass: convolving ...
0
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1answer
66 views
Nyquist Frequency on semi-unevenly sampled data
I have a data set that has 'kind of' constant sampling rate - it switches between 1 min and 2 min. About 70% of the times, samples are taken every 1 minute, and about 30%, samples are taken every 2 ...
-1
votes
1answer
47 views
Effect of Nyquist frequency on Fourier transformed data
Upper plot is the original data's plot, and the bottom plot is Fourier transformed data. For the bottom plot, x-axis is the frequency and y-axis is the amplitude. I don't understand the weird behavior ...
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1answer
1k views
Nyquist Maximum data rate formula for PCM
The Nyquist maximum data rate formula for a binary PCM is given by
$$C = 2B\log_2L$$
I'm not very sure what "$B$" is here. Is it the bandwidth of the signal being sampled or is it the channel ...
1
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1answer
83 views
Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$
I'm asked to sample the signal
$$x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$$
with sampling frequency $F_s = 1000$ and plot the magnitude spectrum for the resulting sampled signal.
My thinking is ...
2
votes
2answers
66 views
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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0answers
166 views
Aliasing from downsampling and Nyquist
In a book Conceptual Wavelets in Digital Signal Processing by Lee Fugal 2009 on page 246 the author talks about aliasing present in DWT subbands due to downsampling by 2 and states:
Recall from DSP ...
