Questions tagged [nyquist]
The nyquist tag has no usage guidance.
171
questions
0
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34 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 ...
-1
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2answers
47 views
Derivation of Nyquist Frequency and Sampling Theorem
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 ...
1
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2answers
62 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 ...
0
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1answer
40 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
42 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 ...
7
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4answers
834 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
63 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
390 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:
$$\begin{align}y_m ...
2
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1answer
160 views
Shannon-Nyquist theorem reconstruct 1Hz sine wave from 2 samples
Lets say I want to set the minimal sampling rate to reconstruct a 1Hz sine wave, according to the Nyquist-Shannon theorem that states that the maximum recoverable frequency is Fs/2 i.e. we must sample ...
1
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3answers
219 views
Why is the high-pass filter result in a discrete wavelet transform (DWT) downsampled?
From Wikipedia's description of the Discrete Wavelet Transform, a signal yields a set of:
approximation coefficients (low-pass: by averaging + downsampling)
detail coefficients (high-pass: convolving ...
0
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1answer
30 views
Nyquist Frequency on semi-unevenly sampled data
I have a data set that has 'kind of' constant sampling rate - it switches between 1 min and 2 min. About 70% of the times, samples are taken every 1 minute, and about 30%, samples are taken every 2 ...
-1
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1answer
38 views
Effect of Nyquist frequency on Fourier transformed data
Upper plot is the original data's plot, and the bottom plot is Fourier transformed data. For the bottom plot, x-axis is the frequency and y-axis is the amplitude. I don't understand the weird behavior ...
1
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1answer
95 views
Nyquist Maximum data rate formula for PCM
The Nyquist maximum data rate formula for a binary PCM is given by
$$C = 2B\log_2L$$
I'm not very sure what "$B$" is here. Is it the bandwidth of the signal being sampled or is it the channel ...
1
vote
1answer
43 views
Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$
I'm asked to sample the signal
$$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
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2answers
56 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 ...
1
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0answers
76 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 ...
0
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0answers
46 views
Practical Signal Processing by Mark Owen Exercise 2.1. and 2.2
The following exercises don't have answers in Practical Signal Processing by Mark Owen. What is the author looking for here? A mathematical proof?
2.1 A cosine wave of frequency f is sampled at $t = ...
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0answers
19 views
relation between Nyquist sampling theory and regression
Regression is mainly about estimating a function when only a finite number of samples of the function are available. Theories usually care about asymptotic performance as the number of samples tends ...
1
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2answers
47 views
What exactly is captured in a Sample of the Nyquist-Theorem variety?
I'm new to DSP and was thinking of sampling in the traditional music creation way, in that you capture a sound and play it back, warp it, etc., but when I thought about the Nyquist theorem, I realized ...
2
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1answer
243 views
Nyquist Plot for transfer functions with poles at the origin
I'm learning Nyquist plots and something has been seriously bugging me when treating poles or zeros in the origin. Nyquist plots obtains information based on the argument principle which states
"If f(...
0
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2answers
54 views
How to select the sampling frequency when the input signal frequency is not known
I am trying to observe the noise produced by UPS present in our lab, under no load (a normal running condition when its power is on). As I don't know its frequency range, I have randomly chosen 4 ...
0
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1answer
56 views
Amplitude Response at greater than half the sampling frequency
I am hoping to clear up some confusion I have. In a lab I am taking, we analyzed the amplitude response of a simple system. We found that as we increased the input signal frequency to greater than ...
0
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0answers
37 views
Minimum sample frequency that allows reconstruction of information signal but VIOLATES Nyquist?
Say in the frequency spectrum, you have an information signal between (-100, 100) Hz, and a noise signal between (-700, -500) and between (500, 700) Hz. What is the minimum possible sample frequency ...
1
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1answer
72 views
Nyquist frequency , sampling distance
I have few questions I tried to solve regarding nyquist theorem, and I would like to see your opinion if I'm doing it correctly?(one I know the answer second one not sure).
1.Let $f(x)$ and $g(x)$ be ...
1
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2answers
86 views
Nyquist sampling
I know that if $f_\mathrm{m}$ is the "Nyquist frequency" (max frequency) and $f_\mathrm{s}$ sampling rate then $f_\mathrm{s}>2f_\mathrm{m}$.
Am I correct so far?
I have a signal $x(t)$ with max ...
1
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1answer
83 views
Do Nyquist samples have the same sum as the integral of the signal?
Assume I sample a signal according to the Nyquist criterion. Then I perform a simple summation / integral over a linearly interpolated signal. Is this equivalent to the integral over the continuous ...
0
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0answers
33 views
Why are patterns repeated in the frequency-power graph of a periodic signal?
The original question was posted here.
I have a signal, which I'd like to treat as a non-continuous function now, let it be $signal(t)$. It looks like this:
Zoomed in a bit:
I create a Lomb-Scargle ...
1
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1answer
48 views
Nyquist Rate (Sampling Frequency) for $ {f}^{2} \left( x, y \right) $
We are given that $f(x,y)$ is highest frequency is $\omega$ what will be the frequency sample rate if we want to restore the function of the form $g(x,y)=f^2(x,y)$
Would it be correct to say that ...
2
votes
2answers
191 views
Why does a higher sampling frequency mess up my bandpass filter?
I was designing a bandpass filter in python using some of the scipy.signal modules.
I am plotting the frequency response of my filter to verify that my desired frequency is in the passband. However, ...
0
votes
1answer
400 views
Calculate bandwidth of a signal for Nyquist–Shannon sampling theorem
I have to calculate the minimum sampling frequency for the Nyquist–Shannon sampling theorem which is Fc > 2*B, where B is the signal bandwidth.
I have this signals: $\text{sinc}^5(t/2 - 4)$ and $\...
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0answers
62 views
Proving Nyquist Sampling theorem for strictly bandlimited signals
I understand that the Nyquist sampling theorem dictates that the minimum sampling frequency, $f_s$, be s.t. $f_s > 2B$, where $ B $, is the bandwidth of the signal. I have read the explanation for ...
0
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1answer
96 views
Effective Nyquist frequency / signal resolution for overlapping time averaged signal samples
Say that I have a continuous signal. If I sample the signal at sampling rate f_sample, then the highest signal frequency that I can resolve without worrying about ...
0
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1answer
57 views
What does the frequency band mean when it comes to finding aliases?
The time signal which i'm trying to find the aliases for is:
$$x:{\mathbb R}\rightarrow {\mathbb R}\\\ x(t)=\cos(50t) +2\cos(70t).$$
If the sample period is $T_s = \frac{\pi}{60}$ then according ...
0
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1answer
41 views
Number of discrete samples required for the longest wavelength
I am trying to understand the effect of the critical Nyquist frequency when applying the Goertzel algorithm for estimating the power spectrum of a discrete signal. (Goertzel doesn't really matter, ...
0
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1answer
27 views
Frequency spectra of a sampled process
I have a process $X$ with frequency spectra
I sample this process with sampling frequency $f_s = 2$.
What will the frequency spectra $R_z(f)$ of the sampled process $Z$ look like? I realize that ...
0
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2answers
270 views
Higher order harmonics during sampling
I am studying about the sampling theorem in conjunction for ADC. I got little confused while reading about aliased frequencies. I see that as per the Nyquist theorem, the sampling frequency (fs) ...
1
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1answer
98 views
Is it possible to lose half the samples, and yet see the full spectrogram as the original signal?
Consider an speech audio signal sampled at 16,000 samples per second. Plot its spctrogram.
If we delete every other sample from input signal, we get y[n] = x[2n] for all n.
It seems that if we plot ...
0
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1answer
94 views
Follow up question regarding: “Complex sampling can break Nyquist?”
I'm having some trouble understanding the sample rate limitations when considering a complex baseband signal.
I understand (based on the linked SE questions below), the either (1) physically ...
1
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1answer
426 views
Minimum Channel Bandwidth for PCM
Please check if my answer to GATE IN 2010 question 11.20 is correct/can be improved upon.
So, every $\frac{1}{f_s}$ sec, a sample is taken. The signal amplitude is quantized into $2^n$ levels such ...
0
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1answer
1k views
Passband vs Baseband Bandwidth
Bandwidth is the difference between the upper and lower frequencies in
a continuous band of frequencies. A key characteristic of bandwidth is
that any band of a given width can carry the same ...
0
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1answer
50 views
Nyquist Stability Test
Currently I'm learning about Nyquist Stability Test and I'm few days stuck on one thing and I don't understand that so I wanted look here for help.
Given is transfer function $K\frac{2s-11}{s(s^2+s+...
0
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1answer
58 views
Nyquist Theorem adding two same frequency near to Nyquist Frequency with phase shift
This is my first question on this platform. Sorry if I made mistakes.
What happens if we add two or more same frequency signals near to Nyquist Frequency with phase shift and sample them?
For ...
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2answers
36 views
Discrepancy in stability conditions when calculating via RH criterion and Nyquist criteria
I have the following open loop transfer function for a unity feedback system.
$$G(s)=\frac{K(s+20)^2}{s^3}$$
1.When using RH criterion it can be easily proved that the closed loop transfer function ...
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4answers
174 views
Nyquist Theorem - Why unique frequencies upto Fs/2 and not Fs? f+Fs is start of Aliasing
If any frequency, f, displays an alias at f + Fs, This shows that unique frequencies have a range of Fs. Why does Nyquist theorem say that actually there is only half of this with unique frequencies ...
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2answers
55 views
Digital Filter Design using difference equations
I am reading a chapter on digital filter design from analog filter design using difference equations. What they do first of all is that they map $s$ (Laplace variable) to $z$ ($z$-transform) by the ...
4
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1answer
507 views
What is Faster Than Nyquist signaling?
Faster than Nyquist signaling is used to improve the spectral efficiency by reducing the time spacing (relaxing the orthogonality constraint) to pack more data in the same channel while tolerating a ...
0
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1answer
360 views
Applying Nyquist's sampling theorem to a real signal
I'm struggling to fully understand the Nyquist-Shannon sampling theorem.
For some message input signal $m(t)$ that is infinite in time (i.e. is not identically $0$ for any interval $t_1<t<\...
0
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2answers
74 views
Is it possible to discretely sample the function
I had a few questions on sampling(I'm quite new witht his), I tried to answer them, I think that I did the first one correct , but not sure about the 2 other:
.
given the next functions,Is it possible ...
0
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2answers
103 views
How do ADC/DACs deal with out of sync signals near Nyquist frequency?
Let's say a converter is sampling continuously at 48 kHz and the incoming waveform is a sine wave at 24 kHz... How does it faithfully recreate the waveform if the samples are taken at points that are ...
0
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2answers
100 views
Understanding the conditions for recovering a discrete time signal through sampling
So, we had a very brief introduction to the Nyquist-Shannon sampling theorem (the discrete time version).
While discussing this, we have seen that multiplying a discrete time signal $x[n]$ by an ...
