Questions tagged [nyquist]
The nyquist tag has no usage guidance.
182
questions
3
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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 ...
1
vote
2answers
83 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
vote
1answer
32 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
votes
1answer
28 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
54 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
votes
1answer
61 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
100 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
30 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
votes
2answers
133 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
votes
0answers
54 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
33 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
...
0
votes
1answer
22 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
votes
2answers
41 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
votes
2answers
186 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 ...
1
vote
2answers
160 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
vote
1answer
126 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
votes
2answers
181 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
votes
4answers
1k 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
votes
1answer
113 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
votes
3answers
414 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:
$$\begin{align}y_m ...
2
votes
1answer
300 views
Shannon-Nyquist theorem reconstruct 1Hz sine wave from 2 samples
Lets say I want to set the minimal sampling rate to reconstruct a 1Hz sine wave, according to the Nyquist-Shannon theorem that states that the maximum recoverable frequency is Fs/2 i.e. we must sample ...
1
vote
3answers
544 views
Why is the high-pass filter result in a discrete wavelet transform (DWT) downsampled?
From Wikipedia's description of the Discrete Wavelet Transform, a signal yields a set of:
approximation coefficients (low-pass: by averaging + downsampling)
detail coefficients (high-pass: convolving ...
0
votes
1answer
49 views
Nyquist Frequency on semi-unevenly sampled data
I have a data set that has 'kind of' constant sampling rate - it switches between 1 min and 2 min. About 70% of the times, samples are taken every 1 minute, and about 30%, samples are taken every 2 ...
-1
votes
1answer
40 views
Effect of Nyquist frequency on Fourier transformed data
Upper plot is the original data's plot, and the bottom plot is Fourier transformed data. For the bottom plot, x-axis is the frequency and y-axis is the amplitude. I don't understand the weird behavior ...
1
vote
1answer
555 views
Nyquist Maximum data rate formula for PCM
The Nyquist maximum data rate formula for a binary PCM is given by
$$C = 2B\log_2L$$
I'm not very sure what "$B$" is here. Is it the bandwidth of the signal being sampled or is it the channel ...
1
vote
1answer
66 views
Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$
I'm asked to sample the signal
$$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
58 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
vote
0answers
119 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
votes
0answers
62 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 = ...
0
votes
0answers
21 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
vote
2answers
60 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
votes
1answer
527 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
votes
2answers
61 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
votes
1answer
93 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
votes
0answers
47 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
vote
1answer
90 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
vote
2answers
100 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
vote
1answer
89 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 ...
1
vote
1answer
50 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
305 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
514 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 $\...
1
vote
0answers
76 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
votes
1answer
130 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
votes
1answer
63 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
votes
1answer
49 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
votes
1answer
31 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
votes
2answers
482 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
vote
1answer
123 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 ...
1
vote
1answer
127 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
vote
1answer
913 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 ...
