Questions tagged [nyquist]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2
votes
0answers
35 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
29 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
17 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
36 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
54 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
71 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
votes
1answer
47 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
51 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
885 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
64 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
394 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
181 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
268 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
35 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
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
vote
1answer
152 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
45 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
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
vote
0answers
86 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
51 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
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
vote
2answers
50 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
288 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
55 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
64 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
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
vote
1answer
75 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
88 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
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
votes
0answers
35 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
vote
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
203 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
430 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
64 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
101 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
61 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
43 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
28 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
301 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
100 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
votes
1answer
101 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
480 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
votes
1answer
2k 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
votes
1answer
54 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
votes
1answer
60 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 ...
1
vote
2answers
40 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 ...
-1
votes
4answers
188 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 ...
-1
votes
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
votes
1answer
568 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
votes
1answer
384 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<\...