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Questions tagged [nyquist]

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1answer
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Sub nyquist sampling, required number of samples for time sparse grouped signals

Question: Does it make sense to perform compressed sampling if the non zero samples are grouped in time? If so, what is the minimal length of the vector x that should be acquired to allow full signal ...
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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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318 views

Stability of open-loop transfer function from its Nyquist plot

I am facing a confusion on understanding system open-loop transfer function stability from its Nyquist plot. According to the formula, for open loop transfer function stability: $$Z=N+P=0$$ where $N$ ...
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1answer
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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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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 ...
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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(...
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4answers
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Nyquist plot interpretation when curve hits the origin

I'm a bit confused about the interpretation of the Nyquist plot when the origin is part of the plot. In this case I'm not even considering closed loops, I'm just looking at the Nyquist Plot of a given ...
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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 ...
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2answers
37 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 ...
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410 views

Why doesn't the sampling theorem work in this case?

In this example, under "Discussion", we can see that the Nyquist sample rate will result in samples with the value zero only. But why is this? I thought the sampling theorem said that if you sample ...
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33 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 ...
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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 ...
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1answer
51 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 ...
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1answer
63 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 ...
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2answers
72 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 ...
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463 views

Nyquist frequency and DC

Im studying the DSP book by Steven W. Smith. On page 41 he covers the Nyquist frequency. He makes up an example by writing the following. ... consider an analog signal composed of frequencies ...
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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 ...
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38 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 ...
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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 ...
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2answers
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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, ...
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1answer
145 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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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 ...
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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 ...
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1answer
40 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, ...
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1answer
26 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 ...
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2answers
132 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) ...
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1answer
81 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 ...
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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 ...
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1answer
145 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 ...
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1answer
585 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 ...
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1answer
40 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+...
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2answers
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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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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
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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 ...
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2answers
3k views

Bandwidth with complex sampling

On the transmit side, I have a 20 MHz carrier frequency carrying a signal with bandwidth of 40 MHz (so 0 Hz to 40 MHz, center at 20 MHz). On the receive side, I have a dual channel ADC with each ...
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1answer
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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 ...
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1answer
195 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<\...
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2answers
69 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 ...
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Invertibility of Room Impulse Response: Reproducing Research Paper

I have been trying to reproduce this paper¹. Few things which are unclear to me. The paper talks about finding whether a given Room Impulse Response(RIR) is invertible or not based on Nyquist plot. ...
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1answer
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Fractional Delay Filters and Cutoff Frequences

I am trying to implement an interpolator for arbitrary sampling rate conversion of a one-dimensional signal (a fractional delay filter). I am aware of the fact that interpolation is in general a ...
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5answers
875 views

Confusion regarding Nyquist Sampling Theorem

The first time Nyquist Theorem was mentioned in class. It stated that we should sample at twice the highest frequency content of the signal. Example: If we wanted to sample $\cos(2 \pi f_0 t)$, the ...
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1answer
621 views

A voice signal is band-limited to 3.3 kHz. What is the Nyquist frequency?

I'm having a some trouble with an assignment I have to do. I don't come from electrical engineering background and would appreciate any help I can get. "A voice signal is band-limited to 3.3 kHz. ...
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If humans can only hear up to 20 kHz frequency sound, why is music audio sampled at 44.1 kHz?

I read in some places that music is mostly sampled at 44.1 kHz whereas we can only hear up to 20 kHz. Why is it?
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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 ...
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2answers
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Root raised cosine pulse shaping filter

What are disadvantages of root raised cosine pulse shaping filter in digital communications and why does it need to be improved? Links: Square Root Raised Cosine Fractionally Delaying Nyquist ...
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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 ...
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1answer
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Distortion of a signal consisting of two periodic components

We have a signal $$x(t)=U_1\cos\omega_1t+U_2\cos\omega_2t$$ whose frequencies are $f_1=100\,\text{Hz}$ and $f_2=600\,\text{Hz}$. This signal is being discretisated in time using unipolar ...
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compensation for irregular timestep for FFT

I want to run a clustering algorithm (svm, knn) on the ferquency spectrum data of a temperature sensor that published at irregular times. Here is the temperature data to take the FFT: I got the ...
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1answer
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Nyquist criterion for zero isi

I am working with the Nyquist criterion for zero ISI when I find something that makes me think that I misunderstood this criterion. What Nyquist says is that to avoid ISI in the sampling we must ...
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2answers
67 views

How to classify filters?

In class, we have defined four types of filters: low-pass, high-pass, band-pass and band-stop. I have understood that in order to classify a filter into one of the fourth, one can use the signals: DC:...