Questions tagged [nyquist]

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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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115 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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108 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
1k 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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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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1answer
1k 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 ...
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1answer
915 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
105 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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187 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 ...
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2answers
363 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 ...
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1answer
117 views

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 rectangular ...
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2k 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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40 views

Conditions for representing (perfectly) an analog signal as a digital signal

Consider the following cases: Sampling with a frequency of the "signal's central frequency" Sampling a BP signal with twice the frequency of the signal BW. Sampling an LP signal with the highest ...
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2answers
90 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:...
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749 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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2answers
164 views

Determine minimum sample rate for continuous sinusoid

Consider a signal $$ x(t) = \cos(175\pi t) $$ which is sampled to produce discrete time signal $$ x[n] = x(nT_s) $$ The fundamental period of $x[n]$ is $$ N_0 = 7 $$ Given this, what is the smallest ...
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870 views

Compensation for Irregular Time Step for DFT (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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2answers
108 views

Sampling theory

Imagine I have a 1 kHz sine wave with very low noise. (Assume a signal generator output with 1v peak to peak clean signal). I am using an ADC to sample this signal. Take the following cases: Sample ...
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1answer
373 views

Does the Nyquist Sampling Theorem hold for a triangular wave?

Does the Nyquist Sampling theorem hold for a triangular wave produced by a function generator? For example, a triangular wave with a frequency of 15 Hz sampled at 60 Hz, 180 Hz and 15000 Hz.
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41 views

Highest frequency of collected force signal [closed]

I have collected force at the footrest during paddling at two occasions. During one occasion I accidently collected the force signals at 150 Hz instead of 1500 Hz. During the other time the data was ...
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2answers
1k views

Minimum possible sampling frequency for continuous time signal

A continuous-time signal $x(t)$ has the magnitude spectrum $\lvert X(F)\rvert$ shown in Figure 6. The signal is sampled to obtain $x(n)$ using the sampling frequency $F_s$. Determine the minimum ...
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1k views

Understanding Nyquist rate

I'm starting to learn signal processing, and am trying to understand Nyquist rate a bit better. From what I understand, if I sample at a rate > Nyquist rate I'm supposed to have no data loss. I'm ...
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1answer
343 views

Smallest sampling frequency to fully reconstruct a signal

Given the spectrum of analog signal $x_a(t)$ which is imaginary and band-limited, find the lowest sampling frequency to be able to reconstruct $x_a(t)$ from samples $x[n]$. My attempt: Bandwidth of ...
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2answers
68 views

Sampling below Nyqust Frequency

My understanding of Nyquist's theorem is that you need to sample at a rate that's twice the bandwidth of a signal to fully recover it. What exactly does the bandwidth mean in this context and what ...
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2answers
329 views

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
284 views

Lock-In Amplifier Sampling Rate

For a digital lock-in amplifier (synchronous demodulator) I have a sinusoidal reference signal in the range of 10-15kHz, the amplitude and phase I want to observe changes very slowly <10Hz. My ...
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1answer
124 views

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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1k views

Nyquist sampling rate

Please i need help in understanding Nyquist sampling rate. What is the implication of sampling at a lower rate than the Nyquist rate, at exactly the Nyquist rate and at a rate higher than the Nyquist ...
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1answer
1k views

Find the nyquist sampling rate?

I have a signal $x(t)$ for which I want to find the Nyquist frequency : $$ x(t) = \frac{\sin{\pi t/2}}{\pi t/2} \ast \sum^\infty_{n=-\infty}\delta(t-10n)$$ I am trying to solve this in the time ...
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1answer
866 views

How does sampling rate impact Discrete-Time Kalman Filter state space modeling assumptions?

Consider a very simple, discrete-time constant position-type model for state updating in a Kalman filter: $$ x_{k+1} = x_k + w_k $$ The Kalman filter will be run with update interval $T_s$ such that ...
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3answers
549 views

Am I violating Nyquist?

I am using a DAC to transmit 2 different voltage levels. High and low. At 1Gsps. There is no carrier wave or anything. These are just raw 0 and 1 time samples going across a wire. On my ADC I am ...
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354 views

Random (Over) Sampling signal and perfect Reconstruction in Nyquist form?

Imagine we have band limited signal with bandwidth of $B$, so the required Nyquist rate would be $f_{nyq}>2B$ that is oversampled with rates $f_s$ where $f_s = M*f_{nyq}$ and $M$ is random and $M&...
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Does a 20 kHz sine wave sampled at 44.1 kHz need to be reconstituted before playback?

I am interested in building a synthesizer but I am confused about the Nyquist-Shannon Theorem and sampling rates. If I sample a 20 kHz sine wave at 200 kHz and plot the data points, the plot looks ...
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Applying Nyquist theorem to digital vs. analog audio quality

I had a recent conversation with a friend about analog vs. digital recordings. He shared his opinion that music recorded by analog techniques is of superior sound quality to music recorded by digital ...
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202 views

Aliasing in audio

Reading wikipedia to be sure and it says: In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) ...
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1answer
154 views

Stable gain nyquist plot

From Modern Control Engineering 5th Edition page 469 The transfer function of a plant controller by a proportional controller is given by $$G(s) = \frac{K(s+0.5)}{s^3 + s^2 + 1}$$ In the book $G(j\...
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1answer
445 views

Under what conditions do the phase margin and Nyquist criteria give the same results?

When designing feedback systems, I often evaluate stability by thinking about phase margin: the closed loop system $$T(s) = \frac{L(s)}{1+L(s)}$$ is stable if $L(s)$ has positive phase margin, i.e., $...
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1answer
315 views

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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2answers
3k views

Link between DFS, DFT, DTFT

My understanding of DFT is as follows For a signal $x[n]$ of finite-length, the DFT is DFS of the periodic extension, $\tilde{x}[n]$, of that signal $x[n]$ and also another way to view DFT is that it’...
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195 views

Discrete Time Processing of Continuous Time Signals LTI Concept

I wonder if the input signal (CT) violates Shannon-Nyquist Theorem for a given sampling rate, is there any chance for the overall system not to be LTI although discrete time system is LTI? Thanks.
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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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1answer
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Power Line interference with different Sampling frequency

I've been playing around with EEG data from an online database. If the power line interference (PLI) is at 50Hz and sampling frequency is 64Hz, then according to the Nyquist theorem, the 50Hz PLI ...
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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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Estimating the Nyquist rate when simulating data

I want to find the power spectrum $\tilde{Q}(\omega)$ of a quantity $Q(t)$. The values of $Q$ are computed at discrete time steps so I have a series $Q(\Delta t)$, $Q(2 \Delta t)$, ... of values, but ...
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2answers
357 views

Changing the Bandwidth of a signal of fixed Sampling frequency [closed]

If sampling frequency is fixed, how can I generate a frequency domain signal of a particular bandwidth from a time domain signal of dimension $1\times N$? e.g. if $f_s=100\,\text{kHz}$, how can I ...
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1answer
364 views

Reconstruct under sampled signal

I have a signal from a PWM inverter that was sampled at 3,84 kHz. The PWM has a switching frequency of 5 kHz. The pwm signal is feeding an induction motor. If I low-pass filter the PWM signal it ...
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1answer
739 views

what is difference between Alias vs. down sampling? [closed]

could someone help me explain downsampling in the context of Nyquist–Shannon sampling theorem and tell the difference between Aliasing and downsampling.Also is downsampling and undersampling the same ?...
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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
5k views

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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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 ...