Questions tagged [nyquist]

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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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308 views

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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2answers
88 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
135 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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1answer
38 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
603 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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2answers
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
180 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
60 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
232 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
166 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
72 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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2answers
765 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
555 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
482 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
345 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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2answers
261 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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2answers
702 views

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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3answers
563 views

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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2answers
160 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
128 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
225 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
245 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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1answer
2k 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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1answer
125 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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2answers
2k views

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
49 views

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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6answers
26k views

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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1answer
36 views

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
260 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
240 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
336 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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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
3k 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
2k views

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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2answers
500 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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2answers
623 views

Nyquist frequency - Sampling theory

If a signal contains frequencies from $500$ to $1000\textrm{ Hz}$, what is the Nyquist sampling frequency, $2$ times $500$ or $2$ times $1000$? Twice the highest frequency of the signal, or twice ...
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2answers
1k views

Determine maximum frequency of input signal to make system LTI

This is question 4.26 from the third edition of Alan Oppenheim's textbook "Discrete-time Signal Processing". It is stated as follows: Firstly, the answer is the input signal should be bandlimited to ...
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1answer
505 views

Digital signal and frequency analysis

I am generating a digital signal with software. I have defined the vector $$[0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0] $$ and my sampling rate is 8 million per second. The frequency spectrum is ...
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2answers
63 views

Minimum recording time for a signal

I am familiar with both Nyquist frequency and Nyquist rate. What I cannot seem to find information on is the minimum time necessary to detect a signal. In my use case I am using a multiplexer to ...
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3answers
402 views

Signal values we will 'miss' between sampling instances during sampling of band limited signals

According to the Nyquist–Shannon sampling theorem, any continuous time signal with a bandwidth $B$ smaller than Nyquist frequency $f_N=f_s/2$ (with $f_s$ the sampling frequency), which is sampled at ...
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5answers
944 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
239 views

Nyquist rate determination and oversampling [duplicate]

I'm new to this. I'm using ShannonGui to generate a sine wave with a $1\textrm{ Hz}$ signal frequency. From what I can tell to determine the Nyquist rate I need to double the highest frequency, since ...
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1answer
804 views

Properties of root raised cosine filter

In communication systems, the transmitted signal is often passed through a root-raised cosine filter to avoid, in textbook language, intersymbol interference (ISI). An identical filter at the receiver ...
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1answer
709 views

Convolving a discrete time sequence with a continuous-time filter?

I am a newbie to DSP, and have what seems to me a fundamental question. I have a discrete-time sequence $g[n]$ of length $N$. I am supposed to pass this signal through a root-raised cosine filter $...
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3answers
393 views

Time Domain Example of Nyquist/Shannon?

I looked at an old thread, Nyquist Frequency Phase Shift, but was left wondering still about oversampling. I learned Shannon 40 years ago, then worked 30 years in (s/w) engineering, but now retired I ...
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1answer
766 views

Sampling theory and frequency spacing

If a CT signal $x(t)$ is sampled for one ($1$) second and $4096$ samples are generated: Isn't the highest frequency that can be sampled without aliasing ($4096/2$) $2048\textrm{ Hz}$? If a $4096$ ...
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1answer
434 views

Elegant way of calculating minimal sampling frequency without aliasing for annoying signals

Given a symmetric Fourier transform with finite support as below, there's an algorithmic procedure to determine the minimal frequency for sampling without aliasing: Find an integer $L>1$ ...
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1answer
229 views

Given a continuous time signal, does the minimum Nyquist sampling rate depend on the choice of the set of basis functions?

This is my first question on a StackExchange. When the basis functions to represent a signal are chosen as $e^{j\omega t}$ such as in a continuous-time Fourier transform then the sample rate $f_\...
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1answer
227 views

Determining the Nyquist rate of signals added and multiplied together

Suppose I have a signal in the frequency domain $x(\omega)$. Suppose I know that its Nyquist rate is $\omega_0$ (and let $\omega_m$ be the its maximum frequency). I need to get the Nyquist rate of $...