Signal Processing

Questions tagged [nyquist]

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51 views

Why are there copies of a signal in the frequency domain? [closed]

I only know about this from images and some videos and articles I've read, but I haven't managed to find an explanation. It only says they exist. This is what I mean: Blue is the frequency domain of ...
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1answer
31 views

Narrowest passband dsp filter one can apply

I was wondering how one would know the narrowest pass-band digital filter one can apply, given the original signal's sampling frequency. For example on a signal coming out from a 14 bit ADC acquiring ...
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4answers
115 views

Why does twice the sampling rate (Nyquist Theorem) seem inadequate?

I was told in my electronics course that "to reproduce a wave, we need to sample it at least twice every period." If I take this to be literally true, then a sine wave with only 2-3 samples ...
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1answer
68 views

Which of the following sampling methods can be used to sample x(t) such that this signal can be uniquely recovered from its samples?

Assuming that a continuous-time $x(t)$ having its frequency content in the frequency band $1612\leq|F|\leq2015(Hz)$ is sampled with the sampling rate $Fs=806$ samples per second. Which of the ...
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3answers
52 views

Why Matlab Spectrogram of slow and rarely sampled signal shows high frequencies

I have a signal, which was measured for 14.4 minutes (= 864 seconds). There are 192 measurements, so one measurement was done in every 4.5 seconds, which results in a 0.22 Hz sampling frequency if I ...
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2answers
226 views

Nyquist frequency isn't working

The situation is that I have a signal with linearly increasing frequency, $$\text{sin}(2\pi\omega(t)t),$$ where $\omega(t)=a+bt$ for some $a$ and $b$, and we constantly sample at one point per second ...
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1answer
34 views

Signal to noise ratio (SNR) of a CW signal

I understand the formula SNR = 6.02N+1.76 for a N-bit ADC which quantizes a modulated tone sampled at twice the BW. I am trying to understand what the same equation would be for a unmodulated CW tones ...
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1answer
62 views

Dealing with normalized cut-off frequencies larger than 1.0

I am trying to create an FIR bandpass filter in python using scipy with the following characteristics: $$f_{c_{low}} = 310\,Hz$$ $$f_{c_{high}} =600\, Hz$$ giving me a bandwidth of: $$Bandwidth = f_{...
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4answers
96 views

DFT after the Nyquist limit

I usually do the DFT using the fft in Matlab. After the Nyquist frequency I don't see any result. Is it possible to perform a dft looking after the Nyquist frequency. I am asking this because I have ...
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1answer
48 views

Optimal sampling frequency

I am working with microcontroller's ADC to sample the data. I know that Nyquist criteria tells us that the sampling frequency should be at least twice the highest frequency, but it might involve ...
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1answer
117 views

Aliasing in Doppler Radar

my book about RADAR says that: If a Continuous wave radar sends a sine wave at frequency $f_T$ to a moving object (at speed V), a frequency $f_R$ is received. Their difference is called Doppler ...
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2answers
97 views

How to reconstruct original signal from sampled signal?

My original signal as f1=2; f2=5; fs=100; Ts=1/fs; t=0:Ts:1; xt=cos(2*pi*f1*t)+cos(2*pi*f2*t); figure plot(t,xt) as shown below figure. and my sampled signal ...
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2answers
60 views

Nyquist Frequency and Window Length

The Nyquist theorem states that the sampling rate must be twice the highest frequency to be observed. How does the length of the interval play into this relationship? The main resource that I found ...
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2answers
1k views

Does the Shannon theorem not apply when the amplitude of a wave is changed faster than half the time period of the wave?

Shannon's version of the sampling theorem states that if a function contains frequencies all strictly less than $B$ hertz, then it is completely determined by giving its ordinates at a series of ...
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1answer
39 views

Selecting the Nyquist rate for a combination of signals

If several sine waves were combined but each had a separate frequency, for example 10 Hz, 20 Hz and and 30 Hz, what would the required Nyquist rate be for analysis? From my research, it suggests that ...
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2answers
93 views

How to deal with "weird" phase plots in bode diagram when designing a controller

I am trying to design a balance controller for a robot. With MATLAB simulink I arrived at the transfer function between the input and the pitch angle for the robot. I have plotted the bode and Nyquist ...
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22 views

Reconstruction of a signal based on non-uniform samples and a well below nyquist sampling rate

I have a set of non-uniform samples that are the following set of data over the course of 1 second: The rightmost column is in milliseconds, and the first three leftmost columns are each different ...
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2answers
2k views

Does the Nyquist frequency of the Cochlear nerve impose the fundamental limit on human hearing?

The bandwidth of human hearing by empirical data is $20 \; Hz$ to $20 \; kHz$. A cochlear implant stimulates the auditory or acoustic or Cochlear nerve directly so that the hearing can be improved in ...
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2answers
47 views

Wavetable and Nyquist: which size do I need?

I was reading this tutorial by the master earlevel, while trying to build some sort of wavetable. He says First, let’s back up and figure out how long our tables need to be. Recalling that we need to ...
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2answers
99 views

Restore real signal from its complex representation if sampled under Nyquist frequency

Assume we have: real signal: $s(t)$ its analytic representation: $s^+(t) = s(t) + j*H(t)$, where $H(t)$ - Hilbert transform of $s(t)$ Spectrum of $s^+(t)$ has only positive part, so may be sampled ...
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0answers
29 views

What is the between spatial frequency of an image and pixel size of the sensor?

In my lecture notes about the sampling of an image I've written that: Since pixels have a finite dimension the spatial frequency response is attenuated before the "ideal" Nyquist frequency ...
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1answer
90 views

What should be IQ sample rate at least?

As i read, IQ sample doesn't need nyquist criteria. What is the mathematical representation of this result? Why IQ sample doesn't need nyquist frequency? I know that can be set to nyquist frequency ...
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1answer
134 views

Aliasing below $f_s/2$

phi = exp(linspace(0, log(511), 1024)) - 1 x = cos(2 * pi * phi) Above will alias, despite peak instantaneous frequency evaluating to ...
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0answers
28 views

Interpreting Nyquist Plot for Phase and Gain Margins

I have an open-loop system transfer function given by $G(s) = \frac{K(ABs^2+As+1)(Cs+1)}{s^2A(s(C+D)+1)}$ so I'd expect two poles at the origin and one at $s=\frac{-1}{C+D}$. After using Matlab to ...
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1answer
41 views

A basic question regarding frequency analysis of an EEG signal

Assume that an EEG signal is sampled at $f_s = 300$ Hz then a 10000-point segment of it is selected, called $x[n]$. The corresponding 10000-point DFT is then computed and called $X[k]$. Assume further ...
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1answer
82 views

Sampling pure tone sine waves [closed]

What would happen if I am using the maximum frequency as the sample rate for sampling a pure tone sine wave? For example, a $10\ \rm kHz$ sampling frequency for a $10\ \rm kHz$ monotone sine wave. ...
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2answers
257 views

Confused on Pulse Filter Bandwidth and Symbol Rate Relation

***Still need help in 2021 - not fully clear still on Jan 20th *** I am confused about the relation between Sinc and Rectangle transform pair and how that relates the Bandwidth of Pulses, Bandwidth of ...
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2answers
670 views

Amplitude modulation vs sampling rate?

As a sampled tone's frequency nears $f_s / 2$, amplitude modulation grows apparent: ("Actual" curve in grey; blue is what we get if taking samples (dots) "at face value"). This is ...
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1answer
78 views

Sampling Dirac function and a DC signal

Can we sample the Dirac function? $$ x(t) = \delta(t) $$ Can we sample a DC signal? $$ x(t) = 1$$ I think that we can't sample $x(t) = 1$ because the Fourier Transform of $x(t) = 1$ is $2\pi \delta(...
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1answer
140 views

Use of the harris-Moerder Nyquist Pulse Shaping Filter

I became aware today through fred harris' excellent presentation at the DSP Online Conference (https://www.dsponlineconference.com/) of the harris-Moerder pulse shaping filter which was published 15 ...
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1answer
695 views

Generating digitized white noise: uniform vs normal sampling

Consider the following two ways of generating noise in the time domain for audio applications: Generate samples from a uniform distribution [-amplitude, +amplitude]...
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2answers
112 views

Can I sample at Nyquist rate if I know that my samples are taken only at the signal's maxima or minima?

I know that in general the sampling rate, $f_s$, must be greater than twice the highest frequency of the signal, $f$. If I sample at the Nyquist rate, it can lead to the following: However, if the ...
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1answer
47 views

SDR Dongle, 2MHz Bandwidth related to Fs but bandwidth range 50-2000 MHz

Having a conceptional issue. If a SDR dongle has a 2MHz signal bandwidth, but that can be anywhere within the range of 50-2000 MHz, why is the bandwidth only 2 MHz. The clock must be double the ...
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2answers
496 views

Determine stability of feedback system from open loop transfer function and Nyquist stability criterion gives different results

I'm confused due to the fact that the Nyquist stability criterion and looking at the transfer function doesn't give the same results whether a feedback system is stable or not. When I have the system ...
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2answers
110 views

Why the Nyquist frequency is 0.5 of Fs, why not 0.55 or 0.65?, brief explanation [duplicate]

This my elaboration of the aliasing issue: a continuous signal can be represented by factors of : $e^{(i2{\pi}ft)}$ if we sample this signal then I will get: $e^{(i2{\pi}fk/N)}$ where $k=0,1,2.., N-1$ ...
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3answers
369 views

aliasing in image processing

I know that aliasing occurs when a signal is subsampled. If the sampling rate is lower than twice the max frequency in a signal, aliasing occurs. How is it in pictures? as far as I know, a sinc-filter ...
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1answer
653 views

Sample rates, Samples per Symbol, and Digital Pulse Shaping

Having some confusion about digital pulse shaping for complex baseband (passband) signals. The complex baseband linear modulation equation is $$s(t)=\sum_{m=-\infty}^{\infty}\text{Re}\{a_m\}h(t-mT)+j\...
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2answers
99 views

When do we divide by $2\pi$ while solving Nyquist problems?

I slightly lost the tempo in the course for a couple of days, so I apologies for the noob question if seemed so. Why do we divide by $2\pi$ in Nyquist problems sometimes and sometimes not? I saw there ...
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5answers
448 views

Positive and negative frequencies in DFT due to frequency folding, or due to negatively indexed frequencies?

When I look for the cause of the mirroring of frequencies in DFT output, I get two types of explanations: The first one which says the frequencies are mirrored because of the complex exponential ...
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1answer
43 views

What is an example of using aliasing to your advantage when recovering an input signal?

Suppose you have an arbitrary analog input signal $x_a(t)$ guaranteed to have frequencies within a bandwidth $[f_1,f_2]$ Hz. Suppose your sampling frequency $F_s$Hz, and sample $x_a(t)$ to produce $...
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1answer
43 views

Multichannel sampling with aliasing

if i have 2 sensors, sensor1 and sensor2, that sample a signal on complementary points so that sensor2 samples always between sensor1s sampling points. can I achieve the doubled sampling rate with the ...
2
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1answer
64 views

Cross Domain Equivalent to Nyquist Sampling Theorem?

In attempting to answer this question by @Oliver here: What characterizies 'causality' for a finite FFT? I have considered the minimum requirement to avoid time domain aliasing in the Discrete ...
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3answers
127 views

Nyquist Rate of cosine modulated function

Here's my understanding: $$y(t) = x(t)~ \cos(\Omega_0 t)$$ I take the Fourier transform of y(t) and I get this result: $$Y(\Omega) = \frac{1}{2}X(\Omega - \Omega_0) + \frac{1}{2}X(\Omega + \...
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2answers
497 views

Sampling and Reconstruction of digital signal in Matlab

I'm trying to write a program in Matlab that samples (using Nyquist theorem) and recovers signal. However, I cannot write sampling part for sum of 2 signal. ...
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1answer
112 views

Whats the difference between spatial and temporal resolution?

Iam trying to understand how super-resolution works. But i think i have not understood correctly the difference between the optical resolution (spatial resolution?) and the resolution i know from a ...
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1answer
66 views

creating this famous basic nyquist theory photo

Hello i ha built this code which create a only one replica of the data, how can i create the whole photo shown bellow of many cycles as shown bellow? i read in the internet that zero padding could ...
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3answers
95 views

Upsampling with time offsets

Suppose I have done 4x oversampling for a continuous time signal, but the successive sampling times have a linearly increasing offset. Specifically, the samples with indices {4k; k=0, 1, 2,...} are ...
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0answers
98 views

Nyquist-Shannon sampling theorem: implications on matching data records?

I have two data records $R_1$ and $R_2$ with sampling periods $T_1$ and $T_2$, where $T_1$ < $T_2$. These records arise from sampling and filtering two signals to remove any noise (including ...
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3answers
91 views

does aliasing occur always if i sample a vibration in real world applications?

I was reading about the aliasing effect and nyquist. I understand that aliasing effect occurs if the sampling rate is lower than twice the maximum frequency in the signal I want to sample. So I was ...
0
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1answer
167 views

Nyquist theorem vs sampling theorem vs shannon sampling theorem?

Is there any difference between these three?or these are just three names of same theorem?

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