Questions tagged [nyquist]

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62
votes
6answers
28k 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?
12
votes
4answers
2k views

Is there such a thing as band-limited non-linear distortion?

So if you generate a square wave by just switching a signal between two values, at sample boundaries, it produces an infinite series of harmonics, which alias and produce tones below your fundamental, ...
9
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3answers
499 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 ...
9
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4answers
2k 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 ...
9
votes
3answers
184 views

Spherical equivalent of Nyquist frequency

Let $\phi$ be a scalar function defined on the surface of a sphere. I have samples of $\phi$ at various locations on the sphere. I want to apply a spherical harmonic transform. I know that $\phi$ is '...
6
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8answers
9k views

Nyquist Frequency Phase Shift

The figure below shows in dashed lines sinusoidal signals of the same frequency at three different phase shifts. The signals are then sampled such that the sinusoidal frequency is exactly a half of ...
6
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2answers
36k views

Difference between Nyquist rate and Nyquist frequency?

So I've been searched online and can't seem to find a clear cut answer to this question. From my understanding, the Nyquist rate is double of the maximum frequency of a signal which Nyquist frequency ...
5
votes
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 ...
4
votes
5answers
746 views

Regarding the Nyquist Criterion

I recently read that with compressive Sensing it possible to sample the signal at a rate lesser than that suggested by Nyquist Criterion. However, I am still not getting how this is possible. Can ...
4
votes
1answer
997 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 ...
4
votes
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 ...
4
votes
1answer
266 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_\...
4
votes
1answer
1k views

What is “Equivalent Time Sampling” and what is it good/used for?

The literature on this method seems scarce, but I know that it has been used on radar systems to 'get away with' not having to sample nearly as fast as Nyquist would otherwise dictate, (at the cost of ...
4
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5answers
207 views

Reconstructing/interpolating small regions of a bandlimited signal by taking the fewest possible samples

I have a signal which is bandlimited and can be sampled at arbitrary continuous positions. The value at any position is given by an expensive computation. I need to do some further computation on ...
4
votes
1answer
9k views

How are signal bandwidth and MSPS related?

In various software defined radios, there are three important parameters to set when receiving: frequency, bandwidth and MSPS (million samples per second?). What does it mean to receive with a triple ...
4
votes
3answers
494 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 ...
4
votes
1answer
224 views

What is the LOW frequency resolution rule analogous to Nyquist?

If I'm analyzing a signal in the frequency domain, I know about the well known Nyquist criteria that the sample frequency must be > 2x of the highest component present in the signal. However, there ...
3
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5answers
2k views

A question about sampling rate of cosine signal

Given $$c(t) = \cos(2\pi\cdot 30 \cdot t) $$ If we sample this signal at the Nyquist rate 60 Hz and at a higher rate of 80 Hz, we get the following: There is no aliasing as $f$ = 30 Hz is less than ...
3
votes
2answers
6k views

Why is a square wave aliased?

I understand an ideal analog square wave contains sine-wave-components above Nyquist frequency (and towards infinity) and is thus subject to aliasing. So obviously we need an anti-aliasing-filter. Or ...
3
votes
2answers
1k views

polyphase sample rate conversion with non-integer factor

I want to do sample rate conversion by subsequently upsampling with factor I=5, and then downsampling with factor D=9. I have designed a nyquist sample rate conversion filter h() of length M, with ...
3
votes
2answers
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’...
3
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2answers
5k 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 ...
3
votes
2answers
317 views

Ignoring Nyquist

What happens if I ignore Nyquist? I have a 16.368MHz digital signal coming out of a GPS front-end chip. My microcontroller (which is reading that digital stream of data) operates at a maximum of ...
3
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1answer
125 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\...
3
votes
1answer
75 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 ...
3
votes
2answers
2k views

What is the proof of the equation for the aliased frequency fa = |R*n - fs|?

R (sampling rate) fs (signal being sampled fN (the Nyquist frequency) fa (aliased frequency) I was hoping someone could explain to me why this is true with a more mathematical proof. it seems ...
3
votes
1answer
282 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 ...
3
votes
1answer
608 views

Benefits of oversampling in a realtime noise-cancellation system

When sampling a signal, it is standard practice to use a sampling rate that is greater than two times the bandwidth of the signal in order to avoid aliasing. The result is then low-pass filtered (and ...
2
votes
3answers
195 views

Soft question: Why do we need to reconstruct a signal?

I am currently reviewing the Nyquist criterion which says I need to sample the signal at 2 times the maximum frequency in order to avoid aliasing in the reconstructed signal. My question is that in ...
2
votes
2answers
1k 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 ...
2
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1answer
101 views
2
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2answers
447 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, ...
2
votes
1answer
607 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 ...
2
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2answers
4k views

The relationship between downsampling and frequency resolution

I am having trouble understanding a concept that I have seen in many published papers. For example, in this paper (http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0082748) they wrote ...
2
votes
1answer
1k views

Downsampling and Gaussian Filtering in the Context of Scale Space Pyramids

In the context of scale space image pyramids using Gaussian filters I noticed that it's common to downsample the image after blurring with $\sigma = 2*\sigma_{init}$ . My question is: What is the ...
2
votes
2answers
71 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 ...
2
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1answer
45 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 ...
2
votes
2answers
103 views

What is the right way to downsample using Fourier method?

I want to know what is the right way to downsample a sampled signal using Fourier transform as the implementation in scipy.signal.resample confuses me. Reading ...
2
votes
2answers
78 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:...
2
votes
1answer
1k 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 $...
2
votes
2answers
652 views

When calculating the Nyquist frequency should carrier frequency be included

This isn't my field, so please forgive any misnomers on my part. I'm looking into buying a amateur radio receiver, and I'm thinking about what sampling rate I need. I'm most interested in satellite ...
2
votes
1answer
133 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]...
2
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1answer
844 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(...
2
votes
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 ...
2
votes
1answer
70 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 ...
2
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0answers
82 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
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3answers
471 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 ...
1
vote
4answers
367 views

Sampling Theorem: How to know the value between two samples of a Signal

According to Sampling theorem, in order to reconstruct a signal we need to sample it at the rate => twice the highest frequency component of that signal. (provided signal is band limited). Let's say, ...
1
vote
2answers
961 views

Sampling frequency lower than half of sampled signal frequency?

In GNURADIO when RTL-SDR Source block is placed there is a parameter Sample Rate (sps) and ...
1
vote
1answer
655 views

Why remove energy at Nyquist before ifft?

I've heard that you should remove the energy at Nyquist before performing the ifft. Why is it that you can't leave the Nyquist energy there, is there danger of aliasing somehow?

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