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Questions tagged [nyquist]

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59
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6answers
25k 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, ...
8
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3answers
350 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 ...
5
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8answers
7k 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 ...
5
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2answers
27k 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
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 ...
5
votes
1answer
182 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 ...
4
votes
5answers
570 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
122 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
1answer
198 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
885 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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3answers
1k 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 ...
3
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2answers
4k 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
274 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
votes
1answer
6k 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 ...
3
votes
2answers
1k 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
219 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
416 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
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3answers
173 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
4answers
265 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, ...
2
votes
2answers
95 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
1k 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’...
2
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2answers
555 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
votes
2answers
2k 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 ...
2
votes
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:...
2
votes
1answer
483 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
544 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
2answers
822 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 ...
1
vote
3answers
286 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
2answers
657 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
478 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?
1
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3answers
479 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 ...
1
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2answers
2k 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 ...
1
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5answers
775 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 ...
1
vote
2answers
135 views

Computing shifted signal without first reconstructing

Looking for a solution to the following problem: A signal $x(t)$ is band limited to $B$ Hz, and sampled above the Nyquist rate, with corresponding $f_s = 1/T$. If the sampled signal is given by ...
1
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3answers
2k views

Explanation of binning in frequency analysis post-FFT

I am creating an Android app which records sound for t seconds at a sampling rate of 44.1kHz with a buffer size of 8192 (16 bit mono samples). I need to plot a ...
1
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1answer
76 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 ...
1
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2answers
412 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 ...
1
vote
1answer
970 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 ...
1
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1answer
649 views

why Sampling with higher than nyquist frequency is causing aliasing?

fm=20000 and I am sampling following signal at 65000 Hz: ...
1
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1answer
151 views

Can I ignore the Nyquist criterion?

If I have a signal with frequencies up to 2000 Hz but I'm only interested in the frequency range up to 500 Hz, is it correct to sample at 1000 Hz $(f_\mathrm s \geq 2 \cdot f_\mathrm{max})$? Or do I ...
1
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1answer
1k views

How to determine Nyquist Rate

I have the Fourier Transform of a signal. How can I determine the Nyquist Rate of that signal? What is the formula for that?
1
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3answers
2k views

What is the relationship between frequency vector and the peak frequency in FFT?

I am fairly new to both Matlab and FFT. I would like someone to explain to me the relationship between the frequency of the wave being processed, the number of point (usually called NFFT), the Nyquist ...
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2answers
25 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 ...
1
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2answers
462 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 ...
1
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1answer
151 views

Find minimum sampling rate of non-ideal notch filter

Old test problem: "You have been asked to design a real-time digital filtering system that eliminates a band of frequencies between 20 and 30 MHz but preserves everything else. The system uses an ...
1
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1answer
589 views

What is the minimum sampling duration to capture a given frequency?

Due to the Nyquist rate, you need to sample twice as fast as the highest frequency you want to measure. Then when you do a FFT the number of samples determines the number of bins and thus the ...
1
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1answer
835 views

The Nyquist-Theorm behind the fft

I saw a code in Python in the scipy.org (http://docs.scipy.org/doc/scipy-dev/reference/tutorial/fftpack.html) and found this: First question: Is it right that T = 1/800 <==> fs = 800 Hz fulfill ...
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1answer
2k views

Calculate Max Number Of Harmonics for given Sample Rate?

How do I calculate the maximum number of harmonics a complex wave can have based on the sample rate? Say I Have a 20hz fundamental and a sampling rate of 44100 hz. My instinct is to take 44100/2 = ...