15 votes

Where are these aliasing artifacts coming from in transmitting audio? (Frequency reflection, duplication)

To perhaps help future readers, here is a graphical explanation of the two behaviors seen: harmonic distortion and aliasing / frequency fold-over: Harmonic distortion can result from any kind of non-...
jpa's user avatar
  • 703
14 votes
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Why does this Moiré pattern look like this?

You'll need to understand the sampling theorem. In short, each signal has what we call a spectrum¹, which is the Fourier transform of the signal as it comes in time domain (if it is a time signal), or ...
Marcus Müller's user avatar
12 votes
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Other end of Nyquist limit

Can't capture high $f$: insufficient sampling rate. Can't capture low $f$: insufficient observation interval. The DFT is a machine that spits out frequency measures, done by correlating against ...
OverLordGoldDragon's user avatar
11 votes
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Where are these aliasing artifacts coming from in transmitting audio? (Frequency reflection, duplication)

This behavior is likely caused by clipping (as nicely illustrated by @OverLordGoldDragon in the comments). Where exactly clipping is occuring is harder to tell, but a simple remedy is to lower the ...
MBaz's user avatar
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8 votes
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Understanding the mathematical proof for the alias frequencies in a sampled sine wave

The reason is that if it is true for any $m$, it is also true for $m=kn$. I will sketch the proof in another way. Call $f_s = 1/t_s$ sampling frequency where $t_s$ is sampling period, the two signal ...
AlexTP's user avatar
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8 votes
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What is the frequency representation of nonuniform sampling?

You might be interested in this particular reference paper: Digital Spectra Of Non-Uniformly Sampled Signals : Theories and Applications is a somewhat obscure reference (from 1988! can't go wrong!) ...
Jdip's user avatar
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7 votes
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Moving average before downsampling: effect on Nyquist frequency?

There is no effect on the Nyquist frequency, which is only dependent on the sample rate. Decimating is the combination of low-pass filtering + downsampling (which is the term for discarding samples ...
Jdip's user avatar
  • 6,055
6 votes

Why is aliasing inherently non-linear?

I think you mean "images", not "aliases". They become aliases if there is foldover from resampling. It's because you are not adding two signals, $x(t)$ and $\operatorname{III}(t)$, you are ...
robert bristow-johnson's user avatar
5 votes
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Freeform band-limited waveforms

this paper was done long before i had MATLAB. the drawings are poor, but the math (at least in this revision, which is what you should use) is spot on. send me an email address (to my ...
robert bristow-johnson's user avatar
5 votes
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Generating digitized white noise: uniform vs normal sampling

Your question is an interesting project for you to research it on your own. Well, maybe with a little help from your friend and the SE community. And, as your question goes, start with generating ...
V.V.T's user avatar
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5 votes
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Is spectral density conserved after aliasing?

No. The aliased component will interfere with the non-aliased components and the interference can constructive or destructive. Trivial example: $$x[n] = \sin\left(\frac\pi2n\right)$$ If you down ...
Hilmar's user avatar
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5 votes

Stanford EE 261 HW6 Q1 - Sampling below Nyquist Rate

The expression $B_2 < f_s < 2B_1$. is only part of the correct answer. The full correct answer is: $${2B_2\over m+1} ≤ f_s ≤ {2B_1\over m}$$ where $m$ is any positive integer ensuring that $f_s ≥...
Richard Lyons's user avatar
5 votes

How to measure aliasing?

Note: it's "Work In Progress", I intend to address some limitations, including "time aliasing". Interested hot visitors may wish to "Follow" the answer. Motivating the ...
OverLordGoldDragon's user avatar
4 votes

What's the impact of aliasing in the time domain?

This may not fully answer your question, but for getting a feeling of aliasing, maybe a simple demonstration can be helpful... Some initial setup: ...
Frank Zalkow's user avatar
4 votes

What's the impact of aliasing in the time domain?

I read Footnote 8, "The complication is that because of the sampling, the total system is not time-translation invariant and so does not have a unique ‘impulse response’ – the response is ...
ruoho ruotsi's user avatar
  • 1,770
4 votes

Illustration of time domain aliasing cancellation (TDAC, MDCT, lapped transform)

Edit: I have recently created two Jupyter Notebooks that illustrate this behaviour and let you play around with some actual matrices and actual signals. I find understanding MDCT easiest if we define ...
Nils Werner's user avatar
4 votes

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

A few approaches to alias-free nonlinear distortion (in increasing order of difficulty): Subband distortion: Use a low pass filter to extract the lower end of the signal. If you choose a cutoff ...
Jazzmaniac's user avatar
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4 votes

unexplainable aliases in spectrogram

Looking at the spectrogram, the prominent artifacts go up or down in frequency synchronously to the 138 MHz signal but have larger bandwidths. That is an indication that they are its harmonics, due to ...
Olli Niemitalo's user avatar
4 votes

Aliasing after downsampling

See this good mathematical treatment of undersampling by Prof. Fowler at Binghamton University, using the comb function as you have done in the time domain, taking the z-transform of the resulting ...
Dan Boschen's user avatar
  • 51.3k
4 votes

Why is aliasing inherently non-linear?

Hints: Can an LTI system generate components in some frequency $\omega_0$ if the input signal $x(n)$ was such that $X(e^{j\omega_0})=0$? Does aliasing do such thing? The answers to these questions ...
Tendero's user avatar
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4 votes
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Determine maximum frequency of input signal to make system LTI

This question, and a number of similar others, from DTSP book can be a little tricky to recognise the fact that it's not actually asking alias free operation (which would require 8 khz cutoff signal ...
Fat32's user avatar
  • 28.2k
4 votes

Effect of aliasing when sampling at higher rate

The name of this effect is Spectral Leakage. Remember the relation $$\frac{k}{N} = \frac{F}{F_S}$$ where $k$ is the bin number, $N$ is the FFT size, $F$ is the continuous frequency in Hz and $F_S$ is ...
QMC's user avatar
  • 784
4 votes

Effect of aliasing when sampling at higher rate

When discussing DFT, you have to remember two things: you're windowing your true signal $x[n]$ (which is periodic, and then infinitely long) with a window $w[n]$ (here a rectangular window) to obtain ...
anpar's user avatar
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4 votes
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Downsampling impact on complex phase

Decimating a signal (selecting every Dth sample and discarding the rest) does not distort the signal within the passband in any way other than to cause aliases from higher frequencies to fold into the ...
Dan Boschen's user avatar
  • 51.3k
4 votes
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Why does my sinusoid look "AM" in shape?

This visual phenomenon appears because the maximum frequency is close to the Nyquist frequency, or half the sampling frequency. Sampling begins to approach the limit of $2$ samples per period, and ...
Laurent Duval's user avatar
4 votes
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Why is the digital frequency highest at $\pi$ and what does it mean in terms of analog frequency?

Check this figure. Consider the signal $x[n]=A$ which is constant but can be written as $x[n]=A\cos(0n)$, so its frequency is zero. There is no oscillation. Let's increase the frequency. For the ...
GKH's user avatar
  • 1,087
4 votes

Why is the digital frequency highest at $\pi$ and what does it mean in terms of analog frequency?

The digital frequency represented with $\pi$ is the Normalized Angular Frequency, and has units of frequency given as radians/sample. This signal can be represented as a rotating phasor on the complex ...
Dan Boschen's user avatar
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4 votes
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How do you sub-sample an FFT?

it seems like the bigger problem is that subsampling the signal would result in aliasing frequencies No, subsampling in frequency domain corresponds to aliasing in time domain. So the idea here is to ...
jithin's user avatar
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4 votes
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Sampling pure tone sine waves

In contrast to common misunderstanding, aliasing does not affect the process of sampling, rather it affects the process of reconstruction. i.e., the samples themselves do not contain error, but their ...
Fat32's user avatar
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