# Tag Info

Accepted

### If humans can only hear up to 20 kHz frequency sound, why is music audio sampled at 44.1 kHz?

The sampling rate of a real signal needs to be greater than twice the signal bandwidth. Audio practically starts at 0 Hz, so the highest frequency present in audio recorded at 44.1 kHz is 22.05 kHz (...
• 15.8k

### If humans can only hear up to 20 kHz frequency sound, why is music audio sampled at 44.1 kHz?

44,100 was chosen by Sony because it is the product of the squares of the first four prime numbers. This makes it divisible by many other whole numbers, which is a useful property in digital sampling. ...
• 753
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### What sampling frequency should I use if Nyquist is not available?

HINT When you sample at below the Nyquist rate, aliasing happens. That means frequencies higher than half the sampling rate get folded back down to below half the sampling rate. Have a read about ...
• 25.9k
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### Does the Nyquist frequency of the cochlear nerve impose the fundamental limit on human hearing?

Does the Nyquist frequency of the Cochlear nerve impose the fundamental limit on human hearing? No. A quick run-through the human auditory system: The outer ear (pinnae, ear canal), spatially "...
• 45.6k

### A question about sampling rate of cosine signal

It is actually not distorted, it is sampled at high enough rate. What fools you is the straight lines drawn between sample points, it gives you a false impression of the waveform. It shows you a ...
• 2,311

### What sampling frequency should I use if Nyquist is not available?

As correctly stated in Peter K.'s answer, this question is about aliasing. Since you can't sample at a rate that is sufficiently high to avoid aliasing - i.e., $f_s>50\textrm{ kHz}$ - you have to ...
• 90.5k
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### Does the Shannon theorem not apply when the amplitude of a wave is changed faster than half the time period of the wave?

Once you start changing the amplitude you are increasing the bandwidth of the signal. That's called "amplitude modulation" and the highest frequency is now the sum of the original frequency ...
• 45.6k

### If humans can only hear up to 20 kHz frequency sound, why is music audio sampled at 44.1 kHz?

The Nyquist rate is above twice the bandlimit of a baseband signal that you want to capture without ambiguity (e.g. aliasing). Sample at a lower rate than twice 20kHz, and you won't be able to tell ...
• 35.4k
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### Amplitude modulation vs sampling rate?

The OP's opening statement is incorrect: $f_s > f_{max}/2$ prevents frequency aliasing for a bandlimited signal, but not amplitude aliasing $f_s > 2 f_{max}$ prevents aliasing. It's as simple ...
• 52.3k

### If humans can only hear up to 20 kHz frequency sound, why is music audio sampled at 44.1 kHz?

Basically, twice the bandwidth is a common requirement for signal sampling, thus $2\times 20 = 40$ kHz is a minimum. Then, a little more is useful to cope with imperfect filtering and quantization. ...

### Given a signal that is not bandlimited, how do you properly take the FFT?

In the real world, there is always some amount of aliasing, because no real signal is actually bandlimited. In many cases, the signal spectrum tends to zero relatively quickly as the frequency ...
• 15.3k
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### What is Faster Than Nyquist signaling?

Harry Nyquist made so many contributions that it's easy to get confused. Related to sampling, Nyquist proved that a signal $s(t)$ bandlimited to $B$ Hz can be reconstructed from samples taken at a ...
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### A question about sampling rate of cosine signal

The actual requirement is to sample at GREATER then twice the bandwidth, not at a rate equal to it... So only your 80Hz same set actually meets the requirement, because the 60Hz case is ambiguous in ...
• 201

### Difference between Nyquist rate and Nyquist frequency?

These terms are indeed named in a confusing manner, as frequency and rate are pretty much synonyms. Either way: Nyquist frequency is the maximum frequency in a signal that can be well recorded given ...
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### Given a continuous time signal, does the minimum Nyquist sampling rate depend on the choice of the set of basis functions?

In the most general case, if you want to sample a continuous-time signal without loss of information, the minimum sampling rate is independent of any choice basis functions. The faster the signal ...
• 90.5k
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### Signal values we will 'miss' between sampling instances during sampling of band limited signals

I don't have a real answer but I have the feeling that this result will help you out: Bernstein's inequality says that, if the signal $x(t)$ is bandlimited to $|f|\leq B$, then \left| \frac{\textrm{...
• 15.3k
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### Nyquist plot interpretation when curve hits the origin

First to clear up the OP's misunderstanding: the Nyquist Stability Criteria involves clockwise encirclements of -1, not the origin, and this would be the polar plot for the open-loop gain specifically....
• 52.3k

### Link between DFS, DFT, DTFT

Yes your understanding is basically correct. The 1st paragraph (2 lines) expresses the fundamental relation between the DFS and the DFT of a finite-length sequence $x[n]$ while the 2nd paragraph tries ...
• 28.3k

### Given a signal that is not bandlimited, how do you properly take the FFT?

If your signal is not band-limited prior to sampling, then without any further information (such as a copy of the signal sampled at a time offset, which could synthesize a higher sampling rate), ...
• 52.3k
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### Is there a way to compute the spectrum effect of a non-linear function?

is there any way to calculate the rate at which the harmonics decrease in power for a given function Yes, but it's complicated and typically not worth the bother. If the non-linearity is static, i.e. ...
• 45.6k
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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 ...
• 6,300
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### Higher order harmonics during sampling

The sampling is indeed analogous to mixing as to my understanding. In the sampling process, we multiply the time domain signal with an impulse train - the impulses in time are represented as impulses ...
• 52.3k
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### Conclusions of sampling around Nyquist Rate

Is the rate of 2B exclusive? Yes. The sampling theorem states that the signal must be band limited to half the sample rate. That implies that the energy at the Nyquist frequency must be zero. In ...
• 45.6k
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### Nyquist noiseless channel capacity; how can bit-rate be two times the bandwidth?

I think you're confusing two different (but related) terms. Nyquist says that in a channel of bandwidth $B$ you can transmit up to $2B$ orthogonal pulses per second. So, $R_p \leq 2B$, where $R_p$ is ...
• 15.3k

### A question about sampling rate of cosine signal

There is no aliasing as 𝑓 = 30 Hz is less than or equal to the folding frequency, 30 Hz and 40 Hz, respectively. Yes and no. There isn't significant aliasing when you're sampling at 80Hz, because ...
• 12.9k
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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 ...
• 1,739
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### Why does twice the sampling rate (Nyquist Theorem) seem inadequate?

Perfect recovery is one thing, niceness is another. Sampling above x2 Nyquist is sufficient for perfect recovery, after which we can FFT-upsample to make it look nice - which is more efficient than ...
• 8,984

### Is there a way to compute the spectrum effect of a non-linear function?

Stealing$^\dagger$ from this answer: For non-linear functions that admit a series expansion (e.g. Taylor/Maclaurin), you can get a decent intuition for how fast the harmonics decay. The Maclaurin ...
Observations I have used +1 and -1 in the sequence instead of your 1 and 0. With $\alpha=1$, the band-limited continuous function $f_m(T)$ in your first two figures (with the above mentioned ...