# 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 (...
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### 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
Accepted

### 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 ...
• 21.7k
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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 "...
• 30.7k

### 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 ...
• 1,451

### 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 ...
• 79.2k

### Difference between Nyquist rate and Nyquist frequency?

Harry Nyquist invented/discovered/proved a lot of things; it can be hard to keep track of them all. The three most important for signal processing and communications are probably these: If you sample ...
• 13.5k
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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 ...
• 30.7k

### 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 ...
• 33.8k

### 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. ...
• 29.7k

### 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 ...
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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 ...
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Accepted

### 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 ...
• 36.1k
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### Downsampling and Gaussian Filtering in the Context of Scale Space Pyramids

You're correct, it has to do with the Cut Off frequency of the Gaussian Blur Filter in its Frequency Domain. In order to see it, just apply a DFT (Using MATLAB it can be achieved by ...
• 39.3k

### 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 ...
• 181
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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 ...
• 13.5k

### Proving Nyquist Sampling Theorem for Strictly Band Limited Signals (Whittaker Shannon Interpolation Formula)

Approaching The Sampling Theorem as Inner Product Space Preface There are many ways to derive the Nyquist Shannon Sampling Theorem with the constraint on the sampling frequency being 2 times the ...
• 39.3k
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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 ...
• 79.2k
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Accepted

### 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....
• 36.1k

### 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 ...
• 26.6k

### Understanding the Conditions for Recovering a Discrete Time Signal Through Sampling

Lets have a higher level of the idea of signal reconstruction from samples. When you try to reconstruct something from partial information it is important to know what you know about the result ...
• 39.3k
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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 ...
• 36.1k
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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 ...
• 30.7k

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

You may not need to explicitly reconstruct. But if you did reconstruct a waveform using the samples that you have, and end up with something different from the actual input, your controller is ...
• 33.8k
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### Soft question: Why do we need to reconstruct a signal?

The concept of reconstruction has nothing to do with the application, rather it has to do with the question: did I get the same signal that is really there. If you cannot recreate the signal back, ...
• 725
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 ...