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28 votes
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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 "...
Hilmar's user avatar
  • 45.4k
21 votes

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 ...
Justme's user avatar
  • 2,303
15 votes

What is the difference between phase noise and frequency noise?

Phase Noise and Frequency Noise are not two different noise sources, they are artifacts of the same noise, it is just a matter of what units you want to use. Frequency and Phase are directly related ...
Dan Boschen's user avatar
  • 52.1k
13 votes

What is the maximum possible frequency of human voice/speech(That can be generated through human vocal cords)?

Especially What is the maximum value of frequency that human speech can have? This depends on how exactly you define it. Fricatives ("s","f","sh" ...) and plosives (&...
Hilmar's user avatar
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12 votes
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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 ...
Dan Boschen's user avatar
  • 52.1k
12 votes

What is the maximum possible frequency of human voice/speech(That can be generated through human vocal cords)?

The fundamental speaking frequency of humans can reach up to around 1kHz, although higher values than, say, 500Hz usually appear only while singing. The harmonics and non-tonal parts of speech can ...
Max's user avatar
  • 2,368
12 votes
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Why is sampling frequency/rate typically abbreviated Fs and not Sf in English?

DSP is in the end a field of math, mostly living on the intersection of analysis, linear algebra and maybe stochastics. As it describes signals, it's also a daughter of Physics. So, it uses the ...
Marcus Müller's user avatar
10 votes
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Why do we calculate the second half of frequencies in DFT?

First, there's some pedantics to get out of the way: it's not FFT or DFT -- the FFT is just a specific method of computing the DFT that's advantageous under many circumstances. Any DFT takes $N$ ...
TimWescott's user avatar
  • 12.8k
9 votes

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 ...
Dan Mills's user avatar
  • 201
9 votes

Estimate Sine Frequency under White Noise — simple and effective method

I assume the model to be: $$ x \left[ n \right] = \sin \left[ 2 \pi \frac{f}{ {f}_{s} } n + \phi \right] + w \left[ n \right] $$ Where $ w \left[ n \right] $ is white noise uncorrelated with the ...
Royi's user avatar
  • 19.7k
9 votes
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How can I determine the frequency of a sine wave signal with gradually increasing frequency?

Instantaneous frequency is the time derivative of phase. Since the OP already has the analytic signal representation of the chirp, every sample can easily be used for the frequency estimate (unlike ...
Dan Boschen's user avatar
  • 52.1k
8 votes

What is the physical significance of negative frequencies?

even though everything important has been said I wanted to add some code and more visual keys on why the following formulas require positve and negative frequencies to make clear that negative ...
OuttaSpaceTime's user avatar
8 votes

Is there other basis possible for DFT?

$k/N$ with $N$ bases is the only basis which is all of: Orthogonal & invertible. Means we don't lose any information. Invertibility can be seen to follow from the DFT being a square (N x N) ...
OverLordGoldDragon's user avatar
8 votes
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Does analytic signal have positive instantaneous frequency?

It is not the case that the instantaneous frequency of an analytic signal is always positive. In general, the instantaneous frequency can become negative, also for analytic signals. I'll show this ...
Matt L.'s user avatar
  • 90.4k
7 votes
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Understanding the $\mathcal Z$-transform

Consider a liner discrete-time system. Assume we can define it in terms of an input-output relation as follows (you can assume a more general model but it is enough for our purpose): $$a_0y[n]+a_{1}y[...
msm's user avatar
  • 4,295
7 votes
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Discrete Time Signal Property

Take a complex exponential $$x[n]=e^{jn\omega}\tag{1}$$ Let's assume that $\omega=\pi$. This gives $$x[n]=e^{jn\pi}=(-1)^n\tag{2}$$ (because $e^{j\pi}=-1$). Eq. $(2)$ shows that a signal with ...
Matt L.'s user avatar
  • 90.4k
7 votes
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Meaning of a null coefficient at 0 Hz

A zero coefficient at DC simply means the mean of the waveform is 0; bin 0 of the DFT is identical to calculating the mean value scaled by $N$. Consider the general expression for the DFT: $$X(k) = \...
Dan Boschen's user avatar
  • 52.1k
7 votes

Estimate Sine Frequency under White Noise — simple and effective method

A common way to do this is to take the FFT of the input signal. Since the frequency might not be right at a FFT bin, usually a second step of interpolation is done after choosing the initial peak. A ...
Engineer's user avatar
  • 3,042
7 votes

Estimate Sine Frequency under White Noise — simple and effective method

If you have a low-noise and well-sampled signal, a quick way to estimate it is to find $\sqrt{-f''(t)/f(t)}$. For a signal $$f(t)=A \sin(\omega t+\phi)$$ the second derivative is $$-A \omega^2 \sin(\...
Nullius in Verba's user avatar
6 votes

A very basic question about processing high frequency signals

In digital signal processing, one almost never deals directly with high-frequency signals. The reason is that the frequency band that a signal occupies is completely irrelevant to the information that ...
MBaz's user avatar
  • 15.3k
6 votes

Discrete Time Signal Property

I think it means the "apparent" frequency of oscillation. It's poorly worded. What's happening is that the frequency is increased to the Nyquist rate in the first half and then above it, causing ...
Peter K.'s user avatar
  • 25.8k
6 votes
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Why is it called continuous-time frequency?

$\Omega$ is the usual angular frequency in radians per second, and is equal to $2 \pi f$. It is the way to measure frequency for continuous-time signals. In discrete-time, frequency is measured in ...
Juancho's user avatar
  • 5,026
6 votes

How can I get the power of a specific frequency band after FFT?

To get the total power across bins, sum the power in each bin. Also you need to compensate for your window loss if you want an accurate result. For a rectangular window, the power in each DFT bin is ...
Dan Boschen's user avatar
  • 52.1k
6 votes

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 ...
TimWescott's user avatar
  • 12.8k
6 votes
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Calculate the magnitude and phase of a signal at a particular frequency in python

You can find the index of the desired (or the closest one) frequency in the array of resulting frequency bins using np.fft.fftfreq function, then use ...
megasplash's user avatar
6 votes

Estimate Sine Frequency under White Noise — simple and effective method

This depends on the precision needed. If it's a pure sine wave that's noise free, you can get a very quick estimate by measuring the difference between two zero crossings. The tricky part is that most ...
Hilmar's user avatar
  • 45.4k
6 votes
Accepted

Unwanted periodicity in data

Some time-frequency analysis with the synchrosqueezed CWT, where I guess fs=10000 but this doesn't matter except for axis labels and physical interpretation. 1. ...
OverLordGoldDragon's user avatar
6 votes
Accepted

(graphic) Relation between FFT and complex signal

Each bin in the DFT result does not represent a sinusoid but is a spinning phasor in the time domain as $x[n] = c_k e^{j\omega_k n}$. For those less familiar, the form $Ke^{j\phi}$ with real $K, \phi$ ...
Dan Boschen's user avatar
  • 52.1k
5 votes

What is the physical significance of negative frequencies?

An easy way of thinking about the problem is to imaging a standing wave. The standing wave (in time domain) can be represented as a sum of two oppositely moving traveling waves (in frequency domain ...
user3320933's user avatar
5 votes

What is the physical significance of negative frequencies?

In the real World, actual event frequency is fundamentally unsigned Frequency is measured in Hz, which is defined as the inverse of the second, and is used to count how often an event repeats. Time is ...
mins's user avatar
  • 463

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