28
votes
Accepted
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 "...
- 42.7k
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 ...
- 2,293
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 ...
- 48.9k
12
votes
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 ...
- 48.9k
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 ...
- 2,215
12
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 (&...
- 42.7k
10
votes
Accepted
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 $N$ ...
- 11.9k
9
votes
Doppler shift in time domain?
The term Doppler Shift is actually a bit of a misnomer. The frequencies are not actually shifted but they are scaled (see http://fourier.eng.hmc.edu/e101/lectures/handout3/node2.html for definition of ...
- 42.7k
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 ...
- 201
9
votes
Accepted
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 ...
- 48.9k
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 ...
- 297
8
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 ...
- 19.3k
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) ...
- 8,815
8
votes
Accepted
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 ...
- 89k
7
votes
Are there libraries for extraction of sound wave features?
From the ones I've been using I can recommend:
YAAFE - very pleasant to work with in Python
ESSENTIA - another one I like particularly due to Python integration
aubio
FEAPI
Aquila - friend of mine ...
- 11.1k
7
votes
Accepted
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):
$$a_0y[n]+a_{1}y[...
- 4,225
7
votes
Accepted
Discrete Time Signal Property
Take a complex exponential
$$x[n]=e^{jn\omega}\tag{1}$$
Let's assume that $\omega=\pi$. This gives
$$x[n]=e^{jn\pi}=(-1)^n\tag{2}$$
(because $e^{j\pi}=-1$). Eq. $(2)$ shows that a signal with ...
- 89k
7
votes
Accepted
Meaning of a null coefficient at 0 Hz
A zero coefficient at DC simply means the mean of the waveform is 0; bin 0 of the DFT is identical to calculating the mean value scaled by $N$.
Consider the general expression for the DFT:
$$X(k) = \...
- 48.9k
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(\...
6
votes
Audio frequency modulation algorithm
You need to build a time varying delay, where you can modulate the delay amount over time.
The peak delay modulation is a function of your maximum desired frequency shift and the modulation ...
- 42.7k
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 ...
- 14.9k
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 ...
- 25.3k
6
votes
Accepted
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 ...
- 4,986
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 ...
- 48.9k
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 ...
- 11.9k
6
votes
Accepted
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 ...
- 396
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 ...
- 42.7k
6
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 ...
- 3,012
6
votes
Estimate Sine Frequency under White Noise — simple and effective method
I wasn't going to answer this, since the question is stale. But I'm a little bit dissatisfied with Royi's answer and with the Kay algorithm as presented.
The Kay method is, at first glance, simply ...
- 20.1k
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. ...
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