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15 votes

How to deal with low fundamental when using AMDF for pitch extraction?

This is what we call in the pitch-detection biz, the "octave problem". First of all, I would change the AMDF to ASDF. And I would not reduce the window size as the lag increases. (Also, I ...
robert bristow-johnson's user avatar
8 votes

Integer multiples of fundamental period in sine wave

A $T$-periodic signal doesn't necessarily have a (sinusoidal) fundamental with period $T$. It never has one if the signal is also periodic with period $T/2$ or $T/3$ etc. (as in your example). But ...
Matt L.'s user avatar
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7 votes

How do I find the fundamental period of the given signal?

If your top equation is really $$ x(t) = 2\cos\left(\frac 45 \pi t\right)\sin^2\left(\frac{16}{3} t\right)\tag{1} $$ You gonna have a hard time getting the fundamental period/frequency as the there ...
Gilles's user avatar
  • 3,406
6 votes
Accepted

How to change speed of audio samples without changing pitch?

This question (about "time-scaling" audio) is closely related to pitch shifting, which is time-scaling combined with resampling. But changing the speed without changing pitch is only time-scaling, so ...
robert bristow-johnson's user avatar
4 votes

Pitch perception - Why does our ear not directly detect the missing fundamental frequency?

Here is roughly how it works. A typically musical note is made out of harmonics and the fundamental. The fundamental is also the spacing between the harmonics. For 100 Hz fundamental you would get ...
Hilmar's user avatar
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4 votes
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How to find the fundamental frequency of a discrete signal using partial autocorrelation?

Very simple: your sampling rate is 512Hz and your sample time is the inverse of this: about 1.953 ms. Multiply with 506 and you get the time length of the fundamental: 0.988s. So you have one beat ...
Hilmar's user avatar
  • 45.6k
4 votes

Change in frequency on differentiation

No, in a conventional sense of a "periodic signal" phrase, but, if you permit me to delve into a math subtlety, differentiation can turn an aperiodic waveform to a periodic one: $$ \frac{\...
V.V.T's user avatar
  • 1,739
4 votes

What is a "pitch period"?

The pitch period of a perfectly periodic function, $x(t)$, is the smallest positive value $P>0$ such that $$ x(t+P) = x(t) \qquad \forall t \in \mathbb{R} $$ Now, simply because a function is ...
robert bristow-johnson's user avatar
3 votes

Confusion regarding calculation of fundamental period?

This seems like more of a semantics problem. A signal is periodic with time $T$ if $$x(t+n\cdot T) = x(t), n \in \mathbb{Z}$$ So the signal is periodic in $0.5$ since the for $T = 0.5 \cdot n$ the ...
Hilmar's user avatar
  • 45.6k
3 votes

Change in frequency on differentiation

No, it's not possible. Proof: let $f : \mathbb{R} \to \mathbb{R}$ periodic, i.e. there exists $T\in\mathbb{R}$ such that $$f(t+T) = f(t) \quad\forall t\in\mathbb{R}.$$ Then it follows that the ...
leftaroundabout's user avatar
3 votes

Pitch estimation using the autocorrelation method

An offset of 20 samples is added as 8 lines above (auto=autocor(21:160)) this offset is cut away from the autocorrelation sequence. In the line you mention, this ...
applesoup's user avatar
  • 647
3 votes
Accepted

Why do the DTFT and FFT give me completely different results for magnitude at a specific frequency?

HINT: Try introducing the sampling frequency $F_s$. Then $f$ in the relation in Equation $(1)$ is relative to the sampling frequency $$ \omega = 2\pi f\quad\text{where}\quad f = \frac FF_s\tag{1} $$ ...
Gilles's user avatar
  • 3,406
2 votes
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Better way to mute fundamental baseband frequency?

To mute the fundamental frequency, consider using a notch filter such as the one shown in the figure below, where $\omega_n =2\pi 60/f_s$, where $f_s$ is your sampling rate, and $\alpha$ is chosen ...
Dan Boschen's user avatar
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2 votes
Accepted

Pitch perception - Why does our ear not directly detect the missing fundamental frequency?

There are two distinct areas or domains to keep in mind when thinking about the idea of pitch, the acoustic signal (in your case a complex tone composed of a set of harmonics based on a fundamental ...
Michael_RW's user avatar
2 votes

Term for integral multiples of fundamental period?

If $T$ is a positive real number such that $$x(t) = x(t+T) ~\text{for all}~t \in \mathbb R\tag{1}$$ for continuous-time signals, or if $T$ is a positive integer and $$x[n] = x[n+T]~\text{for all}~n \...
Dilip Sarwate's user avatar
2 votes

Pitch detection, YIN, pYIN

If there was some code outlining this, I would be interested I don't have the expertise to describe pYin precisely, but I can point you to the original code for that paper https://code.soundsoftware....
xavriley's user avatar
  • 121
2 votes
Accepted

Change in frequency on differentiation

The point about discontinuity was meant to hint at the following example. Consider the (unbounded) signal that is defined by $$ x(t) = \lceil{t}\rceil. $$ It's derivative is $$ x'(t) = \sum_{k=-\infty}...
hops's user avatar
  • 1,422
2 votes
Accepted

Confusion regarding calculation of fundamental period?

The trigonometric functions are essentially exponential. Thus, a doubling of the argument corresponds to a squaring of the function (in a sense). In this case, it can be seen by applying the angle ...
Cedron Dawg's user avatar
  • 7,590
2 votes

Confusion regarding calculation of fundamental period?

If it helps any, generate a unit amplitude sinewave at 1 Hz and its square: Then the sinewave and its square look like this: You can see the DC component: the averaged value of the squared sinewave (...
Ed V's user avatar
  • 795
2 votes
Accepted

Timbre vs sound via oscilloscope

Sorry, your understanding is mostly wrong. Sound is a pressure & velocity wave in a fluid medium, i.e. air. A human speaker will generate a 3 dimensional sound field around them. The sound ...
Hilmar's user avatar
  • 45.6k
2 votes
Accepted

What is a "pitch period"?

So based in @rbj answer, can i try to show you visually ... Take a look in this pure tone signal, one sine at 100hz and sample rate at ...
ederwander's user avatar
  • 2,038
1 vote

Change in frequency on differentiation

Conceptually, I think this can be seen as the defining question for understanding Fourier series. Every well enough behaved periodic signal can be expressed as a Fourier series. Which means summing ...
Cedron Dawg's user avatar
  • 7,590
1 vote
Accepted

How to find fundamental frequency of Fourier Series

Your solution is correct. Obviously, any periodic function with period $T$ is also periodic with period $kT$, $k\in\mathbb{Z}^+$. In the given example, the smallest possible period is $T=1/5$, which ...
Matt L.'s user avatar
  • 90.5k
1 vote

How to determine the phase of a time-sampled periodic signal?

You could try to Fourier transform, $F(k) = \int_{-\infty}^{\infty} x(t) e^{-2\pi i kt} dt$ which can be expressed in terms of magnitude and phase in the following way $F(k) = |F(k)|e^{i\Phi(k)} = ...
Stephen Jackson's user avatar
1 vote

Calculate the Standard Deviation of Fundamental Frequency (MFCC)

You calculate fundamental frequency of the signal with some pitch extraction algorithm, for example YIN, https://github.com/ronggong/pypYIN. It is a vector of numbers, then you calculate standard ...
Nikolay Shmyrev's user avatar
1 vote

Note detection in an audio file.

The pitch of a musical note is very often not the same thing as the frequency peak in an FFT magnitude computation. This is due to all the overtones and harmonics within interesting musical sounds, ...
hotpaw2's user avatar
  • 35.4k
1 vote

how to create a harmonic mask from fundamental frequency?

See this post which describes creating a notch filter using a delay and add: Moving Average for Notch filtering The filter used is generically given as $$H(z) = 1+z^{-N}$$ This results in passing ...
Dan Boschen's user avatar
  • 52.3k
1 vote

YIN pitch estimation algoritm-simplified explanation

There is an older question about YIN where I am expressing lack of impressing. The only thing that is novel in YIN is the Cumulative mean normalized difference function (Step 3): what is plotted ...
robert bristow-johnson's user avatar
1 vote

What are F0 counters in Speech signals? What is represented by F0?

Check this source To begin with, let’s remember what the fundamental frequency is and in what tasks it may be needed. The fundamental frequency, which is also referred to as F0, is the ...
abdoulsn's user avatar
  • 119
1 vote

Octave: Finding the mean fundamental frequency given an audio signal

Your code appears to be looking for zero crossings of the rectified signal, which won’t work reliably if your signal has strong harmonics or overtones of the fundamental frequency within your filter’s ...
hotpaw2's user avatar
  • 35.4k

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