# Tag Info

### How were the coefficients for polynomial linear predictive coding derived?

With the new IETF standards document, this seems pretty obvious now. It's a problem of polynomial interpolation at n+1 points or samples, where n is the order of the predictor, and using the ...

### What is the proper way to implement a real time spectrogram?

It actually depends on what you are trying to achieve. I have two general points here to help you: First, you need to know the specifications of your real-time system. How long do you need to update ...
1 vote

### Why does the derivative of an audio file act like a high-pass filter?

In addition to the excellent existing answers we can also consider the continuous domain: If we have a signal as a fourier series (here in sine-cosine form) f(t) = \frac{a_0}{2} + \sum_{n=1}^\infty \...

### Why does the derivative of an audio file act like a high-pass filter?

@OverLordGoldDragon Your x(n)−x(n−1) expression is called a "first-difference discrete differentiator". Its frequency magnitude response is the blue dashed curve below:

### Why does the derivative of an audio file act like a high-pass filter?

You're doing $x(n) - x(n - 1)$, the finite difference / "discrete derivative", not to be confused with $\frac{d}{dt}x(t)$. The frequency response is where $H(\omega) = 1 - e^{-j 1\omega}$ ...

### Why does the derivative of an audio file act like a high-pass filter?

$\frac{d}{dt}\sin(\omega t) = \omega\cos(\omega t)$ as a consequence of the chain rule. $\sin$ and $\cos$ are the same apart from the phase shift, so the derivative is a filter with a response that's ...
Yes both the time derivative $d/dt$ and the discrete time difference $x[n]-x[n-1]$ are indeed "high pass filters": consider the extreme case of the lowest frequency, which is DC or a ...
The $fs$ you are getting from audioread is the sampling rate and has nothing to do with the actual frequency content of the signal you are analyzing other than the maximum frequency would be $fs/2$. ...