Correlation between sample rate and audible frequency?

[Hayabusa]

No -- it isn't ultrasonic. I don't understand why this misconception persists; perhaps some people are confusing noise shaping with ringing. Totally different concepts.

The ringing is just an effect of taking out >fs/2 frequencies from the signal.
They have no frequency components <fs/2

 

[Julf]

The ringing is just an effect of taking out >fs/2 frequencies from the signal.
They have no frequency components <fs/2

Indeed. People really seem to have a problem understanding this.

 

[xr100]

It's important IMHO not to characterize Shannon's sampling theory

In this context, there seems to have been some equivocation in this thread over the use of the words "theory" and "theorem."

I had a conversation not so long ago with somebody who didn't said that they believe the "sampling theory." (sic.)

Theorem means proven, and it is no more a "theory" than, say, Pythagoras' Theorem, which has and will always give the correct result for the length of the unknown side of a right-angled triangle.

(OK, "real-world" triangles such as one drawn on a piece of paper are bound to be "imperfect" and deviate from an "idealised" right-angled triangle; but, in an abstract/mathematical sense, that's not the point...)

 

[xr100]

176 khz recording of cymbal hit very hard once with drum stick. Notice how it starts at low level and builds. That is because it takes a finite time for the energy to travel across the metal of the cymbal, reflect from the edge, and build to a resonance at higher level. So even hard struck cymbals are NOT like a Dirac pulse thru the ADC/DAC.

For the sake of completeness, synthetically generated sounds, which are after all found on a large proportion of today's recordings, are not subject to physical limitations.

Also, the attack phases of acoustic sounds could be altered by post-processing--e.g. removing the initial attack phase in a waveform editor, or "overshoot" (resulting in a more "impulsive" envelope) as a result of (dynamic range) compressor action.

 

[Julf]

For the sake of completeness, synthetically generated sounds, which are after all found on a large proportion of today's recordings, are not subject to physical limitations.

They are still subject to a lot of physical limitations. If nothing else, most of the "synthetically generated sounds" come from synthesizers and digital audio workstations with limited sample rates.

 

[xr100]

They are still subject to a lot of physical limitations. If nothing else, most of the "synthetically generated sounds" come from synthesizers and digital audio workstations with limited sample rates.

Obviously nothing can be generated above Nyquist; but generating a Dirac pulse in DSP is absolutely trivial.

(In digital synthesis, Nyquist rears its ugly head in the form of aliasing, but that's another matter.)

Generally, the "control" parts of digital synthesizers, e.g. for the amplitude envelope, run at a fraction of the sample rate. Furthermore, the "classical" (subtractive) synthesizer signal path consists of oscillators fed into a low pass filter. So, those are two possible limitations for the synth's output per se (i.e. not withstanding further post-processing.)

 

[Julf]

Obviously nothing can be generated above Nyquist; but generating a Dirac pulse in DSP is absolutely trivial.

Sure, but why would you?

 

[xr100]

Sure, but why would you?

Well, for one thing it's a test signal that can be used to measure the frequency response of plug-ins.

Here's the waveform for the right channel at the start of a mid-80s synth-pop track. It consists of a kick and a "beepy" sounding synth note.

It can be seen that the kick does not have a "smoothly" rising attack phase. The synth note waveform is very "spiky," too.

To be clear, I'm not concerned by the use of "brickwall" linear phase LP filters.

 

[Julf]

Well, for one thing it's a test signal that can be used to measure the frequency response of plug-ins.

 

[captain paranoia]

Obviously nothing can be generated above Nyquist; but generating a Dirac pulse in DSP is absolutely trivial.

It's quite hard to generate an infinite amplitude, zero-width pulse in any sampled-data system...

DSP uses a sampled-data approximation to a Dirac delta function (single sample, unity amplitude). It's not a true Dirac delta function, though.

 

[Blumlein 88]

It's quite hard to generate an infinite amplitude, zero-width pulse in any sampled-data system...

DSP uses a sampled-data approximation to a Dirac delta function (single sample, unity amplitude). It's not a true Dirac delta function, though.

Nor can any real system.

 

[RayDunzl]

Here's the waveform for the right channel at the start of a mid-80s synth-pop track. It consists of a kick and a "beepy" sounding synth note.

It can be seen that the kick does not have a "smoothly" rising attack phase.

Zoom in some more on the "attack phase"...

 

[captain paranoia]

Nor can any real system.

Indeed. A Dirac delta function cannot be realised; it's a purely theoretical tool. A very useful theoretical tool, mind you...

As wiki says:

"It is used to model the density of an idealized point mass or point charge as a function equal to zero everywhere except for zero and whose integral over the entire real line is equal to one.[1][2][3] As there is no function that has these properties, the computations made by the theoretical physicists appeared to mathematicians as nonsense until the introduction of distributions by Laurent Schwartz to formalize and validate the computations."

https://en.wikipedia.org/wiki/Dirac_delta_function

 

[xr100]

DSP uses a sampled-data approximation to a Dirac delta function (single sample, unity amplitude). It's not a true Dirac delta function, though.

Indeed, but in the discrete-time domain it is the "impulse" in impulse response.

Actual "problems" for filters in the discrete-time systems, limited by the absence of infinity in time/frequency domains as relevant, are that for an FIR filter the impulse response must be truncated/windowed, and for an IIR filter the response deviates from the (idealised) "analogue prototype" towards Nyquist (severe cramping with a basic bilinear transform, albeit these days most IIR DSP filter implementations should at least have an improved "decrampled" (Orfandis) response.)

 

[xr100]

Zoom in some more on the "attack phase"...

Sure.

The circled area is the initial "click" transient of the kick.

Zooming further in to that area:

 

[bennetng]

Sure.

View attachment 45719

The circled area is the initial "click" transient of the kick.

Zooming further in to that area:

View attachment 45720

You lost

 

[xr100]

You lost

LOL.

I dunno, my example goes from peak waveform amplitude >-20dB to ~-3dB in 3 samples...

Your example would seem to have a gross amount of DC offset?

(Embedded YouTube video: "Gofer no Yabou Episode II - 40 Space Traveler")

Cool "chiptune." Pretty "clicky" kick!

 

[bennetng]

Your example would seem to have a gross amount of DC offset?

Check the attachment...

 

[xr100]

Check the attachment...

Thank you. Here is the waveform for one of the "kick drum" instances in that recording:

If it must be a competition, then I am happy to consider it a "draw."

Certainly a good example of a fast attack and short duration kick.

 

[ousi]

I think this is a pretty good presentation about the theorem in layman term.