The bird drawing is just a proxy for arbitrary data. In your example, you could convert bitstream into a pattern of black and white squares into a YouTube Video. Send it through the VHS channel, and when you digitize it, you would get back the exact bitstream.

If your argument is that the bandwidth calculation is incorrect, then sure I think that’s fair.

But I don’t think it’s correct to say it’s not a digital channel juts because it doesn’t have optimal bandwidth.

The entire point is that the modulated signal can be reconstructed exactly,

But this isn’t true. Just because a signal is modulated doesn’t mean it can’t be distorted.

A spectrogram is just showing that arbitrary data can be sent though this channel. It’s literally a form of modulation.

My point is that it doesn’t have to be optimal to be considered digital. Which in the general case means basically any communication channel can be digital.

If the argument is that they didn’t correctly calculate the bandwidth, then sure.

Why couldn’t you have a likelihood function for the bird?

As a trivial case, you can just say: Does the spectrum look like a bird? Then you’d have a digital channel by your definition for a single bit.

The actual channel bandwidth is obviously higher than that.

Isn’t this for C++?

• Played through a DAC and speaker to produce an analogue signal (lossy)

• Analogue modulation of bit stream played through DAC (lossy)

These steps are literally the same thing. You’re converting some data into sound for the bird to hear.

Edit: Actually, most physical modulation schemes use sinusoids anyways. So that’s exactly the same as playing a spectrum.

That’s not really how it works in the real world. Usually you have both bandwidth and noise constraints.

Sure you can send something like a square wave but this isn’t practical for real communication channels. Typically you’re sending many sine waves in parallel with multiple amplitudes and phase offsets to represent a sequence of bits (QAM). Then on top of that you’d encode the original data with both a randomizer (to prevent long runs from looking like nothing) and error correction. So usually the system can handle some level of distortion.

What you’re hoping is that by the time the data reaches the user (really, Layer 3), all the errors have already been handled and you never see any issues.

The bird is just another type of noisy channel with its own distortion characteristics.

Minor analogue distortion does not change the information content of the signal unless it is so bad as to flip a bit.

This isn’t true in the general case. In the real world, you can have all kinds of distortions: random noise, time shifts, interference from other signals, etc.

You don’t usually see the effects of these because the protocols are designed with the communication channel characteristics in mind in order to reproduce the original signal.

Using birds is just another communication channel with its own distortion characteristics.

Every signal is ultimately analog. Voltage along a wire, sound, light, the world is analog and it all needs to be converted into our concept of digital (which is typically binary values).

By your definition nothing can be digital since the world is analog. Even the bits in your CPU are voltages in transistors. As such, every real life signal can be distorted.

The problem with CSS is that it’s not very intuitive and too flexible. You need to know how display and position works to understand the basic centering a div example. If you forget to change the display to flex you don’t get an error, it’s still valid CSS. You can examine the element in the browser but you’ll need to know to look for the issue there.

Then you’ll need to inline and block elements, etc.

And it’s a pretty unique system in general.