# Naive question about Analog and Digital Signals

I have just started telecommunications in high school Physics. We are currently studying analog to digital conversion. I have 2 questions :

1. How is a "digital" signal transmitted? As far as I know, you can turn an analog signal digital by sampling and then applying a restriction with bits. But isn't this just an abstract idea? Or does an actual square wave gets formed that then gets transmitted?

The other question depends on the answer to this one.

1. If the answer is yes, a square wave gets forms and that's actually what we transmit: if too many bits are used, that means we can pick tiny fluctuations better. But doesn't this also mean any noise along the way also shows up more?

I am looking for answers for a beginner.

• Re, "isn't this just an abstract idea?" Yes. That is exactly right. Computing systems (including digital signal processing systems) are defined by many layers of abstract ideas. One built on top of another. At the real, physical level, there is no such thing as a "digital signal." But there are analog signals that can be interpreted (or, if you prefer, decoded) as sequences of numbers. And at a higher level of abstraction, those numbers can be interpreted as a representation of some other analog signal. – Solomon Slow Apr 8 '19 at 14:33
• P.S., I misused the word, "analog." A time-varying voltage or current is not an "analog signal," unless the voltage or the current means something. E.g., you can buy an industrial pressure sensor that allows current to flow in a loop, where the current is proportional to the measured pressure. That's "analog" because the current represents a system variable, the measured pressure. If you don't assign any meaning to the voltage or current in a circuit, then that voltage/current is not even analog. It's just voltage or current. dictionary.com/browse/analog – Solomon Slow Apr 8 '19 at 15:33
• @SolomonSlow That seems like an answer, rather than a comment. – rob Apr 8 '19 at 16:56

The answers to your questions above are:

1. An analog signal is sampled, and a sequence of bits is sent that corresponds to the value of the sample. This sequence of bits consists of zeros and ones, or if you prefer, on and off. This is not a "restriction" of bits ... it is a signal encoding that closely represents the analog value that was sampled. Also, it may not be relevant that the digital signal is a square wave. For a zero bit corresponding to a value of 1 volt and a 1 bit corresponding to a value of 5 volts, the device reading the digital stream doesn't care if that signal plots as a square wave as long as it can distinguish the difference between a reading of 1 V and 5V.

2. Too many bits are not used in the digital stream. The number of bits that are used is determined by the precision that you need in the measurement. For example, if you are sampling an analog value that can vary from 1 to 10, and you are using 1 bit to represent the sampled data, the computer reading this data sees a bit value of zero as an analog value of 1 and a bit value of one as an analog value of 10. Obviously, this is very imprecise. If, on the other hand, you use 4 bits to represent the analog measurement, those 4 bits can have 16 possible values. This means that the analog range from 1-10 can be split up into 16 possible values that a computer can read, resulting is quite a bit more precision. For most every-day applications, you would want something like 12-16 bit precision, which gives a high, but not infinite degree, of precision. In other words, the digital signal does not perfectly represent the analog measurement, as the digital signal is not truly continuous because it is represented by a finite number of bits.

Regarding noise in the digital signal, there is no noise that is due to the number of bits that are used. If there is noise in the analog measurement, that noise will be represented in the digital encoding of that measurement. If you know enough about the characteristics of the analog process that you measured, you can do numerical tests on the digital signal and filter the noise out of that signal.

• about 1, how will this sequence be transmitted? I understand, somewhat at least, how for example an aerial can transmit an analog voltage. But I can't really visualize transmitting a sequence. And about 2, "If there is noise in the analog measurement, that noise will be represented in the digital encoding of that measurement". My concern was that if we use a lot of bits and approximate the analog signal so closely, won't the sound we will also now pick up ( as slight fluctuations of the analog) make the output not as good? – Sal_99 Apr 9 '19 at 15:49
• 1) The analog-digital (A/D) converter has to be set up to transmit a certain number of bits to represent a reading. The computer receiving this information has to be set up the same way. In addition, you need to select a sampling rate (e.g., one reading every 0.1 seconds), sample at that frequency, send the info to a computer, and have the computer receive the information at this frequency. – David White Apr 9 '19 at 16:21
• 2) If you know that the phenomenon generating a sound signal cannot change its amplitude (or pitch) faster than at a certain rate, you can filter any excursions from the signal that appear faster than this rate. Assuming that you can tolerate a very slight delay in the signal, you can average the digital signal before an excursion with the digital signal after an excursion, or use some other form of filtering, to eliminate the excursion in the computer's output. For more info, see en.wikipedia.org/wiki/Analog-to-digital_converter – David White Apr 9 '19 at 16:23
• these bits are sent as voltage pulses? Can they be transmitted as RF waves? – Sal_99 Apr 11 '19 at 3:31
• Voltage pulses are common for bits, but that's not the only way to send digital data. It can be sent as light pulses, RF pulses, etc. – David White Apr 11 '19 at 18:32

What makes a signal analog or digital?

Let's say I have a square wave signal. Is this digital or analog? Or neither? It depends on what I do with this signal. Am I sampling this signal at brief intervals of time and then taking decisions based on comparing the value of the signal with a threshold? Then the signal is digital.

Am I driving a stepper motor continuously with the square wave signal? Then it is analog, since I am neither sampling nor quantizing the signal.

Regarding the question on how the RF waves are transmitted, there is no difference in how they are transmitted (be it analog or digital communication). They are transmitted as Electromagnetic waves. What matters is are they encoded and decoded or not. Is the information transmitted as it is without sampling and quantization? Then it is analog communication, else it is digital communication. For digital communication, you have to ensure that the signal is sampled at or above the Nyquist sampling rate for no loss of information (read the Sampling Theorem for more details on that). The continuous time signal is converted to a digital signal at the receiver side, while the digital signal is converted to a continuous time signal at the transmitter side in digital communication. This conversion process is done using modulation at the transmitter side and demodulation at the receiver side.

Regarding the concern of noise, there are clever tricks used to ensure the signal can be transmitted and received even in the presence of noise. The digital signal is compressed, and redundant bits are added to enable error correction. There is the Shannon limit, that tells us the maximum bandwidth of a channel at a particular noise level. Shannon is the Godfather of Information Theory, which is a beautiful field of study in Electrical Engineering that covers topics like information compression and error correction and detection. Noise can also be filtered using digital filters, this is studied in digital signal processing, another beautiful field of study in Electrical engineering that covers topics like signal reconstruction and filtering.

One might also ask questions like Analog is Digital? to which some people (especially those from an electrical engineering background who have not studied quantum physics - as it is evident on Electrical Engineering Stack Exchange and a comment on this question by a user) might erroneously conclude that the digital signal is in fact analog. However, there is no proof that the world is analog and not digital, nor is there proof the other way round. We never know if the signals in the real world are actually continuous, or if it is discrete and appears to be continuous. Does a quantum state take on a continuous set of probabilities or is it just restricted to 0 and 1 (the probability wavefunction breaks down into a discrete value when measured)? Does light travel as a particle or a wave? All we know are theories, and theories can't (atleast so far they haven't) be proven to be an accurate description of reality itself. But using these theories we can do a lot of useful work and build useful inventions.