I have read a lot of information on the internet, but did not find a straight easily understandable answer. Could someone just explain it clearly for me, please?
It all depends on the application that you are talking about, but generally the reason is because a digital circuit is either on or off. So lets say that in order to measure a digital high, the minimum threshold may be around 2-2.7v for 5v logic. And to register a low, it may only need to be as low as 0.8v. So any small amount of noise is generally not going to affect those signals as much since there's a wide range where it can register a high or a low.
An analog signal is basically an infinite number of voltages that it can be and any small amount of noise will change that voltage. With a digital signal you only care if it's high or low. With analog, you care about all of the voltages in between. It gets more susceptible to noise the smaller the signal is. If you have a 2.5v analog signal and 1mV of noise, this may not be too big of a deal depending on the application. But if you have a 25mv Signal that you need to amplify it to 2.5V, you will end up with 100mV of noise on the 2.5v signal once it's amplified. That could be a problem. This is why it's very important to have very little noise with the beginning stages of a small signal amplifier.
All other things being equal, digital signals only need to resolve two levels: a valid ‘0’ or ‘1’. The receiving end sets these thresholds and snaps to one of the valid levels, and so can be designed to reject a considerable amount of noise on the line.
Analog signals are continuous. The entire range of the signal swing contains information. Any added noise present on the signal cannot be directly distinguished from the original signal.
There is a theory that defines this relationship between signal, noise, and a third parameter, bandwidth: Shannon-Hartley Information theory.
Read more about that here: http://www.inf.fu-berlin.de/lehre/WS01/19548-U/shannon.html
The takeaway is, you use a channel (signal) to send bits of information as symbols. A digital signal sends just one bit per symbol, but it uses a lot of bandwidth to send that bit.
For example, telephone voice signal is about 4KHz analog, but needs about 64Kbps to code digitally (8bit samples at 8KHz). That 64Kbps digital signal will need at least 64KHz to send down the wire, but having only 1 bit per symbol, will be very immune to noise.
Between the two extremes (pure digital, pure analog) are a whole range of coding options that trade bandwidth for noise immunity. In the example above, using sophisticated multilevel coding is how a 56kbps modem could squeeze those bits down an ordinary phone line.
So it’s all analog, and it’s all digital: it's information.
An analog circuit is not intrinsically more susceptible to noise than a digital circuit, because a digital circuit is made up of analog devices.
Noise is a signal that interferes with the signal of interest.
The difference in analog circuits and digital circuits is the kind of noise that can be safely tolerated.
In a digital circuit, the important parameter is the level of a signal. In an analog circuit, both the level and frequency of the signal are important parameters.
In a digital circuit only 2 levels are considered. Noise having a lower amplitude than the noise margin of the digital circuit can be tolerated by it, because thresholding is used.
In analog circuits frequency filters have to be used to remove the noise. An analog circuit is more susceptible to radiation if it is not shielded properly. This is because radiation is also a kind of noise that will be picked up by the analog circuit if it is not shielded. In practice, shielding an analog circuit from noise is complicated. Keeping the amplitude of noise that a system could be subjected to below the noise margin is simpler. This is one reason why digital circuits are preferred over analog circuits.