Compare Digital and Analog Signals - Physics

Digital. CPUs process binary data using logic gates and transistors.

High-frequency content appears as a lower frequency due to undersampling. Frequencies above $f_s/2$ fold back into the sampled spectrum.

Sample at $f_s \ge 2f_{max}$. Must sample at least twice the highest frequency to avoid aliasing.

Rounding sampled amplitudes to the nearest allowed discrete level. Converts continuous amplitudes to discrete steps, introducing error.

Amplifier. Increases all signal components equally, including unwanted noise.

Regenerator (digital repeater). Detects bit values and outputs clean digital pulses.

A reduction in signal amplitude as it propagates. Signal weakens due to resistance and energy loss in the medium.

Noise adds directly to the signal and accumulates with distance. Each amplifier adds more noise, degrading signal quality progressively.

A continuous-time signal with continuously varying amplitude. Amplitude can take any value within a range at any instant.

A signal that uses discrete amplitude levels (often $0$ and $1$). Only specific amplitude values are allowed, typically binary.

Continuous values. Can take any value within a range, like voltage or temperature.

Discrete symbols (bits). Uses binary digits to represent information as $0$s and $1$s.

Repeaters can regenerate bits, limiting cumulative noise effects. Clean bits can be perfectly restored at each repeater station.

Digital data. Perfect copies possible since only discrete values are stored.

Digital systems can use error detection and correction codes. Extra bits can detect and fix transmission errors mathematically.

Digital often requires higher bandwidth for the same information rate. Multiple bits needed to represent each analog sample value.

Digital. Small noise won't flip bits if below decision threshold.

$N=8$ bits. Fewer bits means fewer levels, so larger rounding errors.

Analog. Sound waves create continuous voltage variations in microphones.

Aliasing. High frequencies appear as false low frequencies when undersampled.

The number of quantization levels and amplitude resolution. More bits allow finer amplitude distinctions.

Higher data rate (more bandwidth/storage needed). More samples per second means more data to transmit/store.

Rounding amplitudes to the nearest discrete level. Converts continuous amplitudes to nearest allowed discrete value.

$2^n$ levels. Each bit doubles the number of possible amplitude levels.

Sampling frequency must satisfy $f_s \ge 2f_{max}$. Prevents aliasing by sampling at least twice the highest frequency.

Analog. Continuous signals have no amplitude restrictions.

Digital. Discrete levels allow parity bits and checksums.

Thresholded (small noise often does not change the bit). Noise below threshold doesn't flip bits between levels.

Additive (noise directly changes the amplitude). Noise voltage adds to signal voltage, distorting it.