Analog Signal and Sine Wave

What is an analog signal?

An analog signal can take on any value from a continuous range over a given period. Its values change smoothly and are not restricted to a finite set of levels. The physical world around us contains many analog phenomena, including sound waves, light intensity, and temperature changes. Human speech is a classic example of an analog signal.

Sine waves and Fourier series

The sine wave is the simplest form of an analog signal. Under the conditions of Fourier's theorem, a complex periodic signal can be represented as a sum of simple sine waves. Analyzing the sine wave provides a basis for describing the spectrum of analog signals.

Parameters of a sine wave

• Amplitude (A): This is the maximum deviation, or signal value relative to its zero level (the time axis). It describes the signal level and is often interpreted as its intensity. On the graph, it is the distance from the horizontal axis to the peak of the wave.
• Period (T): This is the time it takes for the wave to complete one full cycle, after which its shape begins to repeat. It is measured in seconds [s].
• Frequency (f): This is the number of full cycles the wave completes in one second. It is the inverse of the period and is measured in Hertz [Hz], where 1 Hz = 1 cycle per second.
  Formula: $f = \frac{1}{T}$

From acoustic wave to transmission signal

Physical phenomena like acoustic waves (e.g., human speech) must be converted into a transmission signal (usually electrical) to be sent over telecommunication systems. Such complex signals are also characterized by several parameters.

• Dynamics (D): This is the ratio of the largest signal level that stays within distortion limits to the smallest usable level that remains above noise. For amplitudes, it can be written as the ratio of $A_{\text{max}}$ to $A_{\text{min}}$. This range is often expressed in decibels.
• Frequency Bandwidth ($\Delta f$): This is the range of frequencies contained within the signal, from the lowest ($f_{\text{min}}$) to the highest ($f_{\text{max}}$). For a signal to be transmitted without loss of information, the transmission channel must be able to carry this entire frequency range.