Fundamentals of Signals

Signals are fundamental to communication systems, representing information that can be transmitted over various media. Understanding the key components of signals—amplitude, frequency, and phase—is crucial for analysing and designing systems that process these signals.

Amplitude

Amplitude refers to the height of a wave relative to a reference point, typically measured from the equilibrium position to the peak (maximum) or trough (minimum) of the wave. It quantifies the strength or intensity of the signal.

Characteristics:

• Measurement Units: Amplitude is often measured in volts (V) for electrical signals, but it can also be expressed in other units depending on the context (e.g., pressure for sound waves).
• Impact on Signal Quality: Higher amplitude indicates a stronger signal, which can enhance clarity and reduce the likelihood of interference. Conversely, low amplitude can lead to weaker signals that may be more susceptible to noise.
• Dynamic Range: The difference between the smallest and largest possible amplitude values in a signal is known as its dynamic range. A larger dynamic range allows for more detailed representation of information.

Applications:

• In audio systems, amplitude affects volume; higher amplitudes produce louder sounds.
• In telecommunications, signal amplitude is crucial for maintaining quality over long distances.

Frequency

Frequency is defined as the number of cycles a waveform completes in one second. It is measured in Hertz (Hz), where one Hertz equals one cycle per second.

Characteristics:

• Types of Signals: Different types of signals have varying frequencies. For instance, audio signals typically range from 20 Hz to 20 kHz, while radio frequencies can extend into megahertz (MHz) and gigahertz (GHz).
• Relationship with Period: The frequency is inversely related to the period (T), which is the time taken for one complete cycle of the wave. This relationship is expressed as: $f=\frac{1}{T}$ where $f$ is frequency and $T$ is the period.
• Harmonics: In complex signals, multiple frequencies may exist simultaneously, leading to harmonic content that defines timbre in music or other sound applications.

Applications:

• Frequency determines the pitch of sound; higher frequencies correspond to higher pitches.
• In radio communications, different frequencies are allocated for various channels to prevent interference.

Phase

Phase refers to the position of a waveform relative to a reference point in time. It indicates where a wave starts in its cycle and is usually measured in degrees or radians.

Characteristics:

• Phase Shift: When two signals share the same frequency but start at different points in their cycles, they are said to have a phase difference. This shift can affect how signals interact when combined.
• Constructive and Destructive Interference: When two waves are in phase (0° shift), they reinforce each other (constructive interference). Conversely, if they are out of phase by 180°, they cancel each other out (destructive interference).
• Mathematical Representation: The phase of a sinusoidal signal can be represented mathematically as: $A\sin (2\pi ft+\varphi )$ where $A$ is amplitude, $f$ is frequency, $t$ is time, and $\varphi$ is the phase angle.

Applications:

• In electronics, phase relationships are critical for designing circuits that rely on alternating current (AC).
• In communication systems, maintaining synchronization between transmitted and received signals often involves managing phase differences.