How do amplitude and phase compare an input signal with an output signal?

In control theory, the stability and performance of a system are often evaluated through its frequency response, which measures how the system reacts to a continuously varying input signal across different frequencies. To analyze this response, the output signal is compared to the input signal using two primary metrics:

• Amplitude: This compares the magnitude of the output signal to the input signal, representing the system's gain or attenuation at a specific frequency.1
• Phase: This measures the degree to which the input and output signals are out of step with one another. When two periodic signals are compared, they are considered in phase if their maximum or minimum displacements occur simultaneously. If they do not align, the difference in their phase angle indicates how much one signal leads or lags behind the other.12

By examining these two factors, engineers can determine how a system processes signals and ensure it maintains the desired stability and operational characteristics.1