Frequency Response of a System

Frequency response of a system refers to the behavior of the system when it is subjected to a sinusoidal input. In other words, it is the way in which a system responds to different frequencies of input signals.

Types of Signals

Before discussing the frequency response of a system, it is important to understand the different types of signals.

- Impulse Signal: It is a brief signal having a very short duration and a high amplitude. It represents a sudden change in the system.
- Unit Step Signal: It is a signal that rises from zero to one at t=0.
- Sinusoidal Signal: It is a periodic signal that varies sinusoidally with time.

Frequency Response of a System

The frequency response of a system can be obtained by taking the Fourier transform of the system's impulse response. It is represented by the transfer function of the system, which is the ratio of the output signal to the input signal in the frequency domain.

The transfer function of a system is represented by H(jw), where j is the imaginary unit and w is the frequency of the input signal.

The frequency response of a system can be analyzed by plotting the magnitude and phase of the transfer function as a function of frequency. This plot is known as the Bode plot.

Applications of Frequency Response

The frequency response of a system is an important tool for analyzing and designing control systems. It is used to determine the stability, sensitivity, and performance of a system.

For example, in the design of a filter, the frequency response is used to determine the cut-off frequency and the attenuation of unwanted frequencies.

Conclusion

In conclusion, the response of a system to a sinusoidal input is called the frequency response. It is represented by the transfer function of the system, which is the ratio of the output signal to the input signal in the frequency domain. The frequency response is an important tool for analyzing and designing control systems.