Frequency response

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In

The frequency response characterizes systems in the frequency domain, just as the impulse response characterizes systems in the time domain. In linear systems (or as an approximation to a real system neglecting second order non-linear properties), either response completely describes the system and thus have one-to-one correspondence: the frequency response is the Fourier transform of the impulse response. The frequency response allows simpler analysis of cascaded systems such as multistage amplifiers, as the response of the overall system can be found through multiplication of the individual stages' frequency responses (as opposed to convolution of the impulse response in the time domain). The frequency response is closely related to the transfer function in linear systems, which is the Laplace transform of the impulse response. They are equivalent when the real part ${\displaystyle \sigma }$ of the transfer function's complex variable ${\displaystyle s=\sigma +j\omega }$ is zero.^[2]

Measurement and plotting

Measuring the frequency response typically involves exciting the system with an input signal and measuring the resulting output signal, calculating the

• Applying constant amplitude sinusoids stepped through a range of frequencies and comparing the amplitude and phase shift of the output relative to the input. The frequency sweep must be slow enough for the system to reach its
  steady-state
  at each point of interest
• Applying an impulse signal and taking the Fourier transform of the system's response
• Applying a
  power spectral density
  ) should be used if phase information is required

The frequency response is characterized by the magnitude, typically in

• Bode plots graph magnitude and phase against frequency on two rectangular plots
• parametrically
  against frequency in polar form
• Nichols plots graph magnitude and phase parametrically against frequency in rectangular form

For the design of control systems, any of the three types of plots may be used to infer closed-loop stability and stability margins from the open-loop frequency response. In many frequency domain applications, the phase response is relatively unimportant and the magnitude response of the Bode plot may be all that is required. In digital systems (such as

Frequency response curves are often used to indicate the accuracy of electronic components or systems.[5] When a system or component reproduces all desired input signals with no emphasis or attenuation of a particular frequency band, the system or component is said to be "flat", or to have a flat frequency response curve.^[5] In other case, we can be use 3D-form of frequency response surface.

Frequency response requirements differ depending on the application.^[6] In high fidelity audio, an amplifier requires a flat frequency response of at least 20–20,000 Hz, with a tolerance as tight as ±0.1 dB in the mid-range frequencies around 1000 Hz; however, in telephony, a frequency response of 400–4,000 Hz, with a tolerance of ±1 dB is sufficient for intelligibility of speech.^[6]

Once a frequency response has been measured (e.g., as an impulse response), provided the system is

The form of a frequency response curve is very important for anti-jamming protection of radars, communications and other systems.

Frequency response analysis can also be applied to biological domains, such as the detection of hormesis in repeated behaviors with opponent process dynamics,^[7] or in the optimization of drug treatment regimens.^[8]

See also

References

Notes