* In electronics, an analog multiplier is a device which takes two analog signals and produces an output which is their product. Such circuits can be used to implement related functions such as squares (apply same signal to both inputs), and square roots. Definitions of Frequency doubling on the Web:

* Second harmonic generation (SHG; also called frequency doubling) is a nonlinear optical process, in which photons interacting with a nonlinear material are effectively "combined" to form new photons with twice the energy, and therefore twice the frequency and half the wavelength of the initial ... ANALOG MULTIPLIERS/DIVIDERS

An analog multiplier/divider is a device that produces an output voltage or current that is proportional to the product of two or more independent input voltages or currents. In addition to multiplying and dividing, multipliers can perform squaring, square-rooting and modulation functions. Applications include radar, communications, and industrial controls where a real-time response is required. Analog Devices’ offers the widest selection of multipliers and dividers.

What Is Frequency Response?

Frequency response plots show the complex values of a transfer function as a function of frequency. In the case of linear dynamic systems, the transfer function G is essentially an operator that takes the input u of a linear system to the output y:

For a continuous-time system, the transfer function relates the Laplace transforms of the input U(s) and output Y(s):

In this case, the frequency function G(iw) is the transfer function evaluated on the imaginary axis s=iw. For a discrete-time system sampled with a time interval T, the transfer function relates the Z-transforms of the input U(z) and output Y(z):

In this case, the frequency function G(eiwT) is the transfer function G(z) evaluated on the unit circle. The argument of the frequency function G(eiwT) is scaled by the sampling interval T to make the frequency function periodic with the sampling frequency . Back to Top

How Frequency Response Helps to Validate Models

You can plot the frequency response of a model to gain insight into the characteristics of linear model dynamics, including the frequency of the peak response and stability margins. Frequency-response plots are available for all linear parametric models and spectral analysis (nonparametric) models. Note Frequency-response plots are not available for nonlinear models. In addition, Nyquist plots do not support time-series models that have no input.| The frequency response of a linear dynamic model describes how the model reacts to sinusoidal inputs. If the input u(t) is a sinusoid of a certain frequency, then the output y(t) is also a sinusoid of the same frequency. However, the magnitude of the response is different from the magnitude of the input signal, and the phase of the response is shifted relative to the input signal. Frequency response plots provide insight into linear systems dynamics, such as frequency-dependent gains, resonances, and phase shifts. Frequency response plots also contain information about controller requirements and achievable bandwidths. Finally, frequency response plots can also help you validate how well a linear parametric model, such as a linear ARX model or a state-space model, captures the dynamics. One example of how frequency-response plots help validate other models is that you can estimate a frequency response from the data using spectral analysis (nonparametric model), and then plot the spectral analysis result on top of the frequency response of the parametric models. Because nonparametric and parametric models are derived using different algorithms, agreement between these models increases confidence in the parametric model results. Back to Top

What Does a Frequency-Response Plot Show?

System Identification Tool GUI supports the following types of frequency-response plots for linear...