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In signal processing, a digital biquad filter is a second order recursive linear filter, containing two poles and two zeros. Biquad is an abbreviation of biquadratic, which refers to the fact that in the Z domain, its transfer function is the ratio of two quadratic functions:
The transfer function of a two-port electronic circuit, such as an amplifier, might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electric ...
A biquad filter is a type of linear filter that implements a transfer function that is the ratio of two quadratic functions. The name biquad is short for biquadratic. Any second-order filter topology can be referred to as a biquad, such as the MFB or Sallen-Key. [5] [6] However, there is also a specific "biquad" topology. It is also sometimes ...
The transfer function for this second-order unity-gain low-pass filter is = ... A second-order unity-gain high-pass filter has the transfer function () ...
The log of the absolute value of the transfer function () is plotted in complex frequency space in the second graph on the right. The function is defined by the three poles in the left half of the complex frequency plane. Log density plot of the transfer function () in complex frequency space for the third-order Butterworth filter with =1. The ...
Other all-pole second-order filters may roll off at different rates initially depending on their Q factor, but approach the same final rate of 12 dB per octave; as with the first-order filters, zeroes in the transfer function can change the high-frequency asymptote.
The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams. An example of a closed-loop block diagram, from which a transfer function may be computed, is shown below:
English: Step responses for a second order system defined by the transfer function: = + + where is the damping ratio and is the undamped natural frequency.The equations were obtained from here, plotted using maxima and edited in a text editor to insert the Greek alphabets in the plot.