All low-pass second-order continuous-time filters have a transfer function given by

More generally, the output of a second-order low-pass filter with a very high quality factor responds to a step input by quickly rising above, oscillating around, and eventually converging to a steady-state value.

The transfer function for this second-order unity-gain low-pass filter is

For instance, a second-order low-pass notch filter section only reduces ( rather than eliminates ) very high frequencies, but has a steep response falling to zero at a specific frequency ( the so-called notch frequency ).

This arrangement of passive components forms a resistively-damped second-order low-pass filter.

As such, designing a filter consists of developing specifications appropriate to the problem ( for example, a second-order low pass filter with a specific cut-off frequency ), and then producing a transfer function which meets the specifications.

A common strategy is to realize a higher-order ( greater than 2 ) digital filter as a cascaded series of second-order " biquadratric " ( or " biquad ") sections ( see digital biquad filter ).

* A second-order filter attenuates higher frequencies more steeply.

For example, a second-order Butterworth filter will reduce the signal amplitude to one fourth its original level every time the frequency doubles ( so power decreases by 12 dB per octave, or 40 dB per decade ).

Third-order acoustic crossovers are often built from first-or second-order filter circuits.

A second-order all-pole filter gives an ultimate slope of about 12 dB per octave ( 40dB / decade ), but the slope close to the corner frequency is much less, sometimes necessitating a notch be added to the filter.

The Sallen – Key topology is an electronic filter topology used to implement second-order active filters that is particularly valued for its simplicity.

For example, a second-order Butterworth filter, which has maximally flat passband frequency response, has a of.

A second-order unity-gain high-pass filter with of and of is shown in Figure 4.

A second-order unity-gain high-pass filter has the transfer function

A parametric equalizer, on the other hand, has one or more sections each of which implements a second-order filter function.

A graphic equalizer also implements second-order filter functions in a more user-friendly manner, but with somewhat less flexibility.

Each second-order filter has a fixed center frequency and Q, but an adjustable level.

A fancier second-order filter will reduce those frequencies with a slope of 12 dB per octave and moreover may be designed with a higher Q or finite zeros in order to effect an even steeper response around the cutoff frequency.

A second-order filter decreases at − 12 dB per octave, a third-order at − 18 dB and so on.

If not, Kalman filter based methods are a first-order approximation ( EKF ) or a second-order approximation ( UKF in general, but if probability distribution is Gaussian a third-order approximation is possible ).

This is a second-order ( biquad ) filter.

Sometimes slightly stronger theories such as Morse-Kelley set theory or set theory with a strongly inaccessible cardinal allowing the use of a Grothendieck universe are used, but in fact most mathematicians can actually prove all they need in systems weaker than ZFC, such as second-order arithmetic.

When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak König's lemma, with the equivalence provable in RCA < sub > 0 </ sub > ( a second-order variant of Peano arithmetic restricted to induction over Σ < sup > 0 </ sup >< sub style =" margin-left :- 0. 6em "> 1 </ sub > formulas ).

The algorithm has second-order convergent nature, which essentially means that the number of correct digits doubles with each step of the algorithm.

But it is not so: it is, rather, like the case of orthography, which deals with the word " orthography " among others without then being second-order.

Philosopher and encyclopedist Mortimer Adler includes all such second-order questions about various fields of study, which are often found under various branches of philosophy beginning with the phrase " philosophy of ....", in his taxonomy.

Metaphilosophy also attempts to understand such second-order problems with the aid of the other major branches, e. g. metaphysical knowledge in religion, epistemology in religion, axiology in religion, etc.

A weaker first-order system called Peano arithmetic is obtained by explicitly adding the addition and multiplication operation symbols and replacing the second-order induction axiom with a first-order axiom schema.

This theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors.

For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law and Hooke's law.

Fresnel's partial ether dragging hypothesis ruled out the measurement of first-order ( v / c ) effects, and although observations of second-order effects ( v < sup > 2 </ sup >/ c < sup > 2 </ sup >) were possible in principle, Maxwell thought they were too small to be detected with then-current technology.

A logical characterization of PSPACE from descriptive complexity theory is that it is the set of problems expressible in second-order logic with the addition of a transitive closure operator.

An omnipotent being with both first and second-order omnipotence at a particular time might restrict its own power to act and, henceforth, cease to be omnipotent in either sense.

The SQUID, coupled to a second-order gradiometer and input circuit, along with the application of gradients, are the fundamental entities which allow a research group to retrieve noninvasive images.

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.

In anisotropic materials, the thermal conductivity typically varies with orientation ; in this case is represented by a second-order tensor.

This was still a second-order axiomatization ( expressing induction in terms of arbitrary subsets, thus with an implicit use of set theory ) as concerns for expressing theories in first-order logic were not yet understood.

The arithmetical hierarchy can be defined on any effective Polish space ; the definition is particularly simple for Cantor space and Baire space because they fit with the language of ordinary second-order arithmetic.

Here it should be assumed that the crankshaft with low second-order vibration is used and the first order is balanced by a balance shaft.

Engineers will commonly model these structures as coupled second-order systems, approximating dynamic structure components with springs, masses, and dampers.

* second-order phase transition, associated with " critical points " at which the system exhibits scale-invariant structures.

where is the Cauchy stress tensor, is the infinitesimal strain tensor, is the displacement vector, is the fourth-order stiffness tensor, is the body force per unit volume, is the mass density, is the divergence operator, represents the gradient operator and represents a transpose, represents the second derivative with respect to time, and is the inner product of two second-order tensors ( summation over repeated indices is implied ).

A more refined second-order edge detection approach which automatically detects edges with sub-pixel accuracy, uses the following differential approach of detecting zero-crossings of the second-order directional derivative in the gradient direction: