Thus, VCSOAs can be seen as amplifying filters.

Thus as this portion of the signal decreases in amplitude, the higher frequencies are progressively more sharply attenuated, which also filters out the constant background noise on the tape when and where it would be most noticeable.

Thus, frequencies close to the Nyquist frequency may be distorted in the sampling and reconstruction process, so the bandwidth should be kept below the Nyquist frequency by some margin ( frequency headroom ) that depends on the actual filters used.

Thus, dilation is a particular case of order statistics filters, returning the maximum value within a moving window ( the symmetric of the structuring function support B ).

Thus, using just truncation in the time domain, or equivalently low-pass filters in the frequency domain, one can cut out any convex set in time-frequency space ; just using time domain or frequency domain methods without fractional Fourier transforms only allow cutting out rectangles parallel to the axes.

Thus, advanced equalization filters can be avoided.

Thus, the early color TVs used only notch filters, which cut the luminance off at 3. 5 MHz.

Thus in regard to secretion, he showed that secretory glands, such as the submaxillary, are more than mere filters, and that their secretory action is attended by chemical and thermal changes both in themselves and in the blood passing through them.

Thus, an outdoors utility knife suited for camping or hunting might use a broad three to five-inch fixed blade, while a utility knife designed for the construction industry might feature a replaceable utility or razor blade for cutting packaging, cutting shingles, marking cut lines, or scraping paint.

Thus, many typical household applications already in existence like word processing and email were designed specifically to avoid using floating point operations.

Thus far, no key escrow system has been designed which meets both objections and nearly all have failed to meet even one.

Thus began one of the most famous apprenticeships in the musical theatre, as Hammerstein designed a kind of course for Sondheim on the construction of a musical.

Thus, it is possible to build the overall layout of a product before the parts are designed.

Thus, a battery designed to operate for at ( 77 ° F ) approximately would last only at ( 92 ° F ), and would last only at ( 107 ° F ).

Thus, a battery designed to operate for at ( 77 ° F ) would last at ( 113 ° F ).

Thus they may be more clearly designed for the entertainment of readers.

Thus regulation designed to implement public health and safety, or serve other legitimate state interests, but impact interstate commerce as an incident to that purpose, are subject to a test akin to the rational basis test, a minimum level of scrutiny.

Thus, engines designed to run high-octane fuel exclusively can achieve higher compression ratios.

Thus most game designs through the 1980s were designed through a hard-coded ruleset with a small amount of level and graphics data.

Thus, the Benedictbeurn Passion Play ( thirteenth century ) is still largely composed of Latin ritual sentences in prose and of church hymns, and, being designed to be sung, resembles an oratorio.

Thus, without having a separate brand from the now defunct company, Chrysler looked to re-brand the legacy vehicles inherited through the purchase of AMC instead of trying to fold those outside designed products into Chrysler's existing branch structure.

Thus, in 1649, when Louis XIV was still a child, an artisan named Camus designed for him a miniature coach, and horses complete with footmen, page and a lady within the coach ; all these figures exhibited a perfect movement.

Thus, the Governor Palace was designed by Italians, City Hall by Germans, etc.

Thus, many cryptosystems and security systems are designed with special emphasis on keeping human vulnerability to a minimum.

Thus, the contracts must be designed to ensure that each side is capable of performing the obligations set out.

Thus, there are hair salons that have well designed waiting areas often with magazines and plush sofas for patrons to read and relax while they await their turn.

Thus Interactive TV applications are often designed for the " 10-foot user interface " while PC applications and web pages are designed for the " 3ft user experience ".

Thus CA is neither designed for, nor aimed at, examining the production of interaction from a perspective that is external to the participants ' own reasoning and understanding about their circumstances and communication.

Thus, the more developed market economies agreed with the U. S. vision of post-war international economic management, which was to be designed to create and maintain an effective international monetary system and foster the reduction of barriers to trade and capital flows.

Thus the lower stage motors are designed for use at atmospheric pressure, while the upper stages can use motors suited to near vacuum conditions.

Thus a defensive building might be designed and built with battlements, or a manor house might be fortified by adding battlements, where no parapet previously existed, or cutting crenellations into its existing parapet wall.

Thus, the broadcast domain is the entire inter-connected layer two network, and the segments connected to each switch / bridge port are each a collision domain.

Thus the set of strings of length k in the domain is exactly the set of such strings already enumerated.

Thus an equivalence relation over X, a partition of X, and a projection whose domain is X, are three equivalent ways of specifying the same thing.

Thus a statement of the form is said to be true, under a particular interpretation, if there is some object in the domain of discourse of that interpretation that satisfies the predicate that the interpretation uses to assign meaning to the symbol Phil.

Thus, any periodic summation in the frequency domain can be represented by a Fourier series, whose coefficients are samples of a related continuous time function:

( Thus, a song that is in the public domain is free to play on the radio, regardless of who performs it or when it was performed.

Thus a " Conversation for Action " can be readily tracked and facilitated by a device with little or no ability to model circumstances in the real world other than the ability to register claims by specific agents about a domain.

Thus, the set of all real numbers,, cannot be its domain.

Thus, metaphor works by presenting a target set of meanings and using them to suggest a similarity between items, actions, or events in two domains, whereas metonymy calls up or references a specific domain ( here, removing items from the sea ).

Thus integrity of all three genres is applicable only to its domain.

Thus, eminent domain often invokes concerns of majoritarianism.

Thus free music is either in the public domain or licensed under a free license by the artist or copyright holder themselves, often as a method of promotion.

Thus a Dedekind domain is a domain which satisfies any one, and hence all four, of ( DD1 ) through ( DD4 ).

Thus these are precisely the class of domains for which Frac ( R )/ Prin ( R ) forms a group, the ideal class group Cl ( R ) of R. This group is trivial if and only if R is a PID, so can be viewed as quantifying the obstruction to a general Dedekind domain being a PID.

Thus, the Catholic Church accepts the ' priesthood of all believers ' doctrine – it is not the exclusive domain of Protestantism.

Thus, the domain of the " color-of-the-shape function " is the set of the four shapes, and the codomain consists of the five colors.

Thus once the domain of the first-order variables is established, the meaning of the remaining quantifiers is fixed.

Thus the C-terminal domain acts as an intein and a cholesterol transferase.

The category Top of topological spaces has as morphisms the continuous functions, where a function f is continuous if the inverse image f < sup > − 1 </ sup >( O ) of any open set in the codomain of f is open in the domain of f. Thus any continuous function f from a space X to a space Y defines an inverse mapping f < sup > − 1 </ sup > from Ω ( Y ) to Ω ( X ).

Thus, the ring of integers of Q (√ d ) is a principal ideal domain ( and hence a unique factorization domain ) if and only if the class number of Q (√ d ) is equal to 1.