Because its operations involve only real coefficients until the last computation stage, it was initially proposed as a way to efficiently compute the discrete Fourier transform ( DFT ) of real data.

Because the frequencies in the quantum motion are not multiples of a common frequency, the matrix elements cannot be interpreted as the Fourier coefficients of a sharp classical trajectory.

In general, S denotes the set of all polynomial expressions in α with coefficients in S, which is the smallest ring containing α and S. Because α satisfies this quadratic equation, the required polynomials can be limited to degree one.

Because of its simple structure the equation can be replaced with an equivalent equation with constant coefficients which can then be solved explicitly.

Because tungsten and quartz have different coefficients of thermal expansion, the tungsten electrodes are welded to strips of pure molybdenum metal or Invar alloy, which are then melted into the quartz to form the envelope seal.

Because of metamerism one cannot, in the general case of non zero deviation coefficients, estimate the original spectrum from the L < sup >*</ sup > a < sup >*</ sup > b < sup >*</ sup > values reported by the ASBC method.

Because computer technology is rapidly advancing it is often possible to offer more features in a digital synthesizer than in an analog synthesizer at a given price.

Because digital communications are generally error-free, copies of copies can be made indefinitely.

Because RTTY, using either AFSK or FSK modulation, produces a waveform with constant power, a transmitter does not need to use a linear amplifier, which is required for many digital transmission modes.

Because of its fundamental role in carrying a single phone call, the DS0 rate forms the basis for the digital multiplex transmission hierarchy in telecommunications systems used in North America.

Because of all these advantages, and because recent advances in wideband communication channels and solid-state electronics have allowed scientists to fully realize these advantages, digital communications has grown quickly.

Because of this correspondence, digital signatures are often described as based on public-key cryptosystems, where signing is equivalent to decryption and verification is equivalent to encryption, but this is not the only way digital signatures are computed.

Because channel 9A is not used for television services in or near Sydney, Melbourne, Brisbane, Adelaide or Perth, digital radio in those cities are broadcast on DAB frequencies blocks 9A, 9B and 9C.

Because of the differences in international broadcasting, these copies had been converted to the North American NTSC television standard, and so one chunk of the series remained in its native PAL format, but the majority were found in a poorly-converted ( dating long before digital conversion methods ) NTSC state.

Because of the complexity of the optimization algorithms, most adaptive filters are digital filters.

Because 70mm film and projectors are costly and difficult to mass produce, IMAX debuted a digital projection system in 2008.

Because PGP and implementations allow the use of e-mail digital signatures for self-publication of public-key information, it is relatively easy to implement one's own web of trust.

Because of the uptake of alternative photographic materials, its complex processing requirements, and the widespread transition to digital photography, Kodachrome lost its market share, its manufacturing was discontinued in 2009 and its processing ended in 2010.

Because of this, the FCC requires U. S. TV stations to replicate their analog coverage with their digital signal as well.

Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices such as mobile phones.

Because they vary in size, they can also be found on personal digital assistants ( PDAs ) and some portable media players.

Because of the possibility to create new tapes with DCC-Studio, regardless of the source they were recorded from, the DCC-175 / PC-Link cable / DCC-Studio combination effectively circumvented the SCMS copy protection scheme that all digital audio recording devices for consumers are supposed to have.

Because digital devices are able to simulate an almost limitless variety of real reverberant spaces, as well as replicating the classic tape-based echo effects, physical echo chambers fell into disuse.

Because it has been extremely difficult to carry out DSP operations ( for example performing EQ, balance, panning and other changes in the digital domain ) in a 1-bit environment, and because of the prevalence of studio equipment such as Pro Tools, which is solely PCM-based, the vast majority of SACDs — especially rock and contemporary music which relies on multitrack techniques — are in fact mixed in PCM ( or mixed analog and recorded on PCM recorders ) and then converted to DSD for SACD mastering.

Because these samples are now usually stored in digital memory the information can be quickly accessed.

Because any detector ( eye, film, digital ) used to observe the diffraction pattern can have an intensity threshold for detection, the full diffraction pattern may not be apparent.

Because Somerset currently does not have its own DAB multiplex, the station cannot be heard on digital radio.

Because LPTV stations have already had their limited financial resources drained by having to buy and install new digital equipment, it is unlikely that any LPTV stations will be seen on mobile TV because of this waiver, which also applies to other companies.

Because of this, the term " IR filters " is commonly used to refer to filters that pass infrared light while completely blocking other wavelengths.

Because the wavelengths at which the images were taken do not correspond to the wavelengths of red, green and blue light, the colours in the final image only give an approximate representation of the actual colours of the galaxies in the image ; the choice of filters for the HDF ( and the majority of Hubble images ) was primarily designed to maximize the scientific utility of the observations rather than to create colours corresponding to what the human eye would actually perceive.

Because of that, very steep low-pass filters are used on frequencies above 20 kHz ( the theoretical limit of human hearing ) that may introduce slight distortions into the audible-range signal.

Because of the passband ripple inherent in Chebyshev filters, the ones that have a smoother response in the passband but a more irregular response in the stopband are preferred for some applications.

Because of this blurring, linear filters are seldom used in practice for noise reduction ; they are, however, often used as the basis for nonlinear noise reduction filters.

Because collaborative filters recommend products based on sales or ratings, they cannot usually recommend products with limited historical data.

Because of this, roofing filters are usually crystal filter types.

Because of the nature of plants, oxygen is added to the water as it filters, while nitrogen is removed.

Because the detector is about equally sensitive to EUV and visible photons, and the Sun is about one billion ( 10 < sup > 9 </ sup >) times brighter in visible light than in EUV, special thin foil filters are used to block the visible light while admitting the EUV.

Because unwanted wavelengths are reflected rather than absorbed, dichroic filters do not absorb this unwanted energy during operation and so do not become nearly as hot as the equivalent conventional filter ( which attempts to absorb all energy except for that in the passband ).

* Because light in the stopband is reflected rather than absorbed, there is much less heating of the dichroic filter than with conventional filters

Because of the transparency of glass, the internal stress within these objects can be demonstrated by viewing them through polarizing filters.

Because neutral-gray linear-polarizing filters are easily manufactured, correct color rendition is possible.

Because of the many measurements needed, the amount of time needed to find the shape of a person's auditory filters is very long.

Because most room correction filters are acausal, there is some delay.

Because the Technicolor camera divided the lens image into two beams to expose two film frames simultaneously through color filters, and at twice the normal frames per second, much higher lighting levels were needed.