In the case of PSK, ASK or QAM, where the carrier frequency of the modulated signal is constant, the modulation alphabet is often conveniently represented on a constellation diagram, showing the amplitude of the I signal at the x-axis, and the amplitude of the Q signal at the y-axis, for each symbol.

In the digital QAM case, a finite number of at least two phases and at least two amplitudes are used.

Clenshaw – Curtis quadrature is essentially a change of variables to cast an arbitrary integral in terms of integrals of periodic functions where the Euler – Maclaurin approach is very accurate ( in that particular case the Euler – Maclaurin formula takes the form of a discrete cosine transform ).

Single-sideband has the mathematical form of quadrature amplitude modulation in the special case where one of the baseband waveforms is derived from the other, instead of being independent messages:

* Gaussian quadrature, a special case of numerical integration

The amplitude coefficients are usually represented by lower case r and t.

* Oscillate with a frequency smaller than in the non-damped case, and an amplitude decreasing with time ( underdamped oscillator ).

Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

As for the 50 Tg case involving one third of current nuclear arsenals, they said that the simulation " produced climate responses very similar to those for the 150 Tg case, but with about half the amplitude ," but that " the time scale of response is about the same.

The simplest case would be two electrons starting at A and B ending at C and D. The amplitude would be calculated as the " difference ",, where we would expect, from our everyday idea of probabilities, that it would be a sum.

The modulated waves are summed, and the resulting waveform is a combination of both phase-shift keying ( PSK ) and amplitude-shift keying ( ASK ), or ( in the analog case ) of phase modulation ( PM ) and amplitude modulation.

The amplitude of a wave may be constant ( in which case the wave is a c. w.

A more general representation of the wave equation is more complex, but the role of amplitude remains analogous to this simple case.

The amplitude may be constant ( in which case the wave is a continuous wave ) or may vary with time and / or position.

The probability amplitude for a photon from a monochromatic source to arrive at a certain final point at a given time, in this case, can be modeled as an arrow that spins rapidly until it is evaluated when the photon reaches its final point.

In the case of phase interference fading, the time distribution of the instantaneous field strength usually approximates a Rayleigh distribution when several signal components of equal amplitude are present.

Quality criteria for such circuits may include equalization for amplitude over a specified band of frequencies, or in the case of digital data transported via analogue circuits, may include equalization for phase.

A transverse wave is one in which the amplitude vector is orthogonal to k, which is the case for electromagnetic waves in an isotropic medium.

The interval between the 50 % points of the final amplitude is usually used to determine or define pulse duration, and this is understood to be the case unless otherwise specified.

In the second case, for waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy.

Many radio transmission sites have backup diesel generators — in the case of amplitude modulation ( AM ) radio transmitters, the load presented by the transmitter changes continuously and instantaneously with the signal level.

In the case of a longcase clock whose pendulum is about one metre in length and whose amplitude is ± 0. 1 radians, the θ < sup > 2 </ sup > term adds a correction to equation ( 1 ) that is equivalent to 54 seconds per day and the θ < sup > 4 </ sup > term a correction equivalent to a further 0. 03 seconds per day.

A common technique in signal processing is to consider the squared amplitude, or power ; in this case the resulting plot is referred to as a power spectrum.

In this case, Rayleigh fading is exhibited by the assumption that the real and imaginary parts of the response are modelled by independent and identically distributed zero-mean Gaussian processes so that the amplitude of the response is the sum of two such processes.

However, it is sometimes the case that it is simply the amplitude fluctuations that are of interest ( such as in the figure shown above ).

For the case of a carrier modulated by a single sine wave, the resulting frequency spectrum can be calculated using Bessel functions of the first kind, as a function of the sideband number and the modulation index.

In this case, modulation symbols ( rather than bits, characters, or data packets ) are asynchronously transferred.

It can also be viewed as a change of the frequency of the carrier signal, and phase modulation can thus be considered a special case of FM in which the carrier frequency modulation is given by the time derivative of the phase modulation.

# In this case we will use pulse-width modulation for a dynamically changing tone:

This must be taken into account by the demodulator ( and in the IF filtering ) in the case of certain types of modulation such as single sideband.

In the 10PASS-TS case the VDSL standard is utilized, which is based on the Discrete multi-tone modulation ( DMT ) scheme.

For example, in the case of QPSK modulation and AWGN channel, the BER as function of the Eb / N0 is given by:

# For parallel transmission with equal unit intervals and equal numbers of significant conditions on each channel, the DSR is ( m / T ) log < sub > 2 </ sub > n ; in the case of a two-condition modulation, this reduces to m / T.

In the case where an individual end-to-end telecommunications service is provided by parallel channels, the parallel-channel signaling rate is given by, where PCSR is the total signaling rate for m channels, m is the number of parallel channels, T < sub > i </ sub > is the minimum interval between significant instants for the I-th channel, and n < sub > i </ sub > is the number of significant conditions of modulation for the I-th channel.

In this case the carrier signals are referred to as subcarriers: an example is stereo FM transmission, where a 38 kHz subcarrier is used to separate the left-right difference signal from the central left-right sum channel, prior to the frequency modulation of the composite signal.

In the case of single-sideband modulation ( SSB ), the carrier is suppressed ( and in some forms of SSB, eliminated ).

The hierarchical modulation used on DVB is a unique case, which reduces the range of the full-definition signal, in exchange for an increase in the usable range of the lower-definition part of the video.

A lower bit rate may be chosen during the connection establishment phase due to adaptive modulation-slower but more robust modulation schemes are chosen in case of poor signal-to-noise ratio.

In the first case, a signal that is generated by means of a digital modulation method is considered as converted to an analog signal, while it is considered as a digital signal in the second case.

For the limited case of square or pulse wave signals, this is identical to true ring modulation.

Rudimentary pitch modulation could be achieved by altering the case of the letters — upper case letters being pronounced at a slightly higher pitch.