Sine waves addition

The output is so much larger than the input that you can hardly see any variation on the input. We also notice that the output does look sinusoidal, but seems to be rounded at the top and narrowed at the bottom. The output is not really a pure sine wave and contains some distortion. Distortion means that the output of the amplifier contains frequencies not present in the input For a distortion-free amplifier, if we input a frequency of 1 kHz, the only frequency contained in the output will be 1 kHz. The output of our amplifier does not look like the input thus it contains additional frequencies not present in the input We have two ways to identify these frequencies using PSpice. 

In spite of the many successes of the phase vocoder, numerous problems have limited its use. In the applications of time-scale modification and compression, for example, it is assumed that only one sine wave enters each bandpass filter within the filter bank. When more than one sine wave enters a bandpass filter, the meaning of the input sine-wave amplitude and phase envelope is lost. A particular sine wave also may not be adequately estimated when it falls between two adjacent filters of the filter bank. In addition, sine waves with rapidly-varying frequency due to large vibrato or fast pitch change are difficult to track. A result of using a fixed filter bank is that the frequency of... 

In addition to FM signals with nested modulators, Justice also considered a class of signals modeled by a harmonic sum of sine waves with a slowly varying amplitude, typical of many speech and music sounds... 

The advantage of separating out the additive stochastic component is that the character of noise-like sounds is not modified with the time scale in particular, the noise may be stretched without the tonality that occurs in very large stretching of sine waves. On the other hand, the timbre of transient aharmonic sounds may be altered. In addition, component separation may suffer from a lack of fusion, unlike sine-wave modification which models all components similarly. One approach to improve fusion of the two components is to exploit the property that for many sounds the stochastic component is in synchrony with the deterministic component. In speech, for exam-... 

The braids were tested from — 100°C upwards at a heating rate of 1°C min 1 and a frequency of 1 Hz, using an inertial weight of 4.55 X 10 5 kg m2. The damped sine waves were processed by hand to give log decrement and modulus. The radius of the sample was calculated from the weight per unit length, as above, with the additional assumption that the sample was a right circular cylinder and that there were no voids in the sample. 

Figure 2.32 Damping/amplification of a sine wave electrode profile as a function ofthe applied current density normalized to the diffusion limited value. The numbers correspond to different dimensionless parameter inputs that define the relative strength of additive adsorption, consumption and transport.

Further, to allow for waveforms (or frequency components) that can increase or decrease over time (disturbance changing), we need to introduce an additional (real) exponential term eCTt. So whereas, when doing steady state analysis, we represent a sine wave in the form eJojt, now it becomes e0 x ci"jt = This is therefore a sine wave, but with an... 

Figure 1.35 (a) Combination of odd and even components yields a spectrum with cancellation of signals through the addition of opposite-phased signals, (b) Sine waves are odd, and cosine waves are even. (Reprinted from E. Derome, Modem NMR techniques for chemistry research, copyright 1987, pp. 78-79, with permission from Pergamon Press Ltd., Headington Hill Hall, Oxford 0X3 OBW, U.K.)... 

One more topie to briefly diseuss relates to objeets with very many highly resonant modes. These objeets, when struek, ean makes sounds that vibrate in odd ways. For example, the struek prayer bowl exhibits beating, whieh is the interferenee of modes that are elose together in frequeney. For fun, add sin(7i0 and sin(l. 01 TiO and look at the result. What you aetually end up seeing instead of the addition of two sine waves is instead sin(1.0057iO eos(O.Ol7i05 the... 

In addition to vectors in the space domain, vectors may also be defined in the time domain, in particular rotating vectors with a fixed initial point at the origin of a Cartesian coordinate system. A variable such as the electric field strength may be a vector both in time and space. Every space vector may also be a time vector, and often it is not clear what sort of vector an author actually is dealing with. Vectors in the time domain are used for sine waves when the maxima do not occur simultaneously. These two-dimensional (planar) time vectors are more conveniently represented by complex numbers. 

The harmonic pattern of a full wave diode bridge is well known and well documented in literature. In the diagram of Figure 2, six diodes are used for full wave rectification of a three phase AC supply, feeding the intermediate DC circuit of a VFD. The AC current will exhibit a 6 pulse pattern, resulting from each half of the AC sine wave conducting via a particular diode. This AC current does not have a pure sinusoidal shape anymore it now includes the combination of a fundamental component (50 or 60 Hz) to which additional frequencies are superimposed. 

Figure 5 illustrates the concept of such a switched type converter. Power flow to/from the DC circuit is achieved by proper sequencing and timing of the power switches in relation to the AC supply sine wave. One of the additional benefit here is the inherent ability to regenerate power back to the AC network if required by the driven process terms such as regenerative electrical braking, 4 Quadrant operation etc. are used to qualify this feature of the AFE. 

The horizontal EW and vertical UD components of accelerations recorded at the Wolong seismic station during the 2008 Wenchuan earthquake are scaled for the model loading inputs. The EW and UD components had the dominant frequency of 2.4 Hz and 8.1 Hz, respectively. Based on the recorded accelerations on the shaking table, the excitation frequencies of the horizontal and vertical components are 9.6 Hz (about 4 times of EW-component wave) and 44.3 Hz (about 5 times of UD-component wave). The model slopes are excited, respectively, by the above horizontal (X-direction in Fig. 2), vertical (Z-direction in Fig. 2) waves and their combinations (XZ-direction in Fig. 2). Figure 3 illustrates the time history of horizontal input motion scaled from the EW-component wave and the calculated Fourier amplitude spectrum on the shaking table. In addition, sine waves distinguished by frequency from 5 to 15 Hz are also used to excite the models. 

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