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Acos ˆ + 2 l n + = Acos ˆ n ++2 ln = A cos ˆ n + A cos 2 l – ˆ n – = A cos 2 ln – ˆ n –

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Aperiodic Signal: Fourier Integral Figure 3.1 Construction of a periodic signal by periodic extension of g(t) 14 Find the inverse Fourier transform of (a) Cosine signal and (b) its Fourier spectrum. Energy of Modulated Signals Energy spectral densities of (a) modulating and (b) modulated signals.

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Signal SIN+ A+ Green 10 16 4 9 14 9 11 3 Green SIN- A- Yellow 11 17 5 1 6 1 12 9 Yellow COS+ B+ Blue 3 18 6 10 13 10 13 4 Blue COS- B- Red 4 19 7 2 5 2 14 10 Red Reference Signal REF+ Z+ Purple 5 8 8 3 12 3 7 7 Purple REF- Z- Gray 6 9 9 11 4 11 8 8 Gray Shield Case 1/Case Case Case Case

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If a signal is neither a power signal nor an energy signal, so designate it. Sketch each signal (α is a positive constant). 1 2 (a) ( ) 2sin(8 /4) (b) ( ) ( )t xt t xt eu tα = π+π =− 3. (Fourier series) Using the uniqueness property of the Fourier series, find exponential Fourier series for the following signal: 2 x() sin ( )cos(2 )tt ... a high resonant frequency- large transition energy difference- greater Boltzmann population difference high magnetic moment and hence a stronger signal high rate of precession which induces a greater signal in the detection coil So, the strength of NMR signal is proportional to 3 Noise increases a square-root of observed frequency} S/N 5/2

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The 3D-DCT is based on a set of cosine basis functions which are determined by the dimensions of the 3D signal and thus independent of the input video data. In addition, the 3D-DCT can generate a compact energy spectrum whose high-frequency coefficients are sparse if the appearance samples are similar. 16/5/2017 · Energy Signals • A signal can be categorized into energy signal or power signal: • An energy signal has a finite energy, 0 < E < ∞. • In other words, energy signals have values only in the limited time duration. • For example, a signal having only one square pulse is energy signal. • A signal that decays exponentially has finite ...