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

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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