The Fourier transform $$G(\omega )$$ of the signal g(t) in Fig.(1) is given as
$$G(\omega ) = {1 \over {{\omega ^2}}}({e^{j\omega }} - j\omega {e^{j\omega }} - 1)$$.

Using this information, and the time-shifting and time-scaling properties, determine and Fourier transform of signals in Fig (2), (3) and (4).

Let $$\delta (t)$$ denote the delta function. The value of the the integral $$\int\limits_{ - \infty }^\infty {\delta (t)} \,\,\cos \left( {{{3\,\,t} \over 2}} \right)dt$$ is

A base band signal g(t) band limited to 100 Hz modulates a carrier of frequency $${{f_0}}$$ Hz. The modulated signal g(t) $$\cos 2\,\pi \,{f_0}t$$ is transmitted over a channel whose input x and output y are related by $$y = 2x + {x^2}$$. The spectrum of g(t) is shown in Fig. Sketch the spectrum of the transmitted signal and the spectrum of the received signal.

The Nyquist sampling interval, for the signal Sinc(700t) + Sinc(500t) is