The signal x(t) = $$\sin \,(14000\,\pi t)$$, where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response H(f) as following: $$H(f) = \left\{ {\matrix{ {1,} & {\left| f \right| \le \,12\,kHz} \cr {0,} & {\left| f \right| > \,12\,kHz} \cr } } \right.$$

What is the number of sinusoids in the output and their frequency inkHz?

Consider a continuous-time signal defined as $$x(t) = \left( {{{\sin \,(\pi t/2)} \over {(\pi t/2)}}} \right)*\sum\limits_{n = - \infty }^\infty {\delta (t - 10n)} $$ Where ' * ' denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in samples/sec) for x(t) is __________________.

The Nyquist sampling rate for the signal $$s(t) = {{\sin \,(500\pi t)} \over {\pi \,t}} \times {{\sin \,(700\pi t)} \over {\pi \,t}}$$ is given by

The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without distortion $$x(t) = 5{\left( {{{\sin \,\,2\,\pi \,1000\,t)} \over {\pi \,t}}} \right)^3} + 7{\left( {{{\sin \,\,2\,\pi \,1000\,t} \over {\pi \,t}}} \right)^2}$$

would be