Signal Processing MCQ Questions & Answers | ECE

A signal containing only two frequency components (3 kHz and 6 kHz) is sampled at the rate of 8 kHz, and then passed through a low pass filter with a cut-off frequency of 8 kHz. The filter output

If the signal $$x\left( t \right) = {{\sin \left( t \right)} \over {\pi t}} * {{\sin \left( t \right)} \over {\pi t}}$$     with $$ * $$ denoting the convolution operation, then x(t) is equal to

A sequence x(n) with the z-transform X(z) = z⁴ + z² - 2z + 2 - 3z^-4 is applied as an input to a linear, time-invariant system with the impulse response h(n) = 2δ(n - 3) where
$$\delta \left( n \right) = \left\{ {\matrix{ {1,} & {n = 0} \cr {0,} & {{\rm{otherwise}}} \cr } } \right.$$
The output at n = 4 is

The Laplace transform of i(t) is given by $$I\left( s \right) = {2 \over {s\left( {1 + s} \right)}}$$
As t → ∞, the value of i(t) tends to

A real-valued signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$  is passed through a linear time invariant system whose frequency response is $$H\left( f \right) = \left\{ {\matrix{ {{e^{ - j4\pi f,}}} & {\left| f \right| \le {W \over 2}} \cr {0,} & {\left| f \right| > {W \over 2}} \cr } } \right.$$
The output of the system is

The signal x(t) = sin(14000πt), 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(t) as follows:
\[H\left( f \right) = \left\{ {\begin{array}{*{20}{c}} {1,}&{\left| f \right| \leqslant 12kHz} \\ {0,}&{\left| f \right| > 12kHz} \end{array}} \right.\]
What is the number of sinusoids in the output and their frequencies in kHz?

A signal $$2\cos \left( {{{2\pi } \over 3}t} \right) - \cos \left( {\pi t} \right)$$     is the input to an LTI system with the transfer function $$H\left( s \right) = {e^s} + {e^{ - s}}$$
If C_k denote the k^th coefficient in the exponential Fourier series of the output signal, then C₃ is equal to

Let $$g\left( t \right) = {e^{ - \pi {t^2}}}$$  and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the output is

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is

The result of the convolution
x(- t) ^∗ δ(- t - t₀) is