= {e^{ – 3t}}u\left( t \right)$$ Where u(t) is the unit step function. Which of these systems is time invariant, causal, and stable?" class="read-more button" href="https://exam.pscnotes.com/mcq/the-impulse-response-functions-of-four-linear-systems-s1-s2-s3-s4-are-given-respectively-by-h_1left-t-right-1-h_2left-t-right-uleft-t-right-h_3left-t-ri/#more-58144">Detailed SolutionThe impulse
response functions of four linear systems S1, S2, S3, S4 are given respectively by $${h_1}\left( t \right) = 1,$$ $${h_2}\left( t \right) = u\left( t \right),$$ $${h_3}\left( t \right) = \frac{{u\left( t \right)}}{{t + 1}},$$ $${h_4}\left( t \right) = {e^{ – 3t}}u\left( t \right)$$ Where u(t) is the unit step function. Which of these systems is time invariant, causal, and stable?
href="https://www.youtube.com/channel/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1" target="_blank" class="youtube-subscribe-button"> Subscribe on YouTube
button" href="https://exam.pscnotes.com/mcq/the-amplitude-spectrum-of-a-gaussian-pulse-is/#more-57949">Detailed SolutionThe amplitude spectrum of a Gaussian pulse is
following options is" class="read-more button" href="https://exam.pscnotes.com/mcq/a-stable-linear-time-invariant-lti-system-has-a-transfer-function-hleft-s-right-1-over-s2-s-6-to-make-this-system-causal-it-needs-to-be-cascaded-with-another-lti-system-hav/#more-57354">Detailed SolutionA stable linear time invariant (LTI) system has a transfer function $$H\left( s \right) = {1 \over {{s^2} + s – 6}}.$$ To make this system causal it needs to be cascaded with another LTI system having a transfer function H1(s). A correct choice for H1(s) among the following options is
response y(t) of the system given below to a unit step input u(t) is \[\xrightarrow{{U\left( s \right)}}\boxed{\frac{1}{s}}\xrightarrow{{Y\left( s \right)}}\]
u(t) are respectively," class="read-more button" href="https://exam.pscnotes.com/mcq/the-function-xt-is-shown-in-the-figure-even-and-odd-parts-of-a-unit-step-function-ut-are-respectively/#more-57173">Detailed SolutionThe function x(t) is shown in the figure. Even and odd parts of a unit-step function u(t) are respectively,
tu(t) and u(t)sin(t) are respectively" class="read-more button" href="https://exam.pscnotes.com/mcq/laplace-transforms-of-the-functions-tut-and-utsint-are-respectively/#more-57047">Detailed SolutionLaplace transforms of the functions tu(t) and u(t)sin(t) are respectively
\[x\left[ n \right] = {c_1}\exp \left( { – \frac{{j\pi n}}{2}} \right) + {c_2}\exp \left( {\frac{{j\pi n}}{2}} \right),\] Where c1 and c2 are arbitrary real numbers. The desired three-tap filter is given by h[0] = 1, h[1] = a, h[2] = b and h[n] = 0 for n < 0 or n > 2. What are the values of the filter taps a and b if the output is y[n] = 0 for all n, when x[n] is as given above? \[\xrightarrow{{x\left[ n \right]}}\boxed{\begin{array}{*{20}{c}} {n = 0} \\ \downarrow \\ {h\left[ n \right] = \left\{ {1,a,b} \right\}} \end{array}}\xrightarrow{{y\left[ n \right] = 0}}\]" class="read-more button" href="https://exam.pscnotes.com/mcq/it-is-desired-to-find-three-tap-causal-filter-which-gives-zero-signal-as-an-output-to-and-input-of-the-form-xleft-n-right-c_1exp-left-fracjpi-n2-right-c_2exp/#more-56949">Detailed SolutionIt is desired to find three-tap causal filter which gives zero signal as an output to and input of the form \[x\left[ n \right] = {c_1}\exp \left( { – \frac{{j\pi n}}{2}} \right) + {c_2}\exp \left( {\frac{{j\pi n}}{2}} \right),\] Where c1 and c2 are arbitrary real numbers. The desired three-tap filter is given by h[0] = 1, h[1] = a, h[2] = b and h[n] =
0 for n < 0 or n > 2. What are the values of the filter taps a and b if the output is y[n] = 0 for all n, when x[n] is as given above? \[\xrightarrow{{x\left[ n \right]}}\boxed{\begin{array}{*{20}{c}} {n = 0} \\ \downarrow \\ {h\left[ n \right] = \left\{ {1,a,b} \right\}} \end{array}}\xrightarrow{{y\left[ n \right] = 0}}\]