to h(t), then the Fourier transform of the output is" class="read-more button" href="https://exam.pscnotes.com/mcq/let-gleft-t-right-e-pi-t2-and-ht-is-a-filter-matched-to-gt-if-gt-is-applied-as-input-to-ht-then-the-fourier-transform-of-the-output-is/#more-54947">Detailed SolutionLet $$g\left( t \right) = {e^{ – \pi {t^2}}}$$ 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
output (BIBO) stable system with a pole in the right half of the complex plane. 2. There is no causal and BIBO stable system with a pole in the right half of the complex plane. Which one among the following is correct?
x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in the figure. Then Y(f) is" class="read-more button" href="https://exam.pscnotes.com/mcq/let-xt-and-yt-with-fourier-transforms-xf-and-yf-respectively-be-related-as-shown-in-the-figure-then-yf-is/#more-54340">Detailed SolutionLet x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in the figure. Then Y(f) is
\end{array}} \right]\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right]\] where, $${W_3} = {e^{i\frac{{2\pi }}{3}}}.$$ If another sequence [p, q, r] is derived as, \[\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right] = \] \[\left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^1}&{W_3^2} \\ 1&{W_3^2}&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&{W_3^2}&0 \\ 0&0&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {A/3} \\ {B/3} \\ {C/3} \end{array}} \right]\] then the relationship between the sequences [p, q, r] and [a, b, c] is" class="read-more button" href="https://exam.pscnotes.com/mcq/two-sequences-a-b-c-and-a-b-c-are-related-as-left-beginarray20c-a-b-c-endarray-right-left-beginarray20c-111-1w_3-1w_3/#more-54045">Detailed Solution
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class="screen-reader-text">Two sequences [a, b, c] and [A, B, C] are related as, \[\left[ {\begin{array}{*{20}{c}} A \\ B \\ C \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^{ – 1}}&{W_3^{ – 2}} \\ 1&{W_3^{ – 2}}&{W_3^{ – 4}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right]\] where, $${W_3} = {e^{i\frac{{2\pi }}{3}}}.$$ If another sequence [p, q, r] is derived as, \[\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right] = \] \[\left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^1}&{W_3^2} \\ 1&{W_3^2}&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&{W_3^2}&0 \\ 0&0&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {A/3} \\ {B/3} \\ {C/3} \end{array}} \right]\] then the relationship between the sequences [p, q, r] and [a, b, c] is
is real for all n” option2=”h[n] is purely imaginary for all n” option3=”h[n] is real for only even n” option4=”h[n] is purely imaginary for only odd n” correct=”option1″]
the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude" class="read-more button" href="https://exam.pscnotes.com/mcq/the-pole-zero-diagram-of-a-causal-and-stable-discrete-time-system-is-shown-in-the-figure-the-zero-at-the-origin-has-multiplicity-4-the-impulse-response-of-the-system-is-hn-if-h0-1-we-can-con/#more-53338">Detailed SolutionThe pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude
following type" class="read-more button" href="https://exam.pscnotes.com/mcq/the-pole-zero-pattern-of-a-certain-filter-is-shown-in-figure-the-filter-must-be-of-the-following-type/#more-53149">Detailed SolutionThe pole-zero pattern of a certain filter is shown in figure. The filter must be of the following type
\left( {{{{\omega _0}} \over Q}} \right)s + \omega _0^2}}$$" class="read-more button" href="https://exam.pscnotes.com/mcq/specify-the-filter-type-if-its-voltage-transfer-function-hs-is-given-by-hleft-s-right-kleft-s2-1omega-_02-right-over-s2-left-omega-_0-over-q-rig/#more-53148">Detailed SolutionSpecify the filter type if its voltage transfer function H(s) is given by $$H\left( s \right) = {{K\left( {{s^2} + 1\omega _0^2} \right)} \over {{s^2} + \left( {{{{\omega _0}} \over Q}} \right)s + \omega _0^2}}$$
the system is" class="read-more button" href="https://exam.pscnotes.com/mcq/consider-the-system-shown-in-the-figure-below-the-transfer-function-fracyleft-z-rightxleft-z-right-of-the-system-is/#more-52902">Detailed SolutionConsider the system shown in the figure below. The transfer function $$\frac{{Y\left( z \right)}}{{X\left( z \right)}}$$ of the system is