The outputs of four systems (S1, S2, S3 and S4) corresponding to the input signal sin(t), for all time t, are shown in the figure.
Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?
For a vector $$\overline x $$ = [x[0], x[1], ....., x[7]], the 8-point discrete Fourier transform (DFT) is denoted by $$\overline X $$ = DFT($$\overline x $$) = [X[0], X[1], ....., X[7]], where
$$X[k] = \sum\limits_{n = 0}^7 {x[n]\exp \left( { - j{{2\pi } \over 8}nk} \right)} $$.
Here, $$j = \sqrt { - 1} $$. If $$\overline x $$ = [1, 0, 0, 0, 2, 0, 0, 0] and $$\overline y $$ = DFT (DFT($$\overline x $$)), then the value of y[0] is __________ (rounded off to one decimal place).
Mr. X speaks ____________ Japanese ___________ Chinese.
A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets Rs. 1000 more than S, what is the share of Q (in Rs.) ?