PYQs Based Test - 03 : Signals & Systems

The signum function is given by

sgn≤ft( x ) = ≤ft\{ {*20c x/≤ft| x |;x ≠ 0\\ 0;x = 0 } .

The Fourier series expansion of $sgn\left(cos\left(t\right)\right)$ has

Two discrete-time linear time-invariant systems with impulse responses

h ₁[n] = δ[n - 1] + δ[n + 1] and h ₂[n] = δ[n] + δ[n - 1] are connected in cascade, where δ[n] is the Kronecker delta. The impulse response of the cascaded system is

The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

A cascade system having the impulse response {_1}≤ft( ) = ≤ft\{ {*20l 1, - 1\\ } \} and {_2}≤ft( ) = ≤ft\{ {*20l {1,1}\\ } \} is shown in the figure below, where symbol ↑ denotes the time origin.



The input sequence x(n) for which the cascade system produces an output sequence ≤ft( ) = ≤ft\{ {*20l {1,2,1,- 1,- 2,- 1}\\ } \} is

For the periodic signal x(t) shown below with period T = 8s, the power in the 10${}^{th}$ harmonic is