Let a causal LTI system be governed by the following differential equation $$y(t) + {1 \over 4}{{dy} \over {dt}} = 2x(t)$$, where x(t) and y(t) are the input and output respectively. Its impulse response is

Let an input x(t) = 2 sin(10$$\pi$$t) + 5 cos(15$$\pi$$t) + 7 sin(42$$\pi$$t) + 4 cos(45$$\pi$$t) is passed through an LTI system having an impulse response,

$$h(t) = 2\left( {{{\sin (10\pi t)} \over {\pi t}}} \right)\cos (40\pi t)$$

The output of the system is

Consider the system as shown below:

where y(t) = x(e^t). The system is

The discrete time Fourier series representation of a signal x[n] with period N is written as $$x[n] = \sum\nolimits_{k = 0}^{N - 1} {{a_k}{e^{j(2kn\pi /N)}}} $$. A discrete time periodic signal with period N = 3, has the non-zero Fourier series coefficients : a_$$-$$3 = 2 and a₄ = 1. The signal is