Signals

Two analog signals $x_1(t)$ and $x_2(t)$ ($t$ in second), are sampled at a rate $F_s = 40$ Hz, where $x_1(t) = \cos(20\pi t)$, $t \ge 0$, and $x_2(t) = \cos(100\pi t)$, $t \ge 0$....

Consider a real signal x(t), -∞ < t <∞, such that x(t) = 0 for t <0, x(t) = 2 for 0 ≤ t < 1 and x(t) = 0 for t≥ 1. Let E[x(t)] = ∫_∞^[x(t)]^2dt. Which of the following options corr...

Consider a real baseband signal x(t) = e^{-2t}, for t (in seconds) ≥ 0. If 99% of energy of x(t) lies within B Hz, then which of the following options is TRUE for the value of B?

Let $x_1(t) = \cos(2\pi nt)$ and $x_2(t) = 2\sin(4\pi nt)$ represent two sinusoids for a positive integer $n$ and $-\infty < t < \infty$. Which of the following statements about $x...

A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t). A signal x(0.5t) is applied to another causal and stable LTI system with...

Consider two continuous time signals $x(t)$ and $y(t)$ as shown below If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is ________.

Let m(t) be a strictly band-limited signal with bandwidth B and energy E. Assuming ω₀ = 10B, the energy in the signal m(t) cos ω₀t is

The Fourier transform X(ω) of x(t) = e⁻ᵗ² is Note: ∫₋∞^∞ e⁻ʸ² dy = √π

Consider a discrete-time periodic signal with period N = 5. Let the discrete-time Fourier series (DTFS) representation be x[n] = $\sum_{k=0}^{4} a_k e^{\frac{jk2\pi n}{5}}$, where...

Let x1(t) and x2(t) be two band-limited signals having bandwidth B = 4π × 10³ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is

Let x1(t) = u(t + 1.5) - u(t - 1.5) and x2(t) is shown in the figure below. For y(t) = x1 (t) * x2 (t), the $\int_{-\infty}^{\infty}y(t)dt$ is ________ (rounded off to the nearest...

The Dirac delta Function $$\delta \left( t \right)$$ is defined as

Let $$\delta (t)$$ denote the delta function. The value of the the integral $$\int\limits_{ - \infty }^\infty {\delta (t)} \,\,\cos \left( {{{3\,\,t} \over 2}} \right)dt$$ is

The ACF of a rectangular pulse of duration T is