Recent questions tagged convolution

Let $\mathrm{x}_1(\mathrm{t})=\mathrm{u}(\mathrm{t}+1.5)-\mathrm{u}(\mathrm{t}-1.5)$ and $\mathrm{x}_2(\mathrm{t})$ is shown in the figure below. For $\mathrm{y}(\mathrm{...

Let $x(n)=\sin (2 \pi k n / N), n=0,1, \ldots, N-1$, where $2 k \neq N$ and $0<k \leq N-1$. Then the circular convolution of $\{x(n)\}$ with itself is$N \cos (4 \pi k n /...

Let $u(t)$ be the unit step function that takes value $1$ for $t \geq 0$ and is zero otherwise. Let $f(t)=e^{-t} u(t)$ and $g(t)=u(t) u(1-t)$. Then the convolution of $f(...

Consider a triangular shaped pulse $x$ of base $2 T$ and unit height centered at $0$ , i.e. $x(t)=0$ for $|t|>T, x(t)=1-|t|$ for $t \in[-T, T]$. Then if $x$ is convolved ...

If we convolve $\sin (t) / t$ with itself, then we get$C \sin (t) / t$ for some constant $C$$C \cos (t) / t$ for some constant $C$$C \cos (t) / t^{2}$ for some constant $...

Recall that\[\operatorname{sinc}(t)=\frac{\sin (\pi t)}{\pi t}\]and convolution of functions $x(t)$ and $y(t)$ is defined as\[x(t) \star y(t)=\int_{-\infty}^{\infty} x(t-...

Convolution between two functions $f(t)$ and $g(t)$ is defined as follows: $f(t) * g(t)=$ $\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$. If $f(t) * g(t)=h(t)$, what ...

Let $u(t)$ be the step function. Which of the Waveforms in given figure, $(a)$ - $(d)$ corresponds to the convolution of $u(t)-u(t-1)$ with $u(t)-u(t-2)$ ?

Consider a rectangular pulse $g(t)$ existing between $t=-\frac{T}{2}$ and $t=-\frac{T}{2}$. Find and sketch the pulse obtained by convolving $g(t)$ with itself. The Fouri...

A rectangular pulse train $s(t)$ as shown in the figure is convolved with the signal $\cos ^{2}\left(4 p \times 10^{3} t\right)$. The convolved signal will be a$\text{DC}...

(A) Fourier transform of a Gaussian function(B) Convolution of a Rectangular pulse with itself(C) Current through an inductor for a step input voltageGaussian function Re...

Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function.If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x_{2}...

Consider a continuous-time signal defined as$$x(t)=\left(\dfrac{\sin(\pi t/2)}{(\pi t /2)}\right)\ast \sum _{n=-\infty}^{\infty}\delta(t-10n)$$where $’\ast’$ denotes the ...

The result of the convolution $x(-t) * \delta (-t-t_0)$ is$x(t+t_0)$$x(t-t_0)$$x(-t+t_0)$$x(-t – t_0)$

Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(\frac{1}{2})^nu[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y =\frac{1}{2}$, then $g $ equa...