Recent questions tagged fourier-transform

The continuous time signal $x(t)$ is real, periodic with period $T$ and satisfies the Dirichlet conditions.The Fourier series representation of $x(t)=\sum_{-\infty}^{\inf...

Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $\left[-\omega_{c}, \omega_{c}\right]$, where $\ome...

Let $f(t)$ be a periodic signal with fundamental period $T_{0}>0$. Consider the signal $y(t)=f(\alpha t)$, where $\alpha>1$.The Fourier series expansions of $f(t)$ and $y...

The Fourier transform $X(\omega)$ of $x(t)=e^{-t^{2}}$ isNote: $\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}$$\sqrt{\pi} e^{\frac{\omega^{2}}{2}}$$\frac{e^{-\frac{\o...

Consider a discrete-time periodic signal with period $N=5$. Let the discrete-time Fourier series $\text{(DTFS}$) representation be $x[n]=\sum_{k=0}^4 a_k e^{\frac{j k 2 \...

The two-dimensional Fourier transform of a function $f(t, s)$ is given by\[F(\omega, \theta)=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(t, s) \exp (-j \omega t) \e...

The Fourier transform of\[x(t)=\frac{t^{n-1}}{(n-1) !} \mathrm{e}^{-a t} u(t), \quad a>0\]$(\jmath=\sqrt{-1}, u(t)=1$ for $t \geq 0, u(t)=0, t<0)$ is$(a+\jmath \omega)^{n...

Let $x(t)$ be a signal whose Fourier transform $X(f)$ is zero for $|f|>W$. Using a sampler with sampling frequency $4 W$, which of the following filters can be used to ex...

Statement of Linked Answer Questions $85 a$ and $85b$A sequence $x(n)$ has non-zero values as shown in the figureThe Fourier transform of $y(2 n)$ will be$e^{-j2w} [\cos ...

The function $f(t)$ has the Fourier Transform $g(\omega)$. The Fourier Transform$f f(t) g(t)\left(=\int_{-\infty}^{\infty} g(t) e^{-j \omega t} d t\right)$ is$\frac{1}{2 ...

If the Fourier Transform of deterministic signal $\mathrm{g}(\mathrm{t})$ is $\mathrm{G}(f)$, then(1) The Fourier Transform of $g(t-2)$ is$G(f) e^{-j(4 \pi f)}$(2) The Fo...

The Fourier Transform of the signal $x(t)=\mathrm{e}^{-3 \mathrm{t}^{2}}$ is of the following form, where $A$ and $B$ are constants$\mathrm{A} e^{-\mathrm{B}|f|}$$\mathrm...

One period $(0, T)$ each of two periodic waveforms $W_{1}$ and $W_{2}$ are shown in figure. The magnitudes of the $n$th Fourier series coefficients of $W_{1}$ and $W_{2}$...

A bandlimited signal $x(t)$ with $a^{\prime}$ spectrum $X(f)$ as shown in first figure is processed as shown in second figure is $p(t)$ is a periodic train of impulses as...

A signal $x(t)$ has a Fourier transform $X(\omega)$. If $x(t)$ is a real and odd function of $t$, then $X(\omega)$ isa real and even function of $\omega$a imaginary and o...

The Fourier series representation of an impules train denoted by\[s(t)=\sum_{n=-\infty}^{n} d\left(t-n \mathrm{~T}_{0}\right) \text { is given by }\]$\frac{1}{\mathrm{~T}...

The Fourier transform $G(\omega)$ of the signal $g(t)$ in the figure, given as $G(w)=\frac{1}{\omega^{2}}\left(\mathrm{e}^{j \omega}-j w e^{j \omega}-1\right)$. Using thi...

Which of the following cannot be the Fourier series expansion of a periodic signal ?$x(t)=2 \cos t+3 \cos 3 t$$x(t)=2 \cos \pi t+7 \cos t$$x(t)=\cos t+0.5$$x(t)=2 \cos 1....

The Fourier transform $\mathrm{F}\left\{e^{-t} u(t)\right\}$ is equal to $\frac{1}{1+j 2 \pi f}$. Therefore, $\mathrm{F}\left\{\frac{1}{1+j 2 \pi t}\right\}$ is$e^f u(f)$...

The Fourier transform of a function $x(t)$ is $\mathrm{X}(f)$. The Fourier transform of $\frac{d \mathrm{X}(f)}{d f}$ will be$\frac{dX(f)}{d f}$$j 2 \pi f X(f)$$jf X(f)$$...

The Fourier transform of a voltage signal $x(t)$ is $X(f)$. The unit of $|X(f)|$ isvoltvolt-secvolt/secvolt $^{2}$

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...

The Fourier transform of a conjugate symmetric function is alwaysimaginaryconjugate anti-symmetricrealconjugate symmetric

Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure.Then $Y(f)$ is$-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}...

Consider a system shown in the figure. Let $X(f)$ and $Y(f)$ denote the Fourier transforms of $X(t)$ and $y(t)$ respectively. The ideal HPF has the cutoff frequency $10 \...

Let $x(n)=\left(\frac{1}{2}\right)^{n} u(n), y(n)=x^{2}(n)$ and $\mathrm{Y}\left(e^{j i e}\right)$ be the Fourier transform of $y(n)$. Then $Y\left(e^{j i e}\right)$ is$\...

Match the following and choose the correct combination.$$\begin{array}{ll} \qquad \qquad \quad \textbf{Group 1} & \quad \qquad \qquad \qquad \qquad \textbf{Group 2} \\ \t...

For a signal $x(f)$ the fourier transform is $X(f)$. Then the inverse Fourier transform of $X(3 f+2)$ is given by$\frac{1}{2 x}\left(\frac{t}{2}\right) e^{j 3 \pi t}$$\fr...