Fourier Transform · Signals and Systems · GATE ECE

Let $$m(t)$$ be a strictly band-limited signal with bandwidth B and energy E. Assuming $${\omega _0} = 10B$$, the energy in the signal $$m(t)\cos {\om...

The Fourier transform $$x(\omega )$$ of $$x(t) = {e^{ - {t^2}}}$$ is Note : $$\int\limits_{ - \infty }^\infty {{e^{ - {y^2}}}dy = \sqrt \pi } $$...

Which one of the following is an eight function of the class of all continuous-time, linear, time- invariant systems u(t) denotes the unit-step functi...

If the signal x(t) = $${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$ with * denoting the convolution operation, then x(t) is equal to

The energy of the signal x(t) =$${{\sin (4\pi t)} \over {4\pi t}}$$ is ___________.

Let x(t) $$ \leftrightarrow $$ X($$(j\omega )$$ BE Fourier transform pair. The Fourier Transform of the signal x(5t - 3) in terms of X($$(j\omega )$$ ...

The Fourier transform of a conjugate symmetric function is always

The Fourier transform F $$\left\{ {{e^{ - t}}u(t)} \right\}$$ is equal to $${1 \over {1 + j2\pi f}}$$. Therefore, $$F\left\{ {{1 \over {1 + j2\pi t}}}...

If a signal f(t) has energy E, the energy of the signal f(2t) is equal to

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

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

A modulated signal is given by s(t)= $${e^{ - at}}$$ cos $$\left[ {({\omega _c} + \Delta \omega )t} \right]$$ u (t), where a, $${\omega _c}$$ and $${\...

The Fourier transform of a voltage of a voltage signal x(t) is X(f). The unit of |X(f)| is

The Fourier transform of a function x(t) is X(f). The Fourier transform of $${{dx(t)} \over {dt}}$$ will be

The amplitude spectrum of a Gaussian pulse is

The function f(t) has the Fourier Transform g($$\omega $$). The Fourier Transform of $$$g(t) = \left( {\int\limits_{ - \infty }^\infty {g(t){e^{ - j\...

The Fourier transform of a real valued time signal has

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 o...

The complex envelope of the bandpass signal $$x(t)\, = \, - \sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right)\sin \left( {\pi t - {\pi \ove...

The value of the integral $$\int_{ - \infty }^\infty {12\,\cos (2\pi )\,{{\sin (4\pi t)} \over {4\pi t}}\,dt\,} $$ is

For a function g(t), it is given that $$\int_{ - \infty }^\infty {g(t){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}} $$ for any real value $$\o...

The value of the integral $$\int\limits_{ - \infty }^\infty {\sin \,{c^2}} $$ (5t) dt is

The Fourier transform of a signal h(t) is $$H(j\omega )$$ =(2 cos $$\omega $$) (sin 2$$\omega $$) / $$\omega $$. The value of h(0) is

The signal x(t) is described by $$x\left( t \right) = \left\{ {\matrix{ {1\,\,\,for\,\, - 1 \le t \le + 1} \cr {0\,\,\,\,\,\,\,\,\,\,\,\,\,\,...

For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by

Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Fig.(1) & (2). Then Y(f) is ...

The Hilbert transform of $$\left[ {\cos \,{\omega _1}t + \,\sin {\omega _2}t\,} \right]$$ is

If the Fourier Transfrom of a deterministic signal g(t) is G (f), then Item-1 (1) The Fourier transform of g (t - 2) is (2) The Fourier transf...

The power spectral density of a deterministic signal is given by $${\left[ {\sin (f)/f} \right]^2}$$, where 'f' is frequency. The autocorrelation func...

The autocorrelation function of an energy signal has

If G(f) represents the Fourier transform of a signal g (t) which is real and odd symmetric in time, then

The Fourier transform $$G(\omega )$$ of the signal g(t) in Fig.(1) is given as $$G(\omega ) = {1 \over {{\omega ^2}}}({e^{j\omega }} - j\omega {e^{j\...

Consider a rectangular pulse g(t) existing between $$t = \, - {T \over 2}\,and\,{T \over 2}$$. Find and sketch the pulse obtained by convolving g(t) w...

A signal v(t)= [1+ m(t) ] cos $$({\omega _c}t)$$ is detected using a square law detector, having the characteristic $${v_0}(t) = {v^2}(t)$$. If the Fo...