Fourier Transform

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?

Consider a continuous-time, real-valued signal f(t) whose Fourier transform F(ω) = ∫_(-∞)^∞ f(t) exp(-j ωt) dt exists. Which one of the following statements is always TRUE?

Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $[-\omega_c, \omega_c]$, where $\omega_c$ is in rad/sec. The...

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega)=$$\mathop f\limits_{ - \infty }^\infty $$ f(t) \exp (-j \omega t) d t$ exists. Which one of...

A digital communication system transmits through a noiseless bandlimited channel [-W W]. The received signal z(t) at the output of the receiving filter is given by $z(t) = \sum_n b...

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 ________.

The relationship between any N-length sequence x[n] and its corresponding N-point discrete Fourier transform X[k] is defined as X[k] = F{x[n]}. Another sequence y[n] is formed as b...

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

In the table shown below, match the signal type with its spectral characteristics. Signal type (i) Continuous, aperiodic (ii) Continuous, periodic (iii) Discrete, aperiodic (iv) Di...

Let x(t) = 10 cos(10.5Wt) be passed through an LTI system having impulse response h(t) = π (sin Wt / πt)^2 cos 10Wt. The output of the system is

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

In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a) Continuous, aperiodic (ii) Con...

The Fourier transform X(j$$\omega$$) of the signal $$x(t) = {t \over {{{(1 + {t^2})}^2}}}$$ is ____________.

Let $h[n]$ be a length-7 discrete-time finite impulse response filter, given by $h[0] = 4$, $h[1] = 3$, $h[2] = 2$, $h[3] = 1$, $h[-1] = -3$, $h[-2] = -2$, $h[-3] = -1$, and $h[n]$...

A continuous time signal x(t) = $$4\cos (200\pi t)$$ + $$8\cos(400\pi t)$$, where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $$...

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

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

A Fourier transform pair is given by $${\left( {{2 \over 3}} \right)^n}$$ u $$\left[ {n + 3} \right]\,\mathop \Leftrightarrow \limits^{FT} \,{{A{e^{ - j6\pi f}}} \over {1 - \left(...

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 $$\omega $$. If y(t)=$$\int_{ - \in...

Let $$X(t)$$ be a wide sense stationary $$(WSS)$$ random procfess with power spectral density $${S_x}\left( f \right)$$. If $$Y(t)$$ is the process defined as $$Y(t) = X(2t - 1)$$,...

A real - values signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linear time invariant system whose frequency response is $$H(f) =...

Let g(t) = $${e^{ - \pi {t^2}}}$$, and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the output 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 impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function. The frequency response H(ω) of the sy...

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

The 3 - dB bandwidth of the low - pass signal $${e^{ - 1}}$$ u(t), where u(t) is the unit step function, is given by

A 5-point sequence x [n] is given as x$$\left[ { - 3} \right]$$ =1, x$$\left[ { - 2} \right]$$ =1, x$$\left[ { - 1} \right]$$ =0, x$$\left[ { - 0} \right]$$ = 5, x$$\left[ { - 1} \...

A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where $$g(t)\, = \,\,\sum\limits_{k = - \infty }^\infty {{{( - 10)}^k}\,\delta (t - 0.5x{{10}^{ - 4}}k)} $$...

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

Match the following and choose the correct combination. GROUP 1 E- continuous and aperiodic signal F- continuous and periodic signal G- discrete and aperiodic signal H- discrete an...

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

The Fourier transform of a conjugate symmetric function is always

Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of the system should be

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

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

The amplitude spectrum of a Gaussian pulse is

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) with itself. The Fourier transf...

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

The amplitude spectrum of a Gaussian pulse is

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

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

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 transform of g (t/2) is Item - 2 (A) G(f) $$...

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

The Fourier transform of a real valued time signal has

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 Fourier transform of m(t) is con...

Match each of the items, A, B and C, with an appropriate item from 1, 2, 3, 4 and 5 A. Fourier transform of a Gaussian function B. Convolution of a rectangular pulse with itself C....

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

A signal x(t) = $$\exp ( - 2\pi Bt)\,u(t)$$ is the input to an ideal low pass filter with bandwidth B Hz. The output is denoted by y(t). Evaluate $$\int\limits_{ - \infty }^\infty...