GATE 2014 Electronics & Communication

For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a redution of the spacing between the pl...

A good current buffer has

Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline {x\,} \,\overline y \,$$ $$\overline z $$ Which one of the...

A Y-network has resistances of 10Ω each in two of its arms, while the third arm has a resistance of 11Ω in the equivalent ∆ − network, the lowest value (in Ω) among the three resis...

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z 1 of the first section to the input impedance Z 2...

A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power fa...

The forward path transfer function of a unity negative feedback system is given by $$$G\left(s\right)\;=\;\frac k{\left(s\;+\;2\right)\left(s\;-\;1\right)}$$$ The value of K which...

Let $$X$$ be a real - valued random variable with $$E\left[ X \right]$$ and $$E\left[ {{X^2}} \right]$$ denoting the mean values of $$X$$ and $${{X^2}}$$, respectively. The relatio...

Find the odd one from the following group: W,E,K,O I,Q,W,A F,N,T,X N,V,B,D

$$C$$ is a closed path in the $$z-$$plane given by $$\left| z \right| = 3.$$ The value of the integral $$\oint\limits_c {{{{z^2} - z + 4j} \over {z + 2j}}dz} $$ is

The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to

For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all resident females with income below Rs 8 lakh should fill up Form Al...

The volume under the surface $$z\left( {x,y} \right) = x + y$$ and above the triangle in the $$xy$$ plane defined by $$\left\{ {0 \le y \le x} \right.$$ and $$\,\left. {0 \le x \le...

The Taylor series expansion of $$3$$ $$sin$$ $$x$$ $$+2cos$$ $$x$$ is

A BJT is baised in forward active mode Assume V BE = 0.7 V, kT/q = 25 mV and reverse saturation current I s = 10 -13 A. The transconductance of the BJT (in mA/V) is

A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is the output of the system. $$$\mathop y\limits^ \bullet \left...

In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has...

Consider a random process $$X\left( t \right) = \sqrt 2 \sin \left( {2\pi t + \varphi } \right),$$ where the random phase $$\varphi $$ is uniformly distributed in the interval $$\l...

The capacity of a Binary Symmetric Channel (BSC) with cross - over probability 0.5 is ______ .

In a code - division multiple access (CDMA) system with N = 8 chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is _______.

A two - port network has scattering parameters given by $$[S]$$ $$ = \left[ {\matrix{ {{s_{11}}} & {{s_{12}}} \cr {{s_{21}}} & {{s_{22}}} \cr } } \right].$$ If the port - 2 of the...

A fair coin is tossed repeatedly until a 'Head' appears for the first time. Let L be the number of tosses to get this first 'Head'. The entropy H (L) in bits is _______________.

In spherical coordinates, let $${{{\widehat a}_{_0}},\,{{\widehat a}_{_\phi }}}$$ denote unit vectors along the $$\theta ,\,\,\phi $$directions. $$$E = {{100} \over r}\sin \,\theta...

$$A$$ real $$\left( {4\,\, \times \,\,4} \right)$$ matrix $$A$$ satisfies the equation $${A^2} = {\rm I},$$ where $${\rm I}$$ is the $$\left( {4\,\, \times \,\,4} \right)$$ identit...

Let $$\,{X_1},\,\,{X_2}\,\,$$ and $$\,{X_3}\,$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,1} \right].$$ The probabili...

For matrices of same dimension $$M,N$$ and scalar $$c,$$ which one of these properties DOES NOT ALWAYS hold ?

The phase margin in degrees of G(s)=$${{10} \over {\left( {s + 0.1} \right)\left( {s + 1} \right)\left( {s + 10} \right)}},$$ using the asymptotic Bode plot is ______

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at rando...

Consider the matrix $${J_6} = \left[ {\matrix{ 0 & 0 & 0 & 0 & 0 & 1 \cr 0 & 0 & 0 & 0 & 1 & 0 \cr 0 & 0 & 0 & 1 & 0 & 0 \cr 0 & 0 & 1 & 0 & 0 & 0 \cr 0 & 1 & 0 & 0 & 0 & 0 \cr 1 &...

A train that is 280 meters long, traveling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the p...

Consider a discrete time periodic signal x$$\left[ n \right]$$= $$\sin \left( {{{\pi n} \over 5}} \right)$$. Let a k be the complex Fourier serier coefficients of x$$\left[ n \righ...

When the optical power incident on a photodiode is 10μW and the responsivity is 0.8 A/W, the photocurrent generated (in μA) is ________.

If fixed positive charges are present in the gate oxide of an n-channel enhancement type MOSFET, it will lead to

A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\matrix{ {3\,for\,0 \le t \le 3} \cr {0\,otherwise} \cr } } \...

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...

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is output of the system $$\mathop y\limits^ \bullet \left( t \right) +...

Let x $$\left[ n\right]$$= $${\left( { - {1 \over 9}} \right)^n}\,u(n) - {\left( { - {1 \over 3}} \right)^n}u( - n - 1).$$ The region of Convergence (ROC) of the z-tansform of x$$\...

Consider two real valued signals, $$x\left( t \right)$$ band - limited to $$\,\left[ { - 500Hz,\,\,500Hz} \right]$$ and $$y\left( t \right)$$ band - limited to $$\,\left[ { - 1\,\,...

A depletion type N -channel MOSFET is biased in its linear region for use as a voltage controlled resistor. Assume threshold voltage V TH = -0.5 V, V GS = 2.0 V, V DS = 5 V, W/L=10...

A discrete - time signal x[n] = $${\rm{sin(}}\,{\pi ^2}n)$$, n being an integer is

Which one of the following field patterns represents a TEM wave traveling in the positive $$x$$ direction?

Norton's theorem states that a complex network connected to a load can be replaced with an equivalent impedance

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of c...

The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.

The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is __________ .

The system of linear equations $$\left( {\matrix{ 2 & 1 & 3 \cr 3 & 0 & 1 \cr 1 & 2 & 5 \cr } } \right)\left( {\matrix{ a \cr b \cr c \cr } } \right) = \left( {\matrix{ 5 \cr { - 4...

Let $$X$$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $$100.$$ The expectation, $$E\left[ X \right],$$ is __________.

For an n - variable Boolean function maximum number of prime implicants is

The determinant of matrix $$A$$ is $$5$$ and the determinant of matrix $$B$$ is $$40.$$ The determinant of matrix $$AB$$ is _______.

For $$0 \le t < \infty ,$$ the maximum value of the function $$f\left( t \right) = {e^{ - t}} - 2{e^{ - 2t}}\,$$ occurs at

An unforced linear time invariant (LTI) system is represented by $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \le...

If $$\,\overrightarrow r = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,\,\,$$ and $$\,\left| {\overrightarrow r } \right| = r,$$ then div $$\left( {{r^2}\nabla \left( {\...

In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by

The capacity of band-limited additive white Gaussian noise (AWGN) channel is given by $$C = \,W\,\,{\log _2}\left( {1 + {P \over {{\sigma ^2}\,W}}} \right)$$ bits per second (bps),...

The input to a 1-bit quantizer is a random variable X with pdf $${f_x}(x) = 2{e^{ - 2x}}\,\,for\,\,x \ge 0$$ and $${f_x}(x) = 0\,\,for\,\,x\, < \,0$$. For outputs to be of equal pr...

The power spectral density of a real stationary random process X(t) is given by $$${S_x}\left( f \right) = \left\{ {\matrix{ {{1 \over W},\left| f \right| \le W} \cr {0,\left| f \r...

For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a > b), the cut-off frequency for the $$T{E_{11}}$$ mode is the arithmetic mean of the cut-off frequencie...

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms $${s_1}\,(t)\, = \,\alpha \,\,\cos \,\,\,2\,\pi {f_1}\,t\,and\,\,{s_{2\,}}(t)\,\, =...

If the characteristic equation of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 2\alpha {{dy} \over {dx}} + y = 0\,\,$$ has two equal roots, then the values of $$\alpha...

The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The imaginary part of $$f(z)$$ is

The maximum value of the determinant among all $$2 \times 2$$ real symmetric matrices with trace $$14$$ is ______.

The value of $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^x}\,\,$$ is

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

Assume electronic charge q = 1.6×10 -19 C, kT/q = 25 mV and electron mobility μ n = 1000 cm 2 /V-s. If the concentration gradient of electrons injected into a P-type silicon sample...

An increase in the base recombination of a BJT will increase

In CMOS technology, shallow P-well or N-well regions can be formed using

The input-output relationship of a causal stable LTI system is given as 𝑦[𝑛] = 𝛼 𝑦[𝑛 − 1] + $$\beta $$ x[n]. If the impulse response h[n] of this system satisfies the conditio...

Consider a discrete-time signal $$x\left[ n \right] = \left\{ {\matrix{ {n\,\,for\,\,0 \le n \le 10} \cr {0\,\,otherwise} \cr } } \right.$$ If $$y\left[ n \right]$$ is the convolut...

Let x$$\left[ n \right]$$ = x$$\left[- n \right]$$ . Let X(z) be the z-transform of x$$\left[ n \right]$$. if 0.5 +j 0.25 is a zero of X(z), which one of the folowing must also be...

An FIR system is described by the system function $$$H(z) = 1 + {7 \over 2}{z^{ - 1}} + {3 \over 2}{z^{ - 2}}$$$

If the electric field of a plane wave is $$$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t - kz + {{30}^ \circ }} \right) - \widehat y4\sin \left( {\omeg...

If $$z=xy$$ $$ln(xy),$$ then

A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage V S , the resistance R, the capacitance C, and the current i(t) is gi...

The input $$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applied to a system with transfer function $$\frac{s-2}{s+3}$$. If...

If X and Y are inputs and the Difference (D = X – Y) and the Borrow (B) are the outputs, which one of the following diagrams implements a half-subtractor?

The maximum value of the function $$\,f\left( x \right) = \ln \left( {1 + x} \right) - x$$ (where $$x > - 1$$ ) occurs at $$x=$$________.

The maximum value of $$f\left( x \right) = 2{x^3} - 9{x^2} + 12x - 3$$ in the interval $$\,0 \le x \le 3$$ is __________.

If WL is the Word Line and BL the Bit Line, an SRAM cell is shown in

Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independent and dependent variables respectively?

The desirable characteristics of a transconductance amplifier are

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 $$Y(t) = X(2t - 1)$$,...

Consider an air filled rectangular waveguide with a cross-section of $$5\,\,cm\,\, \times \,\,3\,cm$$. For this waveguide, the cut-off frequency (in MHz) of $$T{E_{21}}\,$$ mode is...

Assume that a plane wave in air with an electric field $$\overrightarrow E = 10\cos \left( {\omega t - 3x - \sqrt {3z} } \right){\widehat a_{_y}}\,\,\,V/m$$ is incident on a non-ma...

In a PCA system, the signal $$m(t) = \{ \sin (100\,\pi \,t)\, + \cos (100\,\pi \,t\} $$ V is sampled at the Nyquist rate. The samples are processed by a uniform quantizer with step...

A real band-limited random process $$X( t )$$ has two -sided power spectral density $$${S_x}\left( f \right) = \left\{ {\matrix{ {{{10}^{ - 6}}\left( {3000 - \left| f \right|} \rig...

Let $${X_1},\,{X_2},$$ and $${X_3}$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,\,1} \right]$$. The probability $$P\le...

A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ________.

Match the application to appropriate numerical method Applications $$P1:$$ Numerical integration $$P2:$$ Solution to a transcendental equation $$P3:$$ Solution to a system of linea...

Let $${X_1},{X_{2,}}$$ and $${X_{3,}}$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,1} \right].$$ The probability $$P\l...

Which one of the following statements is NOT true for a square matrix $$A$$?

The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left( t \right),x\left( 0 \right) = {x_0}.$$ For $${x_0} = \left[ {...

An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is

A modulated signal is $$y\left( t \right)\, = \,\,\,\,\,\,\,\,\,m\left( t \right)\,\cos \left( {40000\pi t} \right),$$ where the baseband signal $$m\left( t \right)\,$$ has frequen...

A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to

At T = 300 K, the hole mobility of a semiconductor $$\mu_p\;=500\;cm^2/V-s$$ and $$\frac{kT}q\;=\;26\;mV$$.The hole diffusion constant D p in cm 2 /s is__________.

The slope of the I D vs. V GS curve of an n-channel MOSFET in linear region is 10 -3 $${\Omega ^{ - 1}}$$ at V DS = 0.1V. For the same device, neglecting channel length modulation,...

In MOSFET fabrication, the channel length is defined during the process of

An ideal MOS capacitor has boron doping concentration of 10 15 cm -3 in the substrate. When a gate voltage is applied, a depletion region of width 0.5 $$\mu m$$ is formed with a su...

For an all-pass system H(z)= $${{({z^{ - 1}} - b)} \over {(1 - a{z^{ - 1}})}}$$ where $$\left| {H({e^{ - j\omega }})} \right| = \,1$$ , for all $$\omega $$. If Re (a) $$ \ne $$ 0,$...

The z-transform of the sequence x$$\left[ n \right]$$ is given by x(z)= $${1 \over {{{(1 - 2{z^{ - 1}})}^2}}}$$ , with the region of convergence $$\left| z \right| > 2$$. Then, $$x...

Let $${H_1}(z) = {(1 - p{z^{ - 1}})^{ - 1}},{H_2}(z) = {(1 - q{z^{^{ - 1}}})^{ - 1}}$$ , H(z) =$${H_1}(z)$$ +r $${H_2}$$. The quantities p, q, r are real numbers. Consider , p=$${1...

The phase response of a passband waveform at receiver is given by $$\varphi \,(f) = - 2\,\pi \,\alpha \,(f - {f_c}) - \,2\pi \beta \,{f_c}$$ where $${f_c}$$ is the centre frequency...

Let h(t) denote the impulse response of a casual system with transfer function $${1 \over {s + 1}}$$. Consider the following three statements. S1: The system is stable. S2: $${{h\l...

The input $$ - 3{e^{2t}}\,\,u\left( t \right)$$, where u(t) is the unit step function$$\, {{s - 2} \over {s + 3}}$$. If the initial value of the output is -2, then the value of the...

Let $$\,x\,\,\left( t \right)\,\,\, = \,\,\,\cos \,\,\,\left( {10\pi t} \right)\,\, + \,\,\cos \,\,\left( {30\pi t} \right)$$ be sampled at $$20\,\,\,Hz$$ and reconstructed using a...

Consider an FM signal $$f\left(t\right)\;=\;\cos\left[2{\mathrm{πf}}_\mathrm c\mathrm t\;+\;{\mathrm\beta}_1\sin\;2{\mathrm{πf}}_1\mathrm t\;+\;{\mathrm\beta}_2\sin\;2{\mathrm{πf}}...

Given the vector $$$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\;+\;\left(\sin\;\mathrm x\right)\left(\cos\;\mathrm y\right)...

Match column A with column B. Column 1. Point electromagnetic source 2. Dish antenna 3. Yagi-Uda antenna Column P. Highly directional Q. End fire R. Isotropic

For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenus...

The unilateral Laplace transform of $$f(t)$$ is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of $$g\left( t \right) = t.f\left( t \...

Consider a transfer function $$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$ with 'p' a positive real parameter. The maximum value of 'p' un...

Parcels from sender $$S$$ to receiver $$R$$ pass sequentially through two post - offices. Each post - office has a probability $${1 \over 5}$$ of losing an incoming parcel, indepen...

For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then

Given $$\,\,\overrightarrow F = z\widehat a{}_x + x\widehat a{}_y + y\widehat a{}_z.\,\,$$ If $$S$$ represents the portion of the sphere $${x^2} + {y^2} + {z^2} = 1$$ for $$\,z \ge...

The directional derivative of $$f\left( {x,y} \right) = {{xy} \over {\sqrt 2 }}\left( {x + y} \right)$$ at $$(1, 1)$$ in the direction of the unit vector at an angle of $${\pi \ove...

With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 4y...

If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier of future calls, the probability distribution fun...

The series $$\sum\limits_{n = 0}^\infty {{1 \over {n!}}\,} $$ converges to

If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will

A BJT in common-base configuration is used to amplify a signal received by a $$50\,\Omega $$ antena. Assume kT/q = 25 mV. The value of the collector bias current ( in mA ) required...

If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution fun...

If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\mathrm{xz}^2\right)\widehat{\mathrm y}+\left(6\mathrm{xyz}\r...

An M - level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth 100 kHz. The bit rate is 200 kbps and the system characteri...

Consider a communication scheme where the binary valued signal X satisfies P{X = + 1} = 0.75 and P {X = - 1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random var...

Consider a discrete-time channel Y = X + Z, where the additive noise Z is signal- dependent. In particular, given the trasmitted symbol $$X\, \in \,\{ \, - \,a,\,\, + \,a\} $$ at a...

For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 m V/m. Given that intrinsic impedance of the free space is 120$$\pi \Omega $$, th...

Let $$X$$ be a zero mean unit variance Gaussian random variable. $$E\left[ {\left| X \right|} \right]$$ is equal to ______

An 8085 microprocessor executes “STA 1234H” with starting address location 1FFEH (STA copies the contents of the Accumulator to the 16-bit address location). While the instruction...

If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{{dx} \over {dt}} + x = 0$$ is

The state transition matrix $$\phi \left( t \right)$$ of a system $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \l...

The magnitude of the gradient for the function $$f\left( {x,y,z} \right) = {x^2} + 3{y^2} + {z^3}\,\,$$ at the point $$(1,1,1)$$ is _________.

In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4 th order all-pole system?

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(...

The cut-off wavelength (in µm) of light that can be used for intrinsic excitation of a semiconductor material of bandgap E g = 1.1 eV is ________.

Consider a silicon sample doped with N D = 1×10 15 /cm 3 donor atoms. Assume that the intrinsic carrier concentration n i = 1.5×10 10 /cm 3 . If the sample is additionally doped wi...

Consider two BJT's biased at the same collector current with area A 1 = 0.2 μm × 0.2 μm and A 2 = 300 μm × 300 μm. Assuming that all other device parameters are identical, kT/q = 2...

The sequence x $$\left[ n \right]$$ = $${0.5^n}$$ u[n], where u$$\left[ n \right]$$ is the unit step sequence, is convolved with itself to obtain y $$\left[ n \right]$$ . Then $$\s...

A stable linear time invariant (LTI) system has a transfer function H(s) = $${1 \over {{s^2} + s - 6}}$$. To make this system casual it needs to be cascaded with another LTI system...

The unilateral Laplace transform of F(t) is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of g(t) = $$t \cdot f\left( t \right)$$

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) =...

A casual LTI system has zero initial conditions and impulse response h(t). Its input x(t) and output y(t) are related through the linear constant - coefficient differential equatio...

The N-point DFT X of a sequence x[n] 0 ≤ n ≤ N − 1 is given by $$X\left[ k \right] = {1 \over {\sqrt N }}\,\,\sum\limits_{n = 0}^{N - 1} x \,[n\,]e{\,^{ - j{{2\pi } \over N}nk}}$$,...