(a) If Laplace transform of a signal f(t) is F(s), then obtain the transform of the signal e"f(5t). (b) Obtain the convolution of the two signals given by x, (t) =1, x,(t)=e. (c) Find the Laplace transform of a rectangular pulse of duration 0.4sec and amplitude 2, defined by 2,-0.2

Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

A:

Q: Find the Fourier transform F(e-az) of f(x) = e-a if x > 0 and f(x) = 0 if x 0.

A:

Q: 4] Find the Laplace Transform of f(t) = { S-1 (-/= + 5 = /₁1) (1te - 1/₁1) (a) (c) S S - I (b) (d) S…

A:

Q: The Fourier transform of a function } (t) iš defihed by F(w) = f(t)e-jwtdt %3D a) Using the above…

A: The Fourier transform of a function f(t) is defined by F(ω)=∫-∞∞f(t) e-jωt dt 1) We have to find the…

Q: Q6) -bt (a) Derive Fourier transform of the following signal: x(t) = 2ce za u(t). Then plot the…

A: Given: xt=2ce-bt2au(t)

Q: Derive the Fourier spectrum of a signal that is given by z(t) = forect (2T) exp(−j10t + jt) dt.…

A:

Q: Find Laplace transform of the function f(t) = cos(2t + 3)+e¬'u(t – 4) + tcosh²2t

A: Use the following formulas while calculating the Laplace transform of the given function.…

Q: 2yy" = 1 + (y')² 2

A:

Q: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…

A: We start with the time-domain signals and their Fourier transforms:Now, the convolution in the time…

Q: Find the Fourier transform of each of the following signals and sketch the magnitude and phase as a…

A: Fourier transform of a signal is derived by using the formulae integral runs from -infinite to…

Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

Q: Find the Fourier Transforms of the indicated function: f (x) = e-3x for x > 0 and f (x) = e2x for x…

A: We have,fx=e-3xx&gt;0e2xx&lt;0 To Do: Find the Fourier Transform of the given function.

Q: Question 4-) Let Fourier Transform of the signal r(t) be X(jw). Assume that g(t) satisfies the…

A: Given that, Fourier transform of the signal xt be Xjw. (a) By the fourier transform of xt=Xjw.…

Q: the Fourier transform of a continuous time signal x(t) is X(ja), then, the Fou ansform of the signal…

A: Given, Fourier transform of a continuous-time signal                                   x(t)  ↔…

Q: Find the Exponential Fourier coefficient Cn for signal f(x) = x Defined on interval [-1 ,1]

A: Complex form of Fourier series is defined as follows: fx=∑n=-∞∞cne-inx2πL where,…

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

A:

Q: -Obtain the Fourier transform of f(t): = sin (30) -t²+7it+12

A:

Q: b) Find the Fourier sine transform of f(x) = 12π, 0 < x < 6π

A: Fourier coefficients represent the amplitude of each harmonically-related sinusoid present in the…

Q: The Laplace Transform of

A:

Q: XP+2ap +2a') ple 23: Find the inverse Fourier sine transform f(x) of F, (P- ap

A:

Q: Which of the following is True about the Fourier transform of the signal x(t) = u(t) — u(−t)? - X(w)…

A:

Q: Q5) Find the Fourier transform of: SCos(nt/t) for lel < x(t)=D .elsewhere) Sketch X(f) versus f.On…

A:

Q: Determine the Fourier transform of the function f(t) = e-cltl.

A:

Q: The number of houses that can be served by a water pipe varies directly as the square of the…

A: Given that, The number of houses that can be served by a water pipe varies directly as the square of…

Q: f(x)= 2+ Show that fe L²(R) and find the L²-norm of the Fourier transform of

A: Answer given below.

Q: Find the Fourier Transform of f(s) = e-ax= a >0

A: The Fourier transform of a function  is given by :

Q: Find the Fourier transform of sinc (2t). (a) 2n A(w/2) 3. (b) п Д(u/4) A(w/8 (d) A(w/16) Moving to…

A:

Q: Find the Fourier transform of f(t) = [Aeat ]u(t) %3D and draw the amplitude and phase spectrum

A:

Q: Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz.,…

A:

Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: Find the Inverse Laplace transform of 5s-2 s² (s+2) (S-1) a) b) S (5² +1 (s²+a²)(s²+b²)' a² # b², ab…

A:

Q: A) Determine the Fourier Transform of the rectangular pulse signal II (t) = (1, -1/2 ≤t≤ 1/1. (o,…

A: This question is about fourier transform