need help with the question below Consider a causal linear-time invariant system described by the differential equation                                   2y′(t) + 6y(t) = x′(t) − 4x(t) 1. Using Laplace transform technique, determine the zero-input response yz (t) if y(0−) = -3. Assume x(0−) and its higher order derivative in the vicinity of t = 0 to be zero. 2. Using the Laplace transform technique, determine the zero-state response if x(t) = δ(t − π)

Q: Q) Find the z-transform f(z) and sketch the pole-zero plot with the ROC for the following sequence.…

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Q: a. First, compute the Laplace transform of f(t). -2s -6s L{f(t)}(s) = b. Next, take the Laplace…

A: d.  The function F(s) and G(s) are given their inverse Laplace is calculated as shown below:…

Q: Determine the Z Transform for the folowing sequence. Sketch the pole-zero plot and indicate the ROC…

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A: Since it is a step down transformer therefore V2<V1 and number of turns in primary will be…

Q: use the leplace transform to determine i(t) if E(t) = E0, a constant. There is no current flowing…

A: Using laplace  transform  of first order differential  equation and  constant term write expression…

Q: x(n) y(-1) = 1, y(-2) = -1, y(-3) = 2, y(-4) = -3, y(-5) = -2 -5 -2 Z-1 N 7 Z-1 4 -6 y(n)

A: Given below clear explanation

Q: A. Determine the z-transform, included the region of convergence for the following sequences: 1.…

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Q: 4. A DC voltage v(t) = u(t) Volt is applied to a circuit, and a current i(t) = sin(wt) u(t) Amperes…

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Q: ix) f(t) = 8t“ + 2cos2t %3D f(t) = 4 + 9t° e³t f(t) = 4e 5t + e3t + 5 t³- 9 х) xi) %3D

A: As per our guidelines, we are supposed to answer only first 3 sub parts question. Kindly repost…

Q: 2- Find the z transform of the following two functions: (a) x₁ (n) = n(0.5)n-2u(n) (b) x2(n) =…

A: We need to find the given z transform following two…

Q: Determine the Zero-state Response when x(n) = 0.25nu(n)+0.75nu(n-3) using the Z-transform, given the…

A: Given below clear explanation

Q: Find the inverse z transform by dividing the function given below into partial fractions.

A: X(z)=z(z+0.5)(z-0.1)2z-0.6

Q: Sequences are generated by sampling a causal continuous-time signal u(t) (t > 0) at uniform…

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Q: A system defined by ℎ(t)=5e−5tu(t) is driven by a sinusoidal signal with frequency 5 rps and…

A: In this question we need to find a amplitude of the output signal in volt

Q: 2. Using the Laplace transform theorems Multiplying t and t" and First shift, derive the Laplace…

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Q: please do 1 and 2 in MATLAB,will give like

A: Approach to solving the question: Detailed explanation:

Q: İn delta function is; δ(t-t0) =0 , t ≠t0 , integrate δ(t-t0) t=0 to t=infinity equals to 1.…

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Q: Determine the Laplace transform of the following function using the definition and/or L.T.…

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Q: X(z) = 3 (² − ³1 ) - 2 (z − ¹) (² - ¹) 3 2

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Q: A- Find the z-transform and the ROC for each of the following signals: i) x1(n) = {2,1,-3,4,5,6) ii)…

A: The time domain signals can be continuous or discrete. The time domain signals can be periodic as…

Q: 2.→ Determine the Laplace transform of the function below using the steps given. Assume ↓ ↓…

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Q: Consider the series RLC circuit in Figure Q4. The initial current is 4A and the initial voltage…

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Q: 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8

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Q: Find the Laplace transform of the signal shown in figure using the definition of Laplace transform.…

A: The signal x(t) isWe need to determine the Laplace transform of the signal x(t) using the definition…

Q: . For the circuit shown in figure find i(t) for 10 using laplace transforms. 0.25 H m 12 V ww 202…

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Q: (a) Find Laplace transform of the following signals. (i) x,(t) = t³e-10tu(t) (ii) x2(t) = e-30t sin…

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Q: 1. sin 3at where a is any positive constant and s> a.

A: Since there are several different numerical problems present, as per the guidelines, in the…

Q: The inverse z-transform of F(z) is: F(z) = 11:²–28z_ (z–2)(z-4) Select one: a. f(k) = (3 × 2*) + (8…

A: The z-transform of a function x(k) is defined as: X(z)=∑k=-∞∞x(k) Z-k Suppose a signal is given by…

Q: 1) For each of the following sequences sketch the pole-zero pattern of their z transform. Include an…

A: From the properties of Z transform..

Q: e-28 – 3e -4s What is the inverse Laplace transform of s+ 2 u(t – 4)e-2(t-2) – 3u(t – 2)e¬2(t-4) u(t…

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Transfer function

A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.

Convolution Integral

Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.