1. Find the Fourier transform of the following signals:(a) y [n] = (-0.8)" u [n](b) y [n] = (0.9)" cos (2n) u [n]||2. Find the zeros and poles of the following transforms(a) X (2) :22 –123+3z²+3z+1=(b) X (2) =z²+1z3+3z²+3z+1z42ª+1(c) X (z) = z²+3z+2(d) X (z) = z exp (z-1)(e) X (2) = z² exp (-z-1)

With the help of z transform we can calculate the fourier transform of the signal. By substituting…

Answered: 1. Find the Fourier transform of the…

Engineering

Electrical Engineering

1. Find the Fourier transform of the following signals: (a) y [n] = (-0.8)" u [n] (b) y [n] = (0.9)" cos (2n) u [n]

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Q: *17.22 Determine the inverse Fourier transforms of: (a) F(w) = 48(w + 3) + 8(@) + 48(w – 3) (b) G(@)…

Q: 5. Detectors of some medical imaging systems can be modeled as rect functions of different sizes and…

Q: -10123 4sč Calculate the Fourier transform of the discrete-time signal x[n] given below.

Q: Find out the discrete time fourier transform of the signal y[n]=an u[n] where a<1.

A: For any discrete time signal y[n], the discrete time Fourier transform of y[n] can be expressed as

Q: The Fourier transform of the signal is real (real) as X (jw) = 2a / (a² + w²) as previously found.…

A: Given fourier transform of x(t) we habe to give reason why it is not complex part

Q: Write the mathematical expression of the periodic signal given below. Calculate and plot t Fourier…

Q: a. Find the Fourier transform of the rectangular pulse signal x(t) defined by x(1) = p,(t) = 0 Iel >…

A: the Fourier transform of the rectangular pulse signal. Inverse Fourier transform of the given X(w)…

Q: 2.8. An LTI system has impulse response h[n] = 5(-1/2)"u[n]. Use the Fourier transform to find the…

A: To solve above problem, one should know about transfer function of a system. Transfer function of a…

Q: A periodic signal (N = 4) is given by (only one period is shown) with x (n ) = 0. 1 0 %3D Find the…

A: Discrete Fourier series

Q: Q2 )a) Evaluate the following integration •o Sin²(8t) dt t2 b)The Fourier transform of the signal…

Q: Question 1: Determine the causal signal x(n) if its z-transform X(z) if ROC is 0.8</z/<1.25. A.…

A: 1. Option E 2.True Explanations are as below

Q: 1.1 State giving reasons whether each of the following statements is TRUE or FALSE. a) If a signal…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: Determine the signal, x(n), having the Fourier transforms of X (0) = cos²0 © (1/4) [ 8/n+2) +…

A: In this question, We need to choose the correct option What is inverse Fourier transform of the…

Q: 3.37. Consider a discrete-time LTI system with impulse response h[n] = Chap. 3 Problems 261 Find the…

A: Given: Consider a discrete-time LTI system with impulse response: hn=12n To find: Find the Fourier…

Q: 3.10. Let x[n] be a real and odd periodic signal with period N = 7 and Fourier coefficients ak.…

Q: Be able to calculate the Fourier transform of a function Find the Fourier transform of each…

Q: The finite-duration sequence a[n] = {-4, 1, 2, 0, – 3} has a Fourier transform X(w). Determine X(0).

A: Solve the problem

Q: PRACTICE PROBLEM17.3 f(1) A Determine the Fourier transform of the "switched-off" exponential func-…

Q: 1. a) Let Fourier series and Fourier transform be two tools and you are asked to pick up only one of…

A: (a) I will pick Fourier transform as my tool for representing a given signal into frequency domain.…

Q: 8A 8A 8A 9 2572 3T 5m 9 (b) 2. 77 ST 37 77 2. -) Using partial fractions, find the inverse Fourier…

Q: 5.19. Find the Fourier transform of the following signals: 1 (a) x(1) 1 where a > 0 je)? " %3D 2п (а…

A: Given : Here in the question they want to know the fourier transform of the given time domain…

Q: Determine the Fourier transform of the following signals: a) x1(n] = 2– sin(2" + ) b) x2[n] = n(u[n+…

Q: 2) Determine the continuous-time signal that corresponds to the following Fourier Transforms (i.e.,…

Q: 5.13 The Fourier transform of a signal x(1) is 2 + πδ(ω) jo X(@) = %3D Derive the Fourier transform…

Q: 1. Find the inverse Fourier transform of the following function, 2jw + 5 (jw)2 + 5jw + 6 F(w) = %3D

A: Inverse Fourier Transform is given by: x(t)=12π∫-∞∞Xωejωtdω Given: F(w)=2jω+5(jω)2+5jω+6

Q: Suppose that h[n] = [)" cos ()] [1). %3D Use Fourier transforms to determine the response to each of…

Q: Q1. Find the Fourier Transform for the following non periodic function. 1, - 1 1

A: In the question, Find the Fourier transform of the non periodic signal.

Q: Be able to calculate the Fourier transform of a function Find the Fourier transform of each…

A: Fourier transform of e-atsinω0t…

Q: 4) Discrete Time Fourier Transform x[n] = a"u[n], 0 < a < 1. Compute X (N) and plot its magnitude.

A: Detail solution in the image

Q: By using Fourier transform, find y, in the circuit of Fig.6. Given i, = 5e 'u(1) A 40 Ω 20 mF Fig.6

A: For the given circuit we have to find the value of voltage Vo

Q: 1. What is the mathematical expression for the given signal? 2. Determine the Fourier transform…

A: In this question, We need to the mathematical expression for the given signal? In the second…

Q: Question 1 Find the signal g(t) whose Fourier transform G(f) is given below. 1, f>0 0.5, f = 0 G(f)…

Q: (b) Prove that X(-jw) = X(jw) given that x(t) is real and even. (c) Use appropriate Fourier…

A: Consider a continuous-time signal x(t). Its Fourier transform is defined as- The…

Q: Prob.34. Determine the z-transform for the following sequences – (i) u(-п) (і) | [u(п)- и(п- 10)]…

A: We need to determine the z-transform for the following sequences : i) 12nu(-n) ii) 12n[u(n)-u(n-10)]…

Q: Problem 3. (a) Determine and plot the magnitude of the Fourier Transform X,(w) of the real-valued…

A: Consider the given expression,

Q: 4. The input-output relationship for a linear, time-invariant, and casual system is defined by the…

A: Fourier series: This is a mathematical tool for expanding the periodic signal in the term of their…

Q: Fast Fourier transform technique is used in the spectrum analyzers to determine/measure the lower…

A: Fast Fourier transform : A FFT is algorithm that computes discrete Fourier transform of a sequence…

Q: width 2a and height 1 (The pulse is symmetrical about the y - axis). (ii) Use the Inverse Fourier…

A: Here part ii) has been solved with the help of the properties of fourier transform.

Q: Obtain the Fourier transform of x(t) = e-1e-0.5t, “u(t) and sketch its magnitude and phase…

A: The given expression x(t) = e-1 e-0.5t u(t) Find the Fourier transform Sketch tha magnitude and…

Q: 3) a) Sketch and label the signal x(t) = En=-o ^(t – 2n) (1+1, -1+1, 0<t< 1 0, -1<1< 0 A(1) =…

Q: A continuous time periodic signal x(t) = cos w,t is multiplied with a rectangular window r(t) to…

Q: 2. Determine the continuous-time Fourier transform (CTFT) of the signal a(t) = 0.5' u(t) – 0.5' u(t…

A: Given, x(t) =0.5tu(t) -0.5tu(t-2) CTFT {x(t)} = ?

Q: A3. Show that for an even function, the Fourier coefficients are: (a) a, = | S(1) cos- dt, r = 1, 2,…

A: A3 The Fourier series of a periodic function f(t) is given as:…

Q: Regarding Signals and Systems, the Fourier Transformation of x(t) is given by X(jω)=F{x(t)}. The…

Q: Q.10 Use Fourier transform to solve y" +6y'+9y e", y(0) = 0, y'(0) =0. %3D %3D

A: Fourier Transform- It is the process in which either a time-domain signal is converted to the…

Q: 3. Consider the system shown below. M(f) (the Fourier transform of m(t)) is also shown. M (f) y(t)…

Q: Q 3. If the F)=3{rect(1}} = 3o Fourier transform of the rectangular pulse -0.5sisos) =sinc(f), using…

A: In the question, Fourier transform of the rectangular wave is given. Find the Fourier transform of…

Q: Consider the circuit shown below. Find the Fourier transform of vo(t), where vs(t)=3u(t) V R=5 0 C=1…

Q: Determine the signal, x(n), having the Fourier transforms of X (0) = cos²0 © (1/4) [ 8(n+2) +…

A: Given here the fourier transform of x(n) is X(w)=cos2w. here we have to find the signal x(n). We…

Question

1. Find the Fourier transform of the following signals:
(a) y [n] = (-0.8)" u [n]
(b) y [n] = (0.9)" cos (2n) u [n]
||
2. Find the zeros and poles of the following transforms
(a) X (2) :
22 –1
23+3z²+3z+1
=
(b) X (2) =
z²+1
z3+3z²+3z+1
z4
2ª+1
(c) X (z) = z²+3z+2
(d) X (z) = z exp (z-1)
(e) X (2) = z² exp (-z-1)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Given the finite-duration sequence below, x[n]={-4,1,2,0,3} where -4 is when n=0, if it has a fourier transform of X(w) , what is the value of X(0)?
Question 1: Determine the causal signal x(n) if its z-transform X(z) if ROC is 0.8</z/<1.25. A. -0.8n u(-n) - 1.25n u(n) B. 0.8n u(n) - 1.25n u(n) C. 0.8n u(n) + 1.25n u(n) D. 0.8n u(n) - 1.25n u(-n) E. 0.8n u(n) + 1.25n u(-n-1) Question 2: The Fourier transform can be used to represent an aperiodic signal for all values of time. A. True B. False
3 After applying a fourier transform we find the results for the basis function k=3 is as follows. Im[k]=2.0, Re[k]= 1.2. This is given in Rectangular/Cartesian form. Give the results for k=3 in Polar form.
A non-periodic signal, s(t), is described as follows: s(t) = 1 for 0 ≤ t ≤ 1 sec s(t) = 0 otherwise. Find out an expression for the magnitude of the frequency spectrum, S(f), for s(t).
Be able to calculate the Fourier transform of a function Find the Fourier transform of each function. In each case, a is a positive real constant. f(t)=te−at,t≥0,f(t)=teat,t≤0.
I have a fourier series function f(t) = -5t 0 < t <1 10-5t 1 < t < 2 The interval here seemingly is [0,2]. Therefore, Period = L - (-L) = 2 - (-2) = 4 2L = 4 hence, L = 2. Is this the correct L value for this function?
Let x(t) = sin^2(2pit), a periodic signal of fundamental period T0 = 1, and y(t) = |sin(2pit)| also periodic of the same fundamental period (a) A trigonometric identity gives that x(t) = 0.5[1-cos(4pit)]. Use this result to find its complex exponential Fourier series (b) Use the Laplace transform to find the Fourier series of y(t) (c) Are x(t) and y(t) identical? Explain. (d) Indicate how you would use an ideal low-pass filter to get a dc source from x(t) and y(t). Indicate the bandwidth and magnitude of the filters. Which of these two signals is used for generating full-waved rectified dc source?
Q/Obtain the Fourier Transform to the rectangular pulse of duration 2 second and having a magnitude of 10 volts. Q/Find the Fourier series for the periodic function giving below: x (t) (cosx, 0, {cos 0
1. Discrete Fourier Transform: Use the Fast Fourier Transform algorithm to compute the 8-point Dis- crete Fourier Transforms of sequences (1,0,1,0,1,0, 1,0) and (1,1,1,1,0,0,0,0). Provide detailed calculations with intermediate steps rather than just the results.
The Fourier transform of a continuous-time signal x(t) is denoted by X(ω). Apply CTFT properties to obtain the Fourier Transform of x(3t+7).
1- Which one of the following pair of antennas are functionally same. a- Parabolic reflector and lense antenna b- Array & parabolic reflector antenna c- Aperture and Parabolic reflector antenna d- None of the above. 2- Inverse Fourier transform on Maxwell's equation is to transform signal from frequency domain to time domain. true or false
Regarding Signals and Systems, the Fourier Transformation of x(t) is given by X(jω)=F{x(t)}. The time duality property is X(jt)=2πx(-ω). My question is how do you go from x(t) to X(jt) and from x(-ω) to X(jω)? Thank you!