We're Open
+44 7340 9595 39
+44 20 3239 6980

[Solved] 1. A function is given by 𝑓(π‘₯) = 1 βˆ’ |π‘₯| 𝑇 , where π‘₯ ∈ [βˆ’π‘‡, 𝑇]. State whether the function is

  100% Pass and No Plagiarism Guaranteed

[Solved] 1. A function is given by 𝑓(π‘₯) = 1 βˆ’ |π‘₯| 𝑇 , where π‘₯ ∈ [βˆ’π‘‡, 𝑇]. State whether the function is even or odd and hence find the Fourier series for this function.

EE2D1: Fundamentals of Signals and Systems

This coursework constitutes 20% of the total module mark. The submission deadline is Monday, 16/01/2017, 12 pm. Please hand in your work in the undergraduate office in MECH G43. Make sure your work has your name and ID number written clearly on each sheet and all the sheets are stapled together. The work should be neatly presented. Credit will be given to well-presented work. Please solve a new question on a new page.

1. A function is given by 𝑓(π‘₯) = 1 − |π‘₯| 𝑇 , where π‘₯ ∈ [−𝑇, 𝑇]. State whether the function is even or odd and hence find the Fourier series for this function.

2. Find the Fourier series for the function 𝑓(π‘₯) = π‘₯ 3 − 2π‘₯ 2 , defined on −πœ‹ < π‘₯ < πœ‹ (Hint: Use the following information to simplify integration. If 𝑂(π‘₯) is odd function and 𝐸(π‘₯) is even function then 𝑔(π‘₯) = 𝑂(π‘₯) ∗ 𝐸(π‘₯) is an odd function and ∫ 𝑔(π‘₯) 𝑇 −𝑇 = 0)

3. Find the Fourier transform of the function 𝑓(𝑑) = { 0 𝑑 < − πœ‹ 2 ⁄ (4𝑑 + 1) − πœ‹ 2 ⁄ ≤ 𝑑 ≤ πœ‹ 2 ⁄ 0 πœ‹ 2 ⁄ < 𝑑 }

4. Using the definition of Laplace Transform, show that: L{ln(π‘₯)} = − ( 𝛾 + ln(𝑠) 𝑠 ), Where, 𝛾 = − ∫ 𝑒 −π‘₯ ln(π‘₯)𝑑π‘₯ ∞ 0

5. Using the formulae of Laplace transforms for derivatives, find the Laplace Transform of L{t sin at} and L{𝑑 cos π‘Žπ‘‘}.

6. Solve for π‘₯(𝑑) the following differential equation which has an impulse input, π‘₯̈+ 6π‘₯Μ‡ + 8π‘₯ = 4. 𝛿(𝑑 − 5) π‘₯(0) = 0, π‘₯Μ‡(0) = 3

7. Given that 𝐻(𝑑) is a Heaviside or step function, solve the following integro differential equation 𝑑π‘₯ 𝑑𝑑 + 6π‘₯ + 9 ∫ π‘₯𝑑𝑑 𝑑 0 = 𝐻(𝑑), where π‘₯(0) = 0

8. Using the method of Laplace Transforms, solve the following initial valued problem 𝑦 ′ + 2𝑦 = 4𝑑𝑒 −2𝑑 , 𝑦(0) = −3

9. Assuming the current at 𝑑 = 0 is zero in the following circuit; find the equation for current 𝑖(𝑑) using the method of Laplace Transforms.

10. Solve the difference equation 𝑦[π‘˜ + 3] − 6𝑦[π‘˜ + 2] + 11𝑦[π‘˜ + 1] − 6𝑦[π‘˜] = 0 subject to 𝑦(0) = 0, 𝑦(1) = 2 and 𝑦(2) = 2 by z-Transform method.

1. A function is given by 𝑓(π‘₯) = 1 − |π‘₯| 𝑇 , where π‘₯ ∈ [−𝑇, 𝑇]. State whether the function is even or odd and hence find the Fourier series for this function.


100% Plagiarism Free & Custom Written,
Tailored to your instructions


International House, 12 Constance Street, London, United Kingdom,
E16 2DQ

UK Registered Company # 11483120


100% Pass Guarantee

STILL NOT CONVINCED?

View our samples written by our professional writers to let you comprehend how your work is going to look like. We have categorised this into 3 categories with a few different subject domains

View Our Samples

We offer a Β£ 2999

If your assignment is plagiarised, we will give you Β£ 2999 in compensation

Recent Updates

Details

  • Title: [Solved] 1. A function is given by 𝑓(π‘₯) = 1 βˆ’ |π‘₯| 𝑇 , where π‘₯ ∈ [βˆ’π‘‡, 𝑇]. State whether the function is even or odd and hence find the Fourier series for this function.
  • Price: Β£ 219
  • Post Date: 2021-10-16T06:04:30+00:00
  • Category: Essays & Coursework
  • No Plagiarism Guarantee
  • 100% Custom Written

Customer Reviews

[Solved] 1. A function is given by 𝑓(π‘₯) = 1 βˆ’ |π‘₯| 𝑇 , where π‘₯ ∈ [βˆ’π‘‡, 𝑇]. State whether the function is even or odd and hence find the Fourier series for this function. [Solved] 1. A function is given by 𝑓(π‘₯) = 1 βˆ’ |π‘₯| 𝑇 , where π‘₯ ∈ [βˆ’π‘‡, 𝑇]. State whether the function is even or odd and hence find the Fourier series for this function.
Reviews: 5

A masterpiece of assignment by , written on 2020-03-12

I have been taking help from Insta Research since 2015 and believe me, this place is incredible in giving the best help in assignments and essays. I also ask them to run plagiarism in my essays that I have written, and they always gave me accurate results. I am literally blessed to have a strong bonding with this site so that in any need of urgency, I contact them and find them always beside me. Thank you!
Reviews: 5

A masterpiece of assignment by , written on 2020-03-12

I received my order last night and now I’m writing my reviews. My assignment has all the points I needed along with a good style. The citations used are relatable and professional. The best thing is the discount I got because I recommended my friend too to use their service. I am so pleased to use this effective service. The features are also amazing, everything is good. Will come again soon!