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

# [Solved] 1. A function is given by π(π₯) = 1 β |π₯| π , where π₯ β [βπ, π]. State whether the function is

100% Pass and No Plagiarism Guaranteed

### [Solved] 1. A function is given by π(π₯) = 1 β |π₯| π , where π₯ β [βπ, π]. 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 π(π₯) = 1 − |π₯| π , where π₯ ∈ [−π, π]. 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 π(π₯) = π₯ 3 − 2π₯ 2 , defined on −π < π₯ < π (Hint: Use the following information to simplify integration. If π(π₯) is odd function and πΈ(π₯) is even function then π(π₯) = π(π₯) ∗ πΈ(π₯) is an odd function and ∫ π(π₯) π −π = 0)

3. Find the Fourier transform of the function π(π‘) = { 0 π‘ < − π 2 ⁄ (4π‘ + 1) − π 2 ⁄ ≤ π‘ ≤ π 2 ⁄ 0 π 2 ⁄ < π‘ }

4. Using the definition of Laplace Transform, show that: L{ln(π₯)} = − ( πΎ + ln(π ) π  ), Where, πΎ = − ∫ π −π₯ ln(π₯)ππ₯ ∞ 0

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

6. Solve for π₯(π‘) the following differential equation which has an impulse input, π₯Μ+ 6π₯Μ + 8π₯ = 4. πΏ(π‘ − 5) π₯(0) = 0, π₯Μ(0) = 3

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

8. Using the method of Laplace Transforms, solve the following initial valued problem π¦ ′ + 2π¦ = 4π‘π −2π‘ , π¦(0) = −3

9. Assuming the current at π‘ = 0 is zero in the following circuit; find the equation for current π(π‘) using the method of Laplace Transforms.

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

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

100% Plagiarism Free & Custom Written,

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

## 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

Nov,10,2018

Nov,10,2018

Nov,10,2018

### Details

• Title: [Solved] 1. A function is given by π(π₯) = 1 β |π₯| π , where π₯ β [βπ, π]. 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 π(π₯) = 1 β |π₯| π , where π₯ β [βπ, π]. State whether the function is even or odd and hence find the Fourier series for this function.
Reviews: 5

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

The support team is quite friendly and gives you the best solutions. I literally came here crying and went smiling like an idiot. My HR assignment is written beautifully with all the specifications I wanted. This is the best platform to get helped in assignments for me. All the people are supportive. Keep it up you all!
Reviews: 5

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

The writer 0223 is really helpful. He gave me the best essay ever. Love you loads for such a great job and thanks again.