Transcribed TextTranscribed Text

1. (7 marks) Starting with the differentiation property of the Fourier Transform given below and without using the time XT shift property of the Fourier Transform, determine the Fourier Transform of the signal shown. Simplify as much as possible and express your answer in terms of the sinc function as defined. You may need to find a suitable trigonometric identity. t T 2T d²: x (t) F dt² (jw)"X(w) sinc(8) = sin 0 (0) 2. (3 marks) The triangle signal shown can be constructed by 4 XT2 the convolution of two identical rectangle signals as also shown. Use the definition of the Fourier Transform and its convolution property as given to determine the Fourier Transform of the triangle signal. Simplify as much as t possible and express your answer in terms of the sinc -T T function. A x(t) = Xorect (t/T) X, = 8 x -jwt f( t) * g(t) F F(w)G(w) sinc(8)= = sin(6 t -T/2 T/2

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Electrical Engineering Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats