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Consider the periodic function f(t) with fundamental interval -T

Consider the periodic function f(t) with fundamental interval -T

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the periodic function f(t) with fundamental interval –7 <t < that is defined by -t - T for -T <t< 0, f(t) : for 0 <t < T, f(t+ 2π) = f(t). (a) Sketch the graph of the function f for -3T <t< 3n, and hence state whether the function is even, odd, or neither even nor odd. (b) Calculate the Fourier series for f(t) and hence show that the first few terms are 3 2 F(t) - cos(t) – cos(3t) 9T -IT 4 1 1 - sin(t) + sin(2t) - sin(3t). 2 3
Transcribed Image Text:Consider the periodic function f(t) with fundamental interval –7 <t < that is defined by -t - T for -T <t< 0, f(t) : for 0 <t < T, f(t+ 2π) = f(t). (a) Sketch the graph of the function f for -3T <t< 3n, and hence state whether the function is even, odd, or neither even nor odd. (b) Calculate the Fourier series for f(t) and hence show that the first few terms are 3 2 F(t) - cos(t) – cos(3t) 9T -IT 4 1 1 - sin(t) + sin(2t) - sin(3t). 2 3
Fourier of f(E) Fourler Series EicSlly (he (seetion to the terms. in quescion. Secies foc periodic function 2.1.ymit 1) F(E) = Aot Z An cos USing Fourier,coefficients +E Bn Sin (2nt) का nat Ehe following formulas to determine the てル f6) dt, -T/2 て2 2nat f(6) Cos (a ) de (n= 12,.) @ Bn= S peo Sin (aEE) dt Where ł fundamer tal Deciod. I the てこ2て Ficstig finding
Transcribed Image Text:Fourier of f(E) Fourler Series EicSlly (he (seetion to the terms. in quescion. Secies foc periodic function 2.1.ymit 1) F(E) = Aot Z An cos USing Fourier,coefficients +E Bn Sin (2nt) का nat Ehe following formulas to determine the てル f6) dt, -T/2 て2 2nat f(6) Cos (a ) de (n= 12,.) @ Bn= S peo Sin (aEE) dt Where ł fundamer tal Deciod. I the てこ2て Ficstig finding
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