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- Plz answer the question in 10 mints plzzzzz it's very urgent plzzzzzCAL CULATE THE FOURIER SERIES IN EXPONIENTIAL FORM BY DIRECTLY CALCULATING ITS COEFFIC- ENTS OF THE FULL- RANGE FOURIER SERIES OF : +2-2t +1 if +2+ 2t +1 iF -14t z0In the Fourier Series an and bn (for any n) are found by multiplying the signal by the nth harmonic (i.e. cos nx or sin nx), and then integrating. This works because multiplying any sinusoid (signal) by a sine or cosine results in a curve with an integral of A if the harmonic (n) is NOT present in the original signal. This process (multiplying the signal by a sinusoid of known frequency and integrating) is called A/ Reminder: Fourier Series: f(x)= ao + Σ(ancosx + b sinx), for all n
- N:10)if the Fourier series coefficients for the signal X[n] with a period N are "ax", calculate the Fourier series coefficients of the following expressions in terms of "ax". (a) x[n-2]+ x[n-(N-4)/2] (N even) (b) -1"x[-n] (N even) (c) yin]={ x[n], it n even 0, otherwiseFind at least three nonzero terms (including ao and at least two cosine terms and two sine terms if they are not all zero) of the Fourier series for the given function, and sketch at least three periods of the function. Which of the following is the Fourier series for the given function? f(x) = 2 O A. f(x) = O B. f(x)= π 4 O D. f(x)= π 4 NI 2 π O c. f(x) = 2 π 2 π + π 4 - π 4 π COS X- COS X- - sin x + COS X- - 4 9μ 4 9μ 4 9₁ 4 - cos 3x... - - sin x- π 4 9μ cos 3x - ... sin 3x + . cos 3x - ... + 4 - sin x + π 4 9μ 4 9μ sin 3x - ... sin 3x + ... f(x) = -X ≤x<0 X 0≤x5) If f(x)= x?; f (x +4)=f (x) b. The coefficient n in this Fourier series is : 2 (-1)". (na) (-1)** . (na) (-1)- cos d) 2 a) b) 0 c)d) Write the corresponding Fourier series of f (x). A periodic function of f (x) is given by [0, f(x)={-x-7, f(x+27). - T < x < 0, 0Find the Fourier series expansion for the following signals once with real coefficients and another with complex coefficients. Please provide a thorough explanation. "Hand written solution plz"Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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