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Standard XII

Mathematics

Period of a Function

The trigonome...

Question

The trigonometric Fourier series expansion of the following periodic waveform contain

Non Zero DC value

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Sine terms

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Zero Dc value

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Cosine terms

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Solution

The correct option is D Cosine terms
(b, c)
f(t) is an even function with DC component
$\Rightarrow a_{0}$ and $a_{n}$ (cosine) terms exist in its Fourier series expansion.

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Similar questions

Q. The

a_{12}

coefficient of the trigonometric Fourier series of the signal whose one period is given as

x (t) = {\begin{matrix} c o s t & 0 \leq t \leq \frac{π}{2} - c o s t & - \frac{π}{2} \leq t \leq 0 \end{matrix}

Where

a_{n}

is coefficient of

c o s n ω_{0} t

in the trigonometric Fourier series expansion

Q. The coefficient

a_{4}

of the trigonometric Fouries series of a periodic signal with period of

2 π

whose one period is given as

x (t) = {\begin{matrix} s i n t, & 0 \leq t \leq π 0, & π \leq t \leq 2 π \end{matrix}

Where

a_{n}

is coefficient of

c o s (n ω_{0} t)

in the trigonometric Fourier series expansion.

The Fourier series expansion of the saw - toothed waveform $f (x) = x, i n t h e i n t e r v e l (- π, π)$ of period $2 π$ gives the series, $1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + . . . . = ?$

Q. A periodic signal x(t) has a trigonometric Fourier series expansion

x (t) = a_{0} + \sum_{n = 1}^{\propto} (a_{n} cos n ω_{0} t + b_{n} sin n ω_{0} t)

If x(t) = -x(-t)

= - x (t - \frac{π}{ω_{0}})

. We can conclude that

Q. The signal shown below will contain the following non-zero trigonometric Fourier series coefficients

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The trigonometric Fourier series expansion of the following periodic waveform contain

The correct option is D Cosine terms (b, c) f(t) is an even function with DC component ⇒a0 and an (cosine) terms exist in its Fourier series expansion.

The correct option is D Cosine terms
(b, c)
f(t) is an even function with DC component
$\Rightarrow a_{0}$ and $a_{n}$ (cosine) terms exist in its Fourier series expansion.