Fourier Series

The continuous time signal x(t) is real, periodic with period T and satisfies the Dirichlet conditions. The Fourier series representation of x(t) = $\sum_{-\infty}^{\infty} a_n e^{...

Let f (t) be a periodic signal with fundamental period T₀ > 0. Consider the signal y(t) = f(αt), where α > 1. The Fourier series expansions of f(t) and y(t) are given by f(t) = $\s...

Let $f(t)$ be a periodic signal with fundamental period $T_0>0$. Consider the signal $y(t)=f(\alpha t)$, where $\alpha>1$. The Fourier series expansions of $f(t)$ and $y(t)$ are gi...

Consider a discrete-time periodic signal with period N = 5. Let the discrete-time Fourier series (DTFS) representation be x[n] = $\sum_{k=0}^{4} a_k e^{\frac{jk2\pi n}{5}}$, where...

In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a) Continuous, aperiodic (ii) Con...

The exponential Fourier series representation of a continu-ous-time periodic signal $X(t)$ is defined as $$ x(t)=\sum\limits_{k=-\infty}^{\infty} a_k e^{j k w_0 t} $$ Where $\omega...

Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎 𝑘 , that is $$x\left( t \right) = \sum\limits_{k = - \inft...

A periodic signal x(t) has a trigonometric Fourier series expansion $$$x\left(t\right)=a_0\;+\;\sum_{n=1}^\infty\left(a_n\cos\;n\omega_0t\;+\;b_n\sin\;n\omega_0t\right)$$$ If $$x\l...

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a k } be the complex Fourier series coefficients of x(t), where k is integer valued. Consi...

Consider a discrete time periodic signal x$$\left[ n \right]$$= $$\sin \left( {{{\pi n} \over 5}} \right)$$. Let a k be the complex Fourier serier coefficients of x$$\left[ n \righ...

The Fourier series of a real periodic function has only P. Cosine terms if it is even Q. Sine terms if it is even R. Cosine terms if it odd S. Sine terms if it is odd Which of the...

Choose the function f (t );−$$\infty$$ < 1 < +$$\infty$$, for which a Fourier series cannot be defined.

Match the following and choose the correct combination. GROUP 1 E- continuous and aperiodic signal F- continuous and periodic signal G- discrete and aperiodic signal H- discrete an...

Which of the following cannot be the Fourier series expansion of a periodic signal?

The trigonometric Fourier series of a periodic time function can have only

The trigonometric Fourier series of an even function of time does not have the

The Fourier Series of an odd periodic function, contains only

A low pass signal m(t) band-limited to B Hz is sampled by a periodic rectangular pulse train, $${p_\tau }(t)$$ of period $${T_s}$$ = 1/(3B) sec. Assuming natural sampling and that...