Fourier Series

A time-limited waveform g(x) is specified as follows: g(x) = { -k, -π < x ≤ 0 +k, 0 < x ≤ π 0, otherwise A new waveform f(x) is constructed from g(x) as follows: f(x) = Σ_{m=-∞}^{∞...

A continuous time periodic signal x(t) is $x(t) = 1 + 2 \cos 2\pi t + 2 \cos 4\pi t + 2 \cos 6\pi t$ If T is the period of x(t), then $\frac{1}{T} \int_{0}^{T} |x(t)|^2 dt = $ ____...

A continuous time periodic signal $x(t)$ is $$ x(t)=1+2 \cos 2 \pi t+2 \cos 4 \pi t+2 \cos 6 \pi t $$ If $T$ is the period of $x(t)$, then $\frac{1}{T} \int_0^T|x(t)|^2 d t=$______...

The discrete-time Fourier transform of a signal x[n] is X($\Omega$) = (1 + cos$\Omega$)e$^{-j\Omega}$. Consider that x$_p$[n] is a periodic signal of period N = 5 such that x$_p$[n...

A periodic function f(t), with a period of 2π, is represented as its Fourier series, f(t) = a₀ + Σ_{n=1}^∞ aₙ cos nt + Σ_{n=1}^∞ bₙ sin nt. If f(t) = { A sin t, 0 ≤ t ≤ π; 0, π < t...

Consider $g(t) = \begin{cases} t - \lfloor t \rfloor, & t \ge 0 \\ t - \lceil t \rceil, & \text{otherwise} \end{cases}$, where $t \in \mathbb{R}$. Here, $\lfloor t \rfloor$ represe...

Let the signal $x(t) = \sum_{k=-\infty}^{+\infty} (-1)^k \delta (t - \frac{k}{2000})$ be passed through an LTI system with frequency response H($\omega$), as given in the figure be...

Consider $$$g\left(t\right)=\left\{\begin{array}{l}t-\left\lfloor t\right\rfloor,\\t-\left\lceil t\right\rceil,\end{array}\right.\left.\begin{array}{r}t\geq0\\otherwise\end{array}\...

The signum function is given by $$$\mathrm{sgn}\left(\mathrm x\right)=\left\{\begin{array}{l}\frac{\mathrm x}{\left|\mathrm x\right|};\;\mathrm x\neq0\\0\;;\;\;\mathrm x=0\end{arra...

For a periodic square wave, which one of the following statements is TRUE?

A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is

The input voltage given to a converter is $${V_i} = 100\sqrt 2 \,\,\,\sin \,\,\,\left( {100\pi t} \right)\,\,V$$ The current drawn by the converter is $${i_i} = 10\sqrt 2 \,\,\,\si...

The Fourier Series coefficients, of a periodic signal $$x\left( t \right),$$ expressed as $$x\left( t \right) = \sum {_{k = - \infty }^\infty {a_k}{e^{j2\pi kt/T}}} $$ are given by...

Let x(t) be a periodic signal with time period T. Let y(t) = x(t - t 0 ) + x(t + t 0 ) for some t 0 . The Fourier Series coefficient of y(t) are denoted by b k . If b k =0 for all...

A signal $$x(t)$$ is given by $$x\left( t \right) = \left\{ {\matrix{ {1, - {\raise0.5ex\hbox{$\scriptstyle T$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}} < t \l...

$$x(t)$$ is a real valued function of a real variable with period $$T.$$ Its trigonometric. Fourier Series expansion contains no terms of frequency $$\omega = 2\pi \left( {2k} \rig...

The Fourier series for the function f(x) = sin 2 x is

A single phase Inverter with square wave output voltage will have in its output waveform a fifth harmonic component equal to ______ percentage of the fundamental