The value of \(\smallint \limits_{ - \infty }^{ + \infty } {e^{ - t}}\delta \left( {2t - 2} \right)dt\), where \(\delta \left( t \right)\) is the Dirac delta function, is
\(\frac{1}{{2e}}\)
Use \(\delta(2t-2)=\tfrac12\delta(t-1)\). Sifting gives \(\int_{-\infty}^{\infty}e^{-t}\delta(2t-2)\,dt=\tfrac12e^{-1}=1/(2e)\).
Important Questions from Standard Signals
The properties of Dirac Delta are
A. δ (t - to)=∞ if t = to
B. δ (t - to)=0 if t = to
C. δ (t - to)=0 if t ≠ to
D. δ (t - to)=∞ if t ≠ to
E. δ (t - to)=1 for all t = to
Choose the correct answer from the options given below:
The correct expression of the following triangular wave is :
The average value of a periodic trapezoidal waveform is given by :
The fourth harmonic of a fundamental frequency is 512 Hz. What is the fundamental frequency?
Consider a continuous-time signal
$x(t) = – t^2 \{u(t + 4) – u(t – 4)\}$
where $u(t)$ is the continuous-time unit step function. Let $\delta(t)$ be the continuous-time unit impulse function. The value of
$\int_{-\infty}^{\infty} x(t) \delta(t + 3)dt$ is
