recategorized by
340 views
1 1 vote

Let $f(t)$ be a periodic signal of period $1$, i.e. $f(t+1)=f(t) \forall t$. Define the averaging operator depending on a fixed parameter $h>0$ as below:
\[g(x)=\frac{1}{2 h} \int_{x-h}^{x+h} f(t) d t .\]

Which of the following is $\text{TRUE}$ for the new signal $g(x)$?

  1. $g(x)$ is aperiodic
  2. $g(x)$ is periodic with period $\frac{1}{2}$
  3. $g(x)$ is periodic with period $1$
  4. The value of $h$ determines whether or not $g(x)$ is periodic
  5. None of the above

Please log in or register to answer this question.

Answer:
Position:
Show:

Related questions

1 1 vote
0 0 answers
248
248 views
admin asked Nov 30, 2022
248 views
Convolution between two functions $f(t)$ and $g(t)$ is defined as follows: $f(t) * g(t)=$ $\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$. If $f(t) * g(t)=h(t)$, what ...
1 1 vote
0 0 answers
284
284 views
admin asked Dec 8, 2022
284 views
Consider a periodic square wave $f(t)$ with a period of $1$ second such that $f(t)=1$ for $t \in[0,1 / 2)$ and $f(t)=-1$ for $t \in[1 / 2,1)$. It is passed through an ide...
1 1 vote
0 0 answers
270
270 views
admin asked Nov 30, 2022
270 views
Recall that\[\operatorname{sinc}(t)=\frac{\sin (\pi t)}{\pi t}\]and convolution of functions $x(t)$ and $y(t)$ is defined as\[x(t) \star y(t)=\int_{-\infty}^{\infty} x(t-...
0 0 votes
0 0 answers
339
339 views
admin asked Oct 2, 2022
339 views
If the Fourier Transform of deterministic signal $\mathrm{g}(\mathrm{t})$ is $\mathrm{G}(f)$, then(1) The Fourier Transform of $g(t-2)$ is$G(f) e^{-j(4 \pi f)}$(2) The Fo...

Add Synced Question

×