1
$\begingroup$

Why is $\delta[an]=\frac 1 a \delta[n]$ in discrete time? Prove.

Hi, I want to prove it but I don’t know on what facts to rely. In continuous time we have integral and dt in that integral that turns to be dt/a for continuous time delta function. But in discrete time, we don’t have dt. So how to prove it then?

Improve this question
$\endgroup$
4
  • $\begingroup$ Where did you find that "identity"? $\endgroup$ – Matt L. Apr 26 '20 at 19:39
  • $\begingroup$ Here: pilot.cnxproject.org/content/collection/col10064/latest/module/… $\endgroup$ – Vitali Pom Apr 26 '20 at 19:39
  • 1
    $\begingroup$ This is a property of the Dirac distribution and follows from a substitution of the integration variable. It does not have an equivalent for the Kronecker unit impulse. $\endgroup$ – Jazzmaniac Apr 26 '20 at 19:50
  • $\begingroup$ Thanks! Marking as correct. $\endgroup$ – Vitali Pom Apr 26 '20 at 19:52
2
$\begingroup$

It's actually good that you couldn't prove it because the claim is wrong. Note that in discrete time we have $\delta[n]=1$ for $n=0$ and $\delta[n]=0$ for $n\neq 0$. So if $a\neq 0$, you simply get $\delta[an]=\delta[n]$ (note that $a$ must be an integer for this to make sense). If $a=0$ then $\delta[an]=1$ (for all $n$).

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thanks Matt. Let’s wait for one more opinion before I mark your answer as the right answer, since I already saw a few things I considered to be wrong and meanwhile my teacher proves I’m the only wrong time after time. Thanks for your answer, it raises my level of confident (besides seemingly being true). $\endgroup$ – Vitali Pom Apr 26 '20 at 19:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.