![]() In extreme case let us assume we have a "sinusoid" such that it exists only for a quarter cycle and even less than that, (its not exactly an sinusoid, BTW) we see that we can never guess the exact frequency of sinusoid. Now if we go on to decrease the length of this sinusoid we will be going away from the exact value of frequency. The frequency of this sinusoid can be determined very closely to the exact value (remember, the principle states that you can measure one of the conjugate variable accurately if other one is not accurate). Now suppose that we have an infinite sinusoid running on entire time axis. Let us write Heisenberg's uncertainty principle in terms of frequency and time. It feels as if you havent been through fourier analysis yet so I will try to explain it in different way. You see that an infinite sinusoid has zero bandwidth while a time limited sinusoid has finite bandwidth. There are many parameters that define bandwidth. I wanted to put it as a comment but couldnt do that and I am by no means an expert.Īs a matter of fact "bandwidth" is ambiguous. $$\max \left| \frac(f) = 0$ for all $|f|>f_0$) and that the infinitely fast changing of the rectangular pulse is well-supported by the infinite bandwidth of the rectangular pulse. As you were told, a pure sinusoid $x(t) = \sin(2\pi f_0t \theta)$ has zero bandwidth (according to the definition of bandwidth that your tutor is using) but that does not mean that the sinusoidal is not changing at all! It is changing and its maximum slope (a.k.a. ![]() This is not correct even in a hand-waving fashion. "tutor explained that the bandwidth indicates how fast the signal is changing"
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