I am from mathematical background and don't know much about signal processing. In DSP they talk about sampling frequency which should be more than the twice of highest frequency that carries significant information. So what about the signals of type exp(t) and t? Any suggested reading are most welcome.
We don't know how much is exp(1 hour), do we? The argument of "exp" function has to be dimensionless. Therefore what we often see is rather the form exp(t/\tau), where \tau is some characteristic time of a system, often called relaxation time. For often encountered signals, containing terms like (1 - exp( -t/\tau)) (for t > 0), or 1/(1 + exp(-t/\tau)) (for any t), the sampling interval equal to \tau (or sampling frequency = 1/\tau)) seems highest (lowest) acceptable/sensible. In systems characterized by few relaxation times the shortest one should determine sampling time/frequency.
Are you sure u mean exp(t)??
In the signal processing case it does not make any sense.. Could it be you mean exp(i \omega t)?
Martin, think not only about oscillatory terms. There should be some kind of damping (decay) as well.
To sample these functions, you choose a period of time(let say 1 second) and draw some values, for example 100 samples. in this situation both of "t" and "exp(t)" functions are low frequency signalss and you do not need to wary about Nyquist frequency criterion.
- Badges
- Science topic
- Similar topics
- Engineering
- Electrical Engineering
- Signal Processing