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Analytic solutionRead more

Created:Dec 07, 2018Last updated:Mar 18, 202153 views0 comments

There are two numbers that are important for FFT resolution: total amount of samples NNN and sampling frequency nnn. If we have fundamental period time TTT, which we may choose to be unity (T=1T=1T=1), then the sampling frequency is simply the amount of samples per unit time, and is called ndt in the code.
The sampling frequency is very important: it sets the upper limit on the highest resolvable frequency. By the Nyquist theorem (also known as the Whittaker–Nyquist–Kotelnikov–Shannon theorem, https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem), for a frequency f0f0f_0 to be resolvable, the sampling frequency has to be at least more than twice that: n>2f0n>2f0n>2f_0. Conversely, with more than two samples, we are able to reconstruct a sine wave perfectly.Read more

Created:Dec 07, 2017Last updated:Mar 25, 202122 views0 comments

Zeitliche Verschiebung kriegen wir durch
[Math Processing Error]F′(ω)=exp[−i(ω−ω0)τ0]F(ω), F'(\omega) = \exp\left[-\mathrm{i}(\omega-\omega_0)\tau_0\right]F(\omega),
wo [Math Processing Error]τ0\tau_0 is die Verschiebung und [Math Processing Error]ω0\omega_0 das Trägerfrequenz.Read more

Created:Jul 18, 2017Last updated:May 10, 202117 views0 comments