Analog Fouriertransformation: 17 Nov 2014, Pre-digital computer 'cranks out' Fourier Transforms. Boffins get a handle on pre-digital computer, restore it to working order Citat: "...designer Albert Michelson...As “Engineer guy” Bill Hammack explains in the video below (third in his series), the machine operation is surprisingly simple: the user sets the wave they want analysed in the rocker bars of the machine and turns the crank. The pen outputs the coefficients - in other words, the sine waves (fundamental and harmonic) that make up the input function, and their relative amplitude...That limits it to analysing a waveform with 20 samples. However, as they note in the book, Michelson also constructed an 80-sample machine...", backup
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asp.ucar.edu
asp.ucar.edu: 8. Spectral Analysis: 8.9 Aliasing Citat: "...The Fourier transform determined from the discrete series thus will include contributions not only from the analyzed frequency $\nu$ but also from all other frequencies that differ from that frequency by an integer multiple of the sampling frequency. This mixing of contributions from different frequency components is called "aliasing." There is no way to separate the various components that contribute to $\tilde g(\nu)$ in (8.55), once they are mixed during sampling...For this reason, we can only analyze Fourier coefficients over a unique range of frequencies varying by $1/\Delta T$, because beyond this range the analysis will simply repeat...To reduce aliasing, low-pass filters can reduce the high-frequency components of a signal before sampling. If this is not done, higher-frequency contributions from the variance spectrum will appear as false contributions to lower parts of the estimated spectrum, and they cannot be eliminated after sampling because information distinguishing the separate contributions from frequencies above and below the Nyquist frequency is lost...", backup
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Analog Fouriertransformation: 17 Nov 2014, Pre-digital computer 'cranks out' Fourier Transforms. Boffins get a handle on pre-digital computer, restore it to working order Citat: "...designer Albert Michelson...As “Engineer guy” Bill Hammack explains in the video below (third in his series), the machine operation is surprisingly simple: the user sets the wave they want analysed in the rocker bars of the machine and turns the crank. The pen outputs the coefficients - in other words, the sine waves (fundamental and harmonic) that make up the input function, and their relative amplitude...That limits it to analysing a waveform with 20 samples. However, as they note in the book, Michelson also constructed an 80-sample machine...", backup
asp.ucar.edu: 8. Spectral Analysis: 8.9 Aliasing Citat: "...The Fourier transform determined from the discrete series thus will include contributions not only from the analyzed frequency $\nu$ but also from all other frequencies that differ from that frequency by an integer multiple of the sampling frequency. This mixing of contributions from different frequency components is called "aliasing." There is no way to separate the various components that contribute to $\tilde g(\nu)$ in (8.55), once they are mixed during sampling...For this reason, we can only analyze Fourier coefficients over a unique range of frequencies varying by $1/\Delta T$, because beyond this range the analysis will simply repeat...To reduce aliasing, low-pass filters can reduce the high-frequency components of a signal before sampling. If this is not done, higher-frequency contributions from the variance spectrum will appear as false contributions to lower parts of the estimated spectrum, and they cannot be eliminated after sampling because information distinguishing the separate contributions from frequencies above and below the Nyquist frequency is lost...", backup
