Appendix F: Miscellaneous
Record Length and Frequency Resolution
Relationship Between Phase and Delay
maximum permitted frequency is called the Nyquist frequency and is 1/2 the sampling rate.
If the signal has frequency components above the Nyquist frequency, they appear on this limited discrete frequency axis too. They appear as no different than noise aliased from the Nyquist frequency. For example, if there is a signal 5 MHz above the Nyquist frequency, it appears as if it is 5 MHz below the Nyquist frequency. On the other hand, in the D/A conversion, a frequency component is output aliased above the Nyquist frequency.
To deal with aliasing, first it is necessary to sample with a clock greater than double the highest frequency component in the signal. Second, a
The frequency spectrum frequency range and resolution depend on the time axis sampling rate and the record length (N).
For the given data length on the time axis, FFT has frequency components from ±N/2 to N/2±1. However, when the real number data on the time axis is transformed, FFT gives results symmetrical about 0 Hz (DC). Because of this symmetry, all the necessary frequency data is contained between 0 and N/2 ± 1. Thus, with FFT if values are given from zero to the positive N/2 point, this is enough. Since the
Since FFT has N/2 sampling points on the discrete frequency axis between DC and the Nyquist frequency (FN), the frequency resolution is FN/(N/2). Since the Nyquist frequency is one half the sampling rate (fs), the frequency resolution can also be expressed as fs/N.
Therefore, if the sampling rate is fixed, when the record length is increased, the frequency resolution rises. On the other hand, if the record length is fixed, raising the sampling rate raises the Nyquist frequency and lowers the frequency resolution.
The phase is the quantitative displacement from the standard time. The cos(2 π ft) has a 0 phase, but sin(2 π ft) has a 90 degree delay. The standard time is the sampling start time.
AWG2021 User Manual | F17 |