The impact of memory depth on FFT results

    In a DSO, the spectrum of a signal can be obtained through the fast Fourier transform (FFT), and then a signal can be analyzed in the frequency domain. For example, the measurement of power supply harmonics requires the use of FFT to observe the spectrum. In the measurement of high-speed serial data, FFT is often used to analyze the noise and interference that cause system failure. For FFT operations, the total amount of acquisition memory available to the oscilloscope will determine the maximum range (Nyquist frequency) in which the signal components can be observed, and the memory depth also determines the frequency resolution △f. If the Nyquist frequency is 500 MHz and the resolution is 10 kHz, consider determining the length of the observation window and the size of the acquisition buffer. To obtain a resolution of 10kHz, the acquisition time is at least: T = 1/△f = 1/10 kHz = 100 ms. For a digital oscilloscope with 100 kB of memory, the highest frequency that can be analyzed is:

△f × N/2 = 10 kHz × 100 kB/2 = 500 MHz

 

Figure 11 Oscilloscope FFT operation

In the example shown in Figure 12, a 266 MHz signal is affected by noise pickup from a 30 kHz noise source. The FFT (lower trace) shows a series of peaks centered at 266 MHz and spaced 30 kHz apart. This type of distortion is very common and can be caused by crosstalk from a switching power supply, DC-DC converter, or other source. It can also be caused by intentional use of spread spectrum clocking.

 

 

Figure 12 FFT analysis of LeCroy oscilloscope

For DSO, long memory can produce better FFT results, increasing both frequency resolution and signal-to-noise ratio. In addition, for some applications, some very detailed information can only be analyzed at a memory depth of 20 Mpts, as shown in Figures 13 and 14.

 

Figure 13: The FFT result of 1M points cannot reveal information about modulation

 

Figure 14 The 20M-point FFT clearly confirms the bimodal distribution of the clock and the related modulation rules

 

    It should be pointed out that FFT analysis of long waveforms requires the oscilloscope to have super data processing capabilities, which often exceeds the computing limit of some oscilloscopes. LeCroy oscilloscopes can perform up to 25M points of FFT analysis, while the oscilloscopes of T Company in the industry can only perform up to 3.125M points of FFT analysis.