Linrad support: fft1 resampling spurs
(Aug 1 2001)
This page shows the resampling spurs that are produced when a time function is produced by back transformation of a part of a fourier transform.

The images are produced with linrad00-21 running at 44100Hz sampling speed for a single real signal. The signal is produced by an audio generator set close to A/D board saturation. The audio board is a Delta44.



Fig 1. Bandwidth is set to 200Hz with a sin to power 3 window. The resampling rate is 1/16 This screen shows that the spur level at 500Hz offset is about -60dB




Fig 2. Bandwidth is set to 200Hz with a sin to power 3 window. The resampling rate is 1/16 This screen shows that the spur level at 1500Hz offset is about -108dB


Figures 1 and 2 show that a selected bandwidth of 200Hz gives a 100dB spur suppression at about 1.5kHz when the decimation rate is 16.

Figures 3 and 4 show how the resampling spurs grow when an inadequate window is used. A dynamic range of 90 dB at a frequency offset of 2.5kHz is not really bad. Most CW signals transmitted by radio amateurs have wider spectrum than that!



Fig 3. Bandwidth is set to 200Hz with a sine window. The resampling rate is 1/16 This screen shows that the spur level at 1500Hz offset is about -35dB




Fig 4. Bandwidth is set to 200Hz with a sine window. The resampling rate is 1/16 This screen shows that the spur level at 2500Hz offset is about -90dB


Figure 5 shows the influence of the resampling rate. By picking a larger part of the spectrum one can suppress the resampling spurs.

The part of the spectrum picked for back transformation is first filtered through a filter that attenuates frequencies at the ends of the spectrum. This simply means that the fourier bins are multiplied by a window function. This window is flat in the center region and the fall off becomes softer if a larger fraction of the original transform is selected.



Fig 5. Bandwidth is set to 200Hz with a sine window. The resampling rate is 1/4 This screen shows that the spur level at 1000Hz offset is about -80dB


Figures 6 and 7 show that with a normal bandwidth, required to locate weak signals, a sine squared window is more than adequate to suppress the resampling spurs.



Fig 6. Bandwidth is set to 20Hz with a sine squared window. The resampling rate is 1/16 The spur level 100Hz away from the carrier is below -100dB.




Fig 7. Bandwidth is set to 200Hz with a sine window. The resampling rate is 1/16 At 450Hz offset the spurs have disappeared in the noise floor at -130dB



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