# DWT on short signals

I have signals with a very short rate of ~100e-6 seconds, sampled at 10MHz,so about 1k samples.

I am wondering, is there a practical limit to the usefulness of time-frequency methods concerning a minimal duration of the signal or a certain sampling frequency for that matter?

i am talking about chirp radar signals which fires 1000 linear chirps each 100us long which I sample at 10 MHz. so the whole frame takes only about 100ms

• I'd say two samples is the least length I could still reasonably apply a DWT to. But that's probably not the "usefulness" you're referring to. However, "Usefulness" is relative to a purpose, which you neglect to state. – Marcus Müller Jun 26 '20 at 22:30
• well ofc I want to extract features both in the time and frequency domain. I reckon that for an audio signal of say 10 seconds this seems appropriate. given a duration od only 100us however, I am wondering if this is jot a period too short of generally being able to reason about features in the time domain – CD86 Jun 27 '20 at 9:38
• again, you're not stating for which purpose you're doing your reasoning! Obviously, you're not sampling audio at 10 MHz, so that's not really a useful reference. The math is the same whether you do it on 1000 Samples sampled at 10 kHz or 10 MHz. The statements are the same. – Marcus Müller Jun 27 '20 at 9:45
• i am talking about chirp radar signals which fires 1000 linear chirps each 100us long which I sample at 10 MHz. so the whole frame takes only about 100ms – CD86 Jun 27 '20 at 10:31
• you really need to add that to your questioN! – Marcus Müller Jun 27 '20 at 10:46

The duration of the time domain data effects the frequency resolution of the DFT result (the ability to uniquely distinguish two closely spaced frequency tones that are approximately the same power level). Without any further windowing applied (a rectangular window) the equivalent noise bandwidth in Hz is given by $$1/T$$ where $$T$$ is the duration in seconds. Any additional windowing applied further increases this bandwidth at the benefit of dynamic range (ability to distinguish two frequency tones at different power levels).