# Mean velocity in unsteady flow

I'm starting hydraulic experiments, where I'd have to measure velocity in an unsteady flow with a device called Acoustic Doppler Velocimeter (acquisition rate: 100 Hz) . In DSP terms, I'd have a nonstationary signal in a shape of waves (https://imgur.com/a/Qd72HjO for streamwise velocity (first curve) with 2 waves). This signal contains the mean component (mean velocity) and noise (turbulence). My goal is to extract the mean velocity.

I have looked up DSP and found many interesting models (Huang-Hilbert Transform, Wavelet Transform, Short Fourier Transform) to denoise. The only problem is that, in steady case, they need about 3 minutes measuring in one point so that they can average (arithmetic averaging) and filter out this noise. Since I'm in unsteady, I'd probably need more. Besides, my signal lasts about 1.5 minute. So I'm a little bit lost: can I still apply the denoising models (They're applied in the literature) ?

Thank you!

• To what figure are you referring? – honeste_vivere Jul 19 '18 at 15:54
• I'm sorry I've edited it. It's here imgur.com/a/Qd72HjO for the streamwise velocity (first curve) with 2 waves – Yassine Jul 19 '18 at 15:56
• Since it is nonstationary signal, if possible, you must go for ensemble average (an average across several experiments at each time point, rather than across time for a given experiment). If that is not practical, then you can Fourier transform the signal; if there is an undisputable peak at the high wavelength end, you can assume that it is your average. – Deep Jul 20 '18 at 9:56
• Actually you described exactly the steps I've gone through in my analysis. I thought I'd go for ensemble average but still not sure how to find the number of runs (in the literature, they just say how much runs, but do not justify it). Besides, since it takes about 20 000 samples (so about 3min at 100 Hz sampling) in steady flow, I might need a huge number of runs. So I thought I could use other dsp method. Fourier transform is indeed used in the literature, but normally shouldn't be used for the nonstationary signal since it's only suited for stationary linear processes – Yassine Jul 20 '18 at 10:55
• It is not true that Fourier transform is only suited for stationary linear processes. All that a Fourier transform does is that it breaks up a signal into sinusoids. It is true that since the signal is of finite duration, periodicity over that time interval is being assumed; but if the time duration is long enough that should cause only a small error; this can be checked by taking signals of different time duration, Fourier transforming them, comparing them, and verifying that they do not change significantly when the signal's duration is beyond a certain threshold. – Deep Jul 22 '18 at 4:11