# Alexey KupriyanovLeibniz Universität Hannover

Alexey Kupriyanov

Master of Science

Doctoral researcher - Leibniz University Hannover

## About

3

Publications

926

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

0

Citations

Citations since 2017

Introduction

**Skills and Expertise**

Additional affiliations

April 2021 - present

Education

October 2018 - December 2020

## Publications

Publications (3)

Electrostatic accelerometers (EA) are one of the limiting factors of space gravimetry missions dominating the error contribution at low frequencies (<10−3Hz). The focus of this study is on the modelling of an optical accelerometer that can improve gravity field retrieval to unprecedented accuracy. Contrary to GRACE(-FO) or GOCE accelerometers, opti...

Accelerometers are integral part of the science instrument payloads of space based gravimetry and gravitational wave measurements. These are either used to detect the actuating forces on the body of the spacecraft, to enable a drag-free scenario where a test mass will follow a geodesic, or combined in pairs as to build a gradiometer. From a technol...

Context: Methane is an essential atmospheric gas representing one fifth of the whole radiative forcing gases. The understanding of the behavior of methane is crucial for studying the climate change. Atmospheric methane concentration evolution through the last decades demonstrates a steady increasing trend and industrial sources of this gas, e.g. me...

## Questions

Question (1)

I am really stucked in the simple, but not trivial problem of finding the amplitude spectrum function from the given PSD or ASD.

So, what I have initially is this ASD and PSD of the signal (see 1-st attached image).

What I want at the end: is a

**signal in time-series domain.**I've read a lot of forum pages and I knew that

*here should take place in order to switch from the frequency domain to the time-domain (for ex. a good algorithm was presented here: https://www.researchgate.net/post/How-do-I-generate-time-series-data-from-given-PSD-of-random-vibration-input)***ifft**The thing is that I also already have a signal in the time domain (acquired from additional software), so I can check myself whether my ifft works correct or not.

To sum up, if everything works correctly, the ASD and PSD of the output time-series signal should coincide with the input ASD and PSD (see 2-nd attached image).

My problem is that I can not calculate correctly the amplitude spectrum in the frequency domain U(f) in order to use it further in the ifft procedure (see 3-rd attached image).

Here on the graphs below the cyan curve is the U(f) as it

**should**be and the grey curve as I have it. And hence the output ASD and PSD do not coincide with the input ones (see 4-th attached image)*Could you tell me please which kind of transformation shall I use in order to get from the input ASD (or PSD) to the correct U(f)?*

Here is the equation for the initial function:

y = (1e-12 * sqrt( (1e-3./f).^4 ./ ((1e-5./f).^4+1) + 1 + (f/1e-1).^4)).^2;
acc_freq_asd = abs(sqrt(y)); %convert to ASD
acc_freq_psd = abs(y); %convert to PSD

The plotted U(f) 'grey curve' was acquired by the following formula:

U_f = sqrt(2*acc_freq_psd.*tslength);

where tslength - is the signal length

But I've also used many more combinations (with the normalizations and etc) but none of them give the correct U(f).

Will be really appreciate for your help!