I measure pulses on some background and my measurment system has an analog band-pass filter. I usually still have to do extra band-pass filtering digitally afterwards in order to remove the various "DC" components in order to "find" the pulses in the data. After my algorithms have found the pulses I would like to do curve fitting of a Gussian pulse (Amp*exp(-(t-t_0)^2/width^2)) to find the best measure of FWHM and amplitude/energy etc.
However, I dont know how I would describe a band-pass filtered Gaussian pulse
Hi Mikael Malmström ,
I guess the best you can do is trying some curve fitting in the frequency domain, using the spectra of Gaussian pulses modified by the band-pass filter(s). There is an example of a comparison in the frequency domain (but without any filter) in Hans G. Schantz: "The Art and Science of Ultrawideband Antennas", 2nd Ed., 2015, on page 199.
If this is successful you can draw a conclusion on the original pulse shape in the time domain, provided you know the phase shift by the filter, too.
Of course, whether you will be able to get meaningful results at all depends on the characteristics of the filter.
Hope this helps.
Dear Mikael Malmström and Joerg Fricke ,
It is possible to create a bandpass filter from low pass Gaussian filter by shifting Gaussian in the frequency domain. We know that Fourier transform of Gaussian is an other Gaussian, by modulating Gaussian with complex exponential we can generate bandpass Gaussian filter. The frequency modulation (f1, see script) is the central frequency in Fourier domain. In fact, it's similar to "1D Gabor filter". You will find attached a Matlab script for filter synthesis and mathematic formulation. For more details, please refer to this paper: Preprint A Simplified Approximation of Gabor Function like Simple Cel...
Thanks Ait Mansour El Houssain for sharing, but i don’t see how that helps me design a pulse in the time-domain without using band pass filters. Maybe I was not clear enough but I would like to describe the pulse in the time domain without going to the frequency domain at all.
You welcome Mikael Malmström
If I understand well your question, the bandpass filter in the time domain can be done by using a real part of simple multiplication between Gaussian function and complex exponential such as: H=exp (-0.5*. t. ^2/sig^2). *exp (1i*2*pi*f1*t) /(sig*sqrt (2*pi)); H=real (H)=exp (-0.5*. t. ^2/sig^2). *cos(2*pi*f1*t) or H=imag(H)=exp (-0.5*. t. ^2/sig^2). *sin(2*pi*f1*t) ; To achieve time domain filter, you make convolution between H and your signal X by using filter() or conv() Matlab functions. The "f1" parameter may adjust central frequency of bandpass filter, and "sig" for filter bandwidth. I wish it will help you.
- Badges
- Science topic