Gaussian wavelet generation with a given frequency How can I generate a Gaussian wavelet (time domain) with a given central frequency. 

I mean if I take the Fourier Transform then its spectrum should be around that given central frequency instead of zero. For example the peak of spectrum is 20Hz and its side lobes becomes nearly zero around  $20\pm 10$.

I carried out a few coding exercise which I tried are here.
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If I understand the question, I don't think you can do what you want to do. The spectrum of a Gaussian time series must contain frequencies down to DC, i.e. very low frequencies (Python code from scipy.org):



A wavelet whose spectrum is a Gaussian is called a Ricker wavelet, or sometimes Mexican Hat wavelet. I often use this wavelet to model seismic reflection data. It has a central frequency, and is bandlimited. As such, the wavelet oscillates around zero amplitude — it does not have a DC component: