I'm attempting to perform multi-resolution analysis via Continuous-Wavelet Transform (CWT) using Pywavelets. I've heard that CWT is supposed to be superior to STFT due to varying frequency content as a function of the time-window.
My test signal is two sinusoids of 1Hz and 5Hz, each lasting 10 seconds (see picture):
f=np.sin(2.*np.pi*t)*((t>=10)&(t<=20))+np.sin(2*np.pi*5*t)*((t>=30)&(t<=40)). The sampling period is 20Hz.
Using Pywavelets, I perform the CWT as follows with the resulting spectrogram:
scales = np.arange(0.6,65,step=0.2) coef, freqs=pywt.cwt(f,scales,'cgau1', sampling_period=dT)
As you can see the frequency resolution is quite lousy, and the peak (complex magnitude) doesn't even seem to line up at 5Hz for the second segment.
In contrast, a STFT using the Gaussian window with a standard deviation of 5 results in much sharper frequency resolution (at the expense of time sharpness):
Am I doing something here? I'm willing to sacrifice time resolution but I do need to sharpen up the frequency.