Noise in morse signal

That noise sounds like mostly Gaussian-like noise. For this, spectral filtering reduces the noise power in proportion to the bandwidth. I suggest FIR filtering as ringing is greater for IIR (biquad) filtering. These components are available in the Audio Libraries.

If the noise is impulsive, the noise blanking can be very effective. This is available in the floating point audio library.

Also, if you know the speed of the CW, the "matched" filter is very effective. In a FIR implementation, this consists of enough samples of a 350 Hz sine wave to occupy a dot length. The 350 Hz is your center frequency, I believe. This ends up with a sine(f)/f type of response, which seems strange, but provides the maximum S/N on a dot.
 
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