# denosing given signal using wavelet

let us suppose that we have given following model

$y(t)=A_1 \sin(\omega_1*t+\phi_1) + A_2 \sin(\omega_2*t+\phi_2) + A_3 \sin(\omega_3*t+\phi_3)+ \ldots +A_p \sin(\omega_p*t+\phi_p)+z(t)$

where $z(t)$ is white noise,we have everything unknown,$p,A_i,\omega_i,\phi_i$,what i want to remove noise using wavelet,i know that is it possible using discrete wavelet,so which mother waveelt is good for deterministic and periodic components?let us suppose that we have data ,some numbers of length $N=294$,which mother wavelet should i choose and which scales?please help me with practical example,because wavelet is new and i want to see what is steps for denoising,there is some link about denosing

http://eeweb.poly.edu/iselesni/DoubleSoftware/signal.html

including matlab codes,but i want to know before i start use some method ,is it relevant for such model?as i know wavelet is good for transient signals,is it ok for steady signals?for periodic ones?if so then which steps is necessary?thanks in advance

• any ideas?can i apply wavelet to sinusoidal data?so that dont harm it's spectral structure?
– user350
Apr 9, 2014 at 5:34

## 1 Answer

If you have reason to believe your signal is sparse in the frequency domain, they you should be denoising in that: use FFTs, not wavelets. Look at the magnitude spectrum and see if it's very spiky, and that will be your cue. If so, attenuate the frequencies with a small response.