Editing Time–frequency analysis (section)

=== Additive white noise ===
* For additive white noise (AWN),
:<math>E[W_g(t,f)] = \sigma</math>
:<math>E[A_x(\eta,\tau)] = \sigma\delta(\tau)\delta(\eta)</math>

* Filter Design for a signal in additive white noise
[[File:Filter design for white noise.jpg|left|thumb|440x440px]]





<math>E_x</math>: energy of the signal

<math>A</math>  : area of the time frequency distribution of the signal

The PSD of the white noise is <math>S_n(f) = \sigma</math>


<math>SNR \approx 10\log_{10}\frac{E_x}{\iint\limits_{(t,f)\in\text{signal part}} S_x(t,f)dtdf}</math>

<math>SNR \approx 10\log_{10}\frac{E_x}{\sigma\Alpha}</math>