How to evaluate the denoising effect of the filter?

If two filters are used, how to evaluate the filtering effect ¹ ?

In order to obtain a high-quality denoised signal, it is necessary to evaluate the filtering effect of the filter, and select the filter with the best denoising effect to denoise the original signal. Generally, the signal-to-noise ratio and peak signal-to-noise ratio are used to quantify the evaluation of the filter. The larger the value of the signal-to-noise ratio and peak signal-to-noise ratio, the better the denoising effect .

1、信噪比
$$SNR=10\ast 1g\left(\sum _{n=1}^N\frac{y^2\left(n\right)}{{\left[x\left(n\right)-y\left(n\right)\right]}^2}\right)$$
$x(n):$ original signal;

$and\left(n\right):$ signal after denoising;

2.
$$PSNR=10\log \left(\frac{{\left(2^n-1\right)}^2}{MSE}\right)$$
$MSE:$ the mean square error of the original signal to the denoised signal;

Example:

Comparing Table 3-2, 3-3 with Table 3-4, 3-5, wavelet threshold denoising is better than FIR filter in terms of signal-to-noise ratio and peak signal-to-noise ratio. So this paper chooses the wavelet threshold filter to denoise the pulse wave and ECG signal.

reference:

---

1. Zheng Yi. Research on Extraction Method of Pulse Wave Feature Parameters[D].Xi'an University of Technology,2021.DOI:10.27398/d.cnki.gxalu.2021.000362. ↩︎