1 / 24

3.3.3 Derivative-based operators to remove low-frequency artifacts

3.3.3 Derivative-based operators to remove low-frequency artifacts. Continuous-time signals:. Differentiation  HPF (highpass filtering). L [d/dt] = s. dx (t)/dt. x (t)dt. X(t). X(t). H(f). H(f). Integration  L PF (lowpass filtering).  dt = 1/s. |H(f)|. |H(f)|. f. f.

ajefferies
Download Presentation

3.3.3 Derivative-based operators to remove low-frequency artifacts

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3.3.3 Derivative-based operators to remove low-frequency artifacts

  2. Continuous-time signals: Differentiation  HPF (highpass filtering) L[d/dt] = s dx(t)/dt x(t)dt X(t) X(t) H(f) H(f) Integration  LPF (lowpass filtering) dt = 1/s |H(f)| |H(f)| f f

  3. Discrete-time signals: Difference  HPF Z[x(n) - x(n-1)] = (1 - z^-1) X(z) y(n) = [x(n) – x(n-1)]/T, T = sampling frequency x(n) + x(n-1) y(n) x(n) X(n) H(z) H(z) Z[x(n) + x(n-1)] = (1 + z^-1) X(z) Summation  LPF (lowpass filtering) |H(f)| |H(f)| f f

  4. Matlab command: freqz

  5. Matlab command: freqz In MatLab, Normalized with respect to fs/2 Normalized with respect to fs

  6. ECG signal with baseline drift (, and high-frequency noise) What we want：to eliminate the baseline drift. Baseline drift In this section, three derivative-based operators will be introduced. They are Filter 1, Filter 2, & Filter 3.

  7. Filter 1: First-order difference operator Difference  HPF Z[x(n) - x(n-1)] = (1 - z^-1) X(z) y(n) = [x(n) – x(n-1)]/T, T = sampling frequency y(n) x(n) H(z)

  8. How to generate pole-zero plot in Matlab (1. Use “Matlab help” (2. Search “pole-zero plot” (3. Choose “zero-Pole Analysis” (4. Use “fvtool” Example: Fvtool([1 -1],[1])

  9. Filter 1: First-order difference operator >>help freqz [H,F] = FREQZ(B,A,N,Fs) and [H,F] = FREQZ(B,A,N,'whole',Fs) return frequency vector F (in Hz), where Fs is the sampling frequency (in Hz). B = [1 -1]; A = [1]; freqz(B,A,200,1000)

  10. Estimation of the frequency components of ECG

  11. Filter 1: frequency response Frequency: f(T) < f(P) < f(QRS) < f(noise) Amplification: A(T) < A(P) < A(QRS) < A(noise) QRS (17 Hz) P (5.6Hz) T (4.5 Hz) High-frequency noise Baseline drift Any problem in phase response? No, because of phase linearity Figure 3.22

  12. Filter 1: the output Figure 3.24 Why do P and T waves disappear? What is the gain for them?

  13. Filter 2: How to attenuate HF as well as LF noise y3(n) x(n) H3(z) [H3 w3] = freqz([1/2,0,-1/2])

  14. Filter 2 --- frequency response [H3 w3] = freqz([1/2,0,-1/2])

  15. Filter 2  frequency response High-frequency noise Figure 3.23

  16. Filter 2  the output Figure 3.25

  17. Filter 3  y(n+1) = x(n+1) - x(n) + 0.995 * y(n) y(n) = x(n) - x(n-1) + 0.995 * y(n-1)

  18. Filter 3  frequency response

  19. Filter 3: Figure 3.26

  20. Filter 3  frequency response Figure 3.27

  21. Filter 3  the output Figure 3.28

More Related