Matlabc E XERCISE II FOR SC 3011 TN : A CADEMIC Y EAR 16/17 Matlab c Exercise II: Adaptive Noise Can- celing Applied to Fetal Electrocardiogra- phy Michel Verhaegen, Laurens Bliek and Tijmen van Oldenrijk February 23, 2017 Delft University of Technology Delft Center for Systems and Control Mekelweg 2, NL-2628 CD Delft, The Netherlands [email protected] c 2015 by Michel Verhaegen .ii Copyrighted material. . . 3 2. . . . . . . .2 Exercise . . . . . . . . . . . . . . . .1 Theoretical Reference . 1 2 Active Noise Control: the Matlab c exercise 3 2. . . . . . Contents 1 The problem of Active Noise Cancellation 1 1. . . .3 Reporting . . . . . . . .1 The data . . . . . . . . 4 iii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Contents Copyrighted material. c 2015 by Michel Verhaegen . 1 . The measured fetal electrocardiogram signal (FECG) from the abdomen of the mother is usually dominated by the maternal heartbeat signal that propagates from the chest cavity to the abdomen. The example app is not required for this exercise. The goal is to remove the interference signal from the measured signal by using a reference signal that is highly correlated with the interference signal. The goal of the adaptive noise canceller in this task is to adaptively remove the maternal heartbeat signal from the fetal electrocardio- gram signal. The measured maternal electrocardiogram signal (MECG) is obtained from the chest of the mother.mathworks. We will use the theory from Chap- ter 7 of the reader in this application. This propagation path can be described by a linear FIR filter. We wish to use the theory of Wiener filters to recover the underlying fetal heartbeat signal. The example considered here is an application of adaptive filters to fetal electrocardiography. nl. The maternal heartbeat signal is much stronger and also has a different frequency than the fetal heartbeat. and the DSP system toolbox.1 Theoretical Reference This exercise is an adaptation of the example in . in which a maternal heartbeat signal is adaptively removed from a fetal heartbeat sensor signal. Chapter 1 The problem of Active Noise Cancellation 1.html You can open that example app in Matlab and play around with it by typing adaptiveNoiseCancellationExampleApp in the command window1 . In adaptive noise canceling. a measured signal consists of two signals: an unknown signal of interest and an interference signal.com/help/dsp/examples/adaptive-noise-canceling-anc-applied-to-fetal-electrocardiography. 1 May require Matlab version 2016 or higher. c 2015 by Michel Verhaegen .2 Chapter 1 The problem of Active Noise Cancellation Copyrighted material. This can be done using the following formulae: N N 1 X 1 X r̂x (τ ) = x(n)x(n − τ ). not covered in this course) has also been included as variable FECG LMS. w. but please specify the meanings of all the symbols and their relation to the two measured signals FECG and MECG. using the symbols x. 1 point 3. d. The re- covered fetal signal using an LMS filter (which is a different filter than a Wiener filter. Formulate the problem as a Minimum Variance FIR Wiener Problem. the auto. Make sure that both x and d do not require the unknown underlying fetal heartbeat signal that is to be recovered.1 in the reader.2 Exercise For recovering the fetal ECG from the two measured ECG signals. and explain how the different terms in the equation relate to the two measured ECG signals. If only the measured signals are given. as variables FECG and MECG. Chapter 2 Active Noise Control: the Matlab c exercise 2. the following Parts need to be solved. r̂dx (τ ) = d(n)x(n − τ ). Determine the Wiener-Hopf equation for this problem.1) N N n=τ +1 n=τ +1 3 . dˆ and e as in Figure 7. 2 points 2. 2. No numerical values are required.and cross-correlations used in the Wiener-Hopf equation need to be approximated.1 The data The measured fetal and maternal ECG signals are contained in the Matlab c Workspace opdracht2data. 1. The Workspace can be downloaded from the Blackboard site. Also explain how to finally recover the fetal heartbeat signal when the Wiener problem has been solved. (2.mat resp. 5. . q − 1. . You are free to choose q. It is hard to make a comparison. . Your answer should consist of: (1) A plot of the recovered fetal heartbeat using the two different methods. Your answer should consist of the used code and 1 point the first 10 values of the auto. Which of the two methods gives the results that you think are closest to the 1 point underlying fetal heartbeat? Please motivate your answer. This report containing the names of the members of your group and their student number should be dated and handed in following the Course Schedule (see Blackboard). however. We will filter the noise using a simple moving average filter. 6. 3 points 9. 1 point (2) The used code and your choice of q (plus motivation).and cross-correlations (τ = 0. Use a moving average filter of the following form: q−1 X y(n) = bk u(n − k).8 from the reader. The Matlab c scripts c should be included as text in your reports as well as your Matlab plots. 7. Your answer should consist of the used code and the 10 filter coeffi- cients.2 from the reader. 9). Using a 10-th order FIR Wiener filter. c 4 Chapter 2 Active Noise Control: the Matlab exercise Calculate the approximations of the auto. 2.2 and 6.and cross-correlations using the measured ECG signals.2) k=0 with bk = 1/q for k = 0. . Hint: the toeplitz command may be useful when defining your 1 point covariance matrix.3 Reporting The report of this Matlab c exercise should consist of the requested answers to the above 4 Parts also nicely ordered in 8 corresponding parts. 1 point after filtering the recovered signal with a moving average filter. 3 points 8. Your answer should consist of the used code and a plot with both the measured maternal ECG and the recovered fetal heartbeat (not the mea- sured fetal ECG). Copyrighted material. together with your answers to exercises 5. Hint: the filter command can be useful when using 1 point the Wiener filter. 4. calculate the optimal filter coeffi- cients. . since the recovered fetal heartbeat signal still contains a lot of noise. . Solve exercise 5. The results of this other method have been included in the data as the variable FECG LMS. We wish to compare this method to recover the fetal heartbeat with another method that uses an LMS filter. as the LMS filter is not dis- cussed in this course and is based on a different principle that adapts itself on-line. . (2. c 2015 by Michel Verhaegen . Calculate the recovered fetal heartbeat signal using the optimal Wiener fil- ter.8 from the reader. 1. Solve exercise 6.