1. Electrocardiogram (ECG) is a recording of the electrical activity of the heart which is clinically utilized to monitor patients and diagnosis life threatening cardiac arrhythmias [1]. See Figure 1. Remote monitoring in a patient'shome or office could be used to alert medical personnel to intervene prior to a major cardiac event. These remote monitors have the ability for automated analysis utilizing a signal sampled up to 1000 Hz. The remote monitors would alert medical personnel if an life threatening cardiac event was imminent. Cardiologists are trained to read the ECG and provide the standard for diagnosis based on the ECG. The higher frequency components in the remote monitored ECG are not required for visually ECG interpretation. A reduction of the sampling rate would facilitate transmission to a physicians portable electronic device for immediate evaluation. Given an electrocardiogram acquired and recorded remotely at a sampling rate of 1,000 Hz, decrease the sampling rate to 125 Hz. Antialiasing filtering is required in digital as well as analog sampling. The 8 to 1 sampling rate reduction requires digital low-pass filtering prior to sample rate reduction to 125 Hz.
Figure 1: Electrocardiogram (12 lead) from a normal healthy individual. [https://en.wikipedia.org/wiki/Electrocardiography]
Figure 1 contains a 12 lead ECG presented in a typical format required for visual diagnosis. Figures 2 and 3 show the electrode placement for these leads. The augmented leads (aVR, aVL and aVF) are derived from the Einthoven limb leads (I, II, and III). Therefore, the ECG signals from the nine recorded limb (I, II, and III) and precordial leads (V1 - V6) are sufficient for transmission to a remote reader.
Given the recording in the MATLAB data file "recording 1 .mat" containing recording for (V1 - V6, I, II and III):
1. The recorded ECG magnitude in the structure array "Data.ECG" is in Volts, multiply each column in the array by 103 to convert the magnitude to mV. Reduce the sampling rate from 1000 Hz to 125 Hz for all nine ECG recordings without aliasing the signal. You can use the MATLAB "decimate" function to perform sample rate reduction. It has a built in antialiasing filter.
2. Display all nine sampled signals. Label the y-axis with its appropriate lead name which are stored in Data.Labels. Label the x-axis in seconds starting a zero. Include the units for both the x and y axes.
3. Find the spectrum of each lead in the recording using the MATLAB function "pwelch" which divides the data into segments and utilizes the FFT on each segment to obtain an estimate of the spectrum from the average of the magnitude of the FFT from all the segments. Use a window L=116 for pwelch.
4. Display the magnitude of the spectrum for each lead as dB vs frequency (Hz). Label each spectrum with its lead designation. Label both the y and x axes.