Explain what a Markovian process is. (b) (6 Points) Use the 1-step transition ma

Question

Explain what a Markovian process is. (b) (6 Points) Use the 1-step transition matrix P below to find H12 S1 S2 S3 s1 0.1 0.8 0.1 s2 0 0.3 0.7 s3 0.2 0.4 0.4 (c) (10 Points) An amateur gardener with training in botany is tinkering with cross-pollinating pink irises with red, orange, and white irises. Annual experiments show that pink can produce 45% pink, 15% red, and 40% white; red can produce 40% red, 50% pink, and 10% orange: orange can produce 35% orange, 30% pink, and 35% white; and white can produce 20% pink, 10% red, 10% orange, and 50% white. If the gardener started the cross-pollination with 1000 of each color of iris, how many of each color of iris would there be in 3 years? (d) Bonus Point (T/F): The one-step transition matrix from part b ergodic.

Explanation / Answer

A hidden Markov model (HMM) is employed to improve noise robustness when tracking the dominant frequency of atrial fibrillation (AF) in the electrocardiogram (ECG). Following QRST cancellation, a sequence of observed frequency states is obtained from the residual ECG, using the short-time Fourier transform. Based on the observed state sequence, the Viterbi algorithm retrieves the optimal state sequence by exploiting the state transition matrix, incorporating knowledge on AF characteristics, and the observation matrix, incorporating knowledge of the frequency estimation method and signal-to-noise ratio (SNR). The tracking method is evaluated with simulated AF signals to which noise, obtained from ECG recordings, has been added at different SNRs. The results show that the use of HMM improves performance considerably by reducing the rms error associated with frequency tracking: at 4-dB SNR, the rms error drops from 0.2 to 0.04 Hz.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.