3. A BME student designed a QRS detector for a heart rate monitor. The detector supposed to have a band-pass filter characteristic with central frequency 30 Hz, bandwidth 30 Hz (± 15 Hz around the center frequency) and gain of 100 at 30 Hz. He designed the filter and found out that the impulse response h(t) = 100e¬40t cos(180t + 12.5°). a. Find the transfer function of the filter. b. Determine the natural resonance frequency (on) and damping coefficient (5) of the filter. Draw the frequency response of the filter. C.

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3. A BME student designed a QRS detector for a heart rate monitor. The detector supposed to have a
band-pass filter characteristic with central frequency 30 Hz, bandwidth 30 Hz (± 15 Hz around the
center frequency) and gain of 100 at 30 Hz. He designed the filter and found out that the impulse
response h(t) = 100e¬40t cos(180t + 12.5°).
a. Find the transfer function of the filter.
b. Determine the natural resonance frequency (on) and damping coefficient (5) of the filter.
Draw the frequency response of the filter.
C.
d. Does the response meet student's expectations? If not, what parameters need to be
modified and what supposed to be their values?
Hint: Transform pairs: u(t) é÷ ; e
e-at cos(wot) A
sta
;; e-at
sin(wot) →
wo
(s+a)²+wo²
cos(a + b) = cos a cos b – sin a sin b
(s+a)²+w,²
Transcribed Image Text:3. A BME student designed a QRS detector for a heart rate monitor. The detector supposed to have a band-pass filter characteristic with central frequency 30 Hz, bandwidth 30 Hz (± 15 Hz around the center frequency) and gain of 100 at 30 Hz. He designed the filter and found out that the impulse response h(t) = 100e¬40t cos(180t + 12.5°). a. Find the transfer function of the filter. b. Determine the natural resonance frequency (on) and damping coefficient (5) of the filter. Draw the frequency response of the filter. C. d. Does the response meet student's expectations? If not, what parameters need to be modified and what supposed to be their values? Hint: Transform pairs: u(t) é÷ ; e e-at cos(wot) A sta ;; e-at sin(wot) → wo (s+a)²+wo² cos(a + b) = cos a cos b – sin a sin b (s+a)²+w,²
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