An ECG amplifier's smoothing stage acts as a boxcar (rectangular) averager: unit-area…

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Signals, systems, control and digital signal processing · Signals, systems, control and digital signal processing

Electronics for Measurement, Ch Linear systems, the impulse response and convolution

Problem

An ECG amplifier's smoothing stage acts as a boxcar (rectangular) averager: unit-area impulse response

h(t) = 250\,\mathrm{s^{-1}}

for

0 \le t \le 4\,\mathrm{ms}

, zero otherwise. It is driven by a rectangular voltage pulse

x(t) = 8\,\mathrm{mV}

for

0 \le t \le 6\,\mathrm{ms}

, zero otherwise. ((a)) Using flip-and-slide, calculate the output

y(t)

t = 2\,\mathrm{ms}

5\,\mathrm{ms}

and

8\,\mathrm{ms}

, and sketch

y(t)

with numbers on both axes. ((b)) The five-point moving average discussed earlier gives zero output for a tone whose one full cycle exactly spans its averaging window. State the frequency, in hertz, at which this boxcar averager similarly gives zero output for a sinusoidal input, and explain briefly, in terms of

Y(f)=X(f)H(f)

, why that frequency is a null.

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