FE Electrical & Computer Practice Question Solution included after investigation
CASE E-025 · FE

The Digital Filter That Lagged a Perfect Step

A perfect step arrived. The filter answered 2.0 instead of 10.

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Case E-025 engineering failure visual
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Follow the investigation process used in the field — in five guided steps.

1

Inspect

Review the problem, diagram, and evidence.

2

Commit

Choose your hypothesis.

3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

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Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A digital sensor filter uses y[n] = 0.8y[n-1] + 0.2x[n]. Its DC gain is one, so a review note claims a step from 0 to 10 should produce y[0] = 10 immediately. With y[-1] = 0, the actual first output is 2.0 and the next is 3.6. Diagnose the lag and choose a coefficient change that gives at least 5.0 on the first sample while preserving unity DC gain.

Signal Processing Electrical & Computer Design Verification Root Cause Analysis Safe Correction
E-025
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What looked wrong

A unity-gain filter produced only 2.0 on the first sample of a 10-unit step.

What was missed

The previous-output state creates a discrete-time transient.

Corrected model

Apply the difference equation sample by sample; use DC gain for the eventual constant-input value.

QUICK ANSWER

For y[n] = 0.8y[n-1] + 0.2x[n] with zero initial state and a step to 10, y[0] = 2.0 and y[1] = 3.6. The output approaches 10 only over time; unity DC gain describes the final constant-input value, not the first sample.

ENGINEERING TAKEAWAY

Use the difference equation sample by sample. Unity DC gain describes the eventual constant-input response; the recursive state creates a gradual transient.

CASE QUESTIONS

Questions this case should settle.

What is y[0] for y[n]=0.8y[n-1]+0.2x[n] with y[-1]=0 and x[0]=10?

2.0.

Does unity DC gain mean the first sample equals the input?

No. It means the steady-state output equals the constant input.

How do recursive digital filters create smoothing?

They combine current input with stored previous output, so changes are spread across samples.

NEXT FE PRACTICE QUESTION

The 1 kHz Filter That Only Passed 70.7%

Signal Processing · 5–10 min

Continue Practice →
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