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The equation for Heq(s) is \(\frac{\sum_{K=0}^M b_K s^K}{\sum_{K=0}^N a_K s^K}\).(a) True(b) FalseI have been asked this question during an interview for a job.This key question is from Backward Difference Method in portion Digital Filters Design of Digital Signal Processing |
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Answer» RIGHT choice is (a) True Best explanation: The analog filter in the time DOMAIN is governed by the following difference EQUATION, \(\sum_{K=0}^N a_K y^K (t)=\sum_{K=0}^M b_K x^K (t)\) Taking LAPLACE transform on both the sides of the above differential equation with all INITIAL conditions set to zero, we get \(\sum_{K=0}^N a_K s^K Y(s)=\sum_{K=0}^M b_K s^K X(s)\) =>Heq(s)=Y(s)/X(s)=\(\frac{\sum_{K=0}^M b_K s^K }{\sum_{K=0}^N a_K s^K}\). |
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