Math 1050 Question

Question

A band-pass filter in electronics allows certain frequencies within a range (or band) to pass through to the receiver and eliminates all other frequencies. Write an absolute value inequality that allows any frequency  F within 11 Hz (inclusive) of the carrier frequency  Fc to pass.

Answer 1

Jenn, the absolute value is the distance a number is from 0, or the carrier frequency in this case.  Distance is always measured positively.  Even if I tell you to walk backward 10 feet, you didn't walk -10 feet, right?  So, the absolute value of -10 is the same as the absolute value of 10, because they are both 10 away from 0.

 

Now, we are looking for something that falls within 11 Hz, inclusive.  This means that anything within 11 Hz of the carrier frequency, meaning 11 Hz in either direction, passes through, so we want the distance from our carrier frequency to be less than or equal to 11 Hz.

 

So, our answer is |F| < 11