{"id":52834,"date":"2024-04-15T23:45:09","date_gmt":"2024-04-15T23:45:09","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=52834"},"modified":"2024-04-15T23:45:09","modified_gmt":"2024-04-15T23:45:09","slug":"a-system-with-transfer-function-hz-has-impulse-response-hn-defined-as-h2-1-h3-1-and-hk-0-otherwise-consider-the-following-statements-s1-hz-is-a-low-pass-filter-s2-hz-is-an","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-system-with-transfer-function-hz-has-impulse-response-hn-defined-as-h2-1-h3-1-and-hk-0-otherwise-consider-the-following-statements-s1-hz-is-a-low-pass-filter-s2-hz-is-an\/","title":{"rendered":"A system with transfer function H(z) has impulse response h(n) defined as h(2) = 1, h(3) = -1 and h(k) = 0 otherwise. Consider the following statements. S1 : H(z) is a low-pass filter. S2 : H(z) is an FIR filter. Which of the following is correct?"},"content":{"rendered":"

[amp_mcq option1=”Only S2 is true” option2=”Both S1 and S2 are false” option3=”Both S1 and S2 are true, and S2 is a reason for S1″ option4=”Both S1 and S2 are true, but S2 is not a reason for S1″ correct=”option3″]<\/p>\n

The correct answer is: C. Both S1 and S2 are true, and S2 is a reason for S1.<\/p>\n

A low-pass filter is a filter that passes low frequencies and attenuates high frequencies. An FIR filter is a filter whose impulse response is finite in length. The impulse response of the system in the question is $h(2) = 1$, $h(3) = -1$, and $h(k) = 0$ otherwise. This impulse response is finite in length, so the system is an FIR filter. The system also passes low frequencies and attenuates high frequencies, so it is a low-pass filter. Therefore, both S1 and S2 are true, and S2 is a reason for S1.<\/p>\n

Here is a brief explanation of each option:<\/p>\n