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What is the first backward difference of y(n)?

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What is the first backward difference of y(n)?

(a) [y(n)+y(n-1)]/T

(b) [y(n)+y(n+1)]/T

(c) [y(n)-y(n+1)]/T

(d) [y(n)-y(n-1)]/T

I had been asked this question in homework.

My doubt is from Backward Difference Method in portion Digital Filters Design of Digital Signal Processing

1 Answer

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Right option is (d) [y(n)-y(n-1)]/T

Explanation: A simple approximation to the first order derivative is given by the first backward difference. The first backward difference is defined by

[y(n)-y(n-1)]/T.

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