Basic question on numerical precision

Question

I appreciate this opportunity to submit a query on this forum.

When studying the continuous-time & discrete-time distinction, specifically with reference to discrete signals being identical when separated by 2*pi, it has struck me that a basic premise, per google calc, doesn't hold:

exp(2 * pi * sqrt(-1)) = 1
exp(4 * pi * sqrt(-1)) = 1
exp(6 * pi * sqrt(-1)) = 1
exp(8 * pi * sqrt(-1)) = 1

but...

exp(10 * pi * sqrt(-1)) = 1 - 1.2246468 × 10^-15 i

Any thoughts on the above (discrepancy?) would be appreciated.

Regards,

wirefree

This has nothing to do with discrete signals but with the computer representation of numbers. — , Sep 16 '15 at 12:47
pi does not equal $\pi$ exactly; it is an approximation (correct to $7$ or $8$ decimal places) to $\pi$ — Dilip Sarwate, Sep 16 '15 at 12:56
If you use a program capable of symbolic (not just numeric) computation, you'll get the exact result. Example using Wolfram Alpha. — MBaz, Sep 16 '15 at 13:27

score 2 · Accepted Answer · answered Sep 16 '15 at 12:34

2

Writing another way

$$1 - 1.2246468 × 10^{-15} i = 1 - 0.0000000000000012246468i$$

It is just rounding errors adding up due to having a limited number of bits in whatever computer is doing the calculation.

answered Sep 16 '15 at 12:34

geometrikal

3,616
15
27

Basic question on numerical precision

1 Answers1