I am studying proakis book digital signal processing using matlab 3rd ed

but i am bit confused about calculation of value complex multiplier W

fig is attached. i am not able to understand how the values of W are found/calculated in this fig in red enclosure

how/why we know that W base 4 and raised to the power 1 is equal to -j

enter image description here


Using Euler's formula you can see that


With $j^2=-1$ it should be easy to verify that


It's important to develop a geometric intuition which allows you to immediately see these equivalences. Multiplication with $j$ corresponds to a rotation by $\pi/2$ in the complex plane, and multiplication with $-j$ is a rotation by $-\pi/2$. So in general for $k\in\mathbb{Z}$ you have



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.