Recent content by matlabber

interval -\pi:\pi split into M equal intervals. midpoints are y_K

"Proof Beyond Scope of Course" Homework Statement \frac{1}{M}\sum_{j=1}^{M}\cos(mx_{j})=\begin{cases} 1, & \ m \equiv 0\pmod{M}\\ 0, & \text{else} \end{cases} Homework Equations The Attempt at a Solution is statement truthfully accurate? how to show this?

Homework Statement \sum_{t=0}^{n-1}cos2 \pi ft(x_{t}- \mu-Acos2 \pi ft-Bsin2 \pi ft) Homework Equations The Attempt at a Solution I know to set = 0 I just am not knowing what to do with the cos after the sum...how do I take this sum?

thank you very much!

is it \frac{1-exp(2 \pi fi)^{t}}{1-exp(2 \pi fi)}

but do I include exp() when I do geometric series?

Homework Statement I try to simplify to get rid of sum \sum_{k=0}^{n-1}cos(2 \pi fk) Homework EquationsThe Attempt at a Solution I discover I shall use euler equation to form: \sum_{k=0}^{n-1}\frac{1}{2}(e^{2 \pi fki}+e^{-2 \pi fki}) but how to sum exponentials?

Using Geometric Series I get... \frac{1-e^{2 \pi ifn}}{1-e^{2 \pi if}} =\frac{e^{2 \pi ifn}-1}{e^{2 \pi if}-1} Do I want to split up the pieces in the numerator? or Factor?

Hi, You are correct my mistake.\sum_{t=0}^{n-1}e^{2 \pi ift}=\frac{e^{2 \pi ifn}-1}{e^{2 \pi if}-1}=e^{\pi if(n-1)}\frac{e^{\pi ifn}-e^{-\pi i f n}}{e^{ \pi if}-e^{-\pi if}}\\\\\\\\

Homework Statement Show if true: \sum_{i=1}^{n-1}e^{2 \pi ift}=\frac{e^{2 \pi ifn}-1}{e^{2 \pi if}-1}=e^{\pi if(n-1)}\frac{e^{\pi ifn}-e^{-\pi i f n}}{e^{ \pi if}-e^{-\pi if}}\\\\\\\\ Homework Equations I'm really stuck here, just looking for a suggestion as to what equation to use... Can I...

Hi, I have a mathematics/Matlab question. Suppose I have a speaker that serves as a sound source, and two IDENTICAL microphones to the left and right of this speaker. Suppose that each microphone collects data regarding the sound level of the speaker, and that there are over 3,000 data values...