Hi Pallavi,
This is by no means any complex case: period of your discrete function
is determined by the longest one of its components, sin(pi*n/8) and
is equal to 16 - due to both sine and cosine are 2*pi periodic functions.
Rgds,
Andrew
> Subject: Solving complex trignometric equations
> Posted by: gpallavi2
> Date: Fri Jan 23, 2009 5:01 am ((PST))
>
> Hi,
>
> The problem to be solved is -> whether the below digital signal is periodic
> and if it is, then what is its fundamental period?
>
> x(n) = cos(pi*n/2) - sin(pi*n/8) + 3cos(pi*n/4 + pi/3)
>
> But my question is how does one solve such complex trigonometric functions
> to reach an answer?
>
> I don't remember anything beyond the below expansions in trigonometry:
> (cos(x) - cos(y))
> (cos(x) + cos(y))
> (sin(x) - sin(y))
> (sin(x) + sin(y))
>
> Solving x(n) into one single sinusoid and finding its periodicity is driving
> me crazy! Is there a simpler approach to find the needed periodic frequency
> other than going into detailed mathematical calculation. If so how?
> I think I have missed big time trigonometry classes!! Please refer me to
> some good books/sites as well if you could, to solve these kind of tricky
> questions beyond the normal cos and sin matters.
>
> Thanks in advance,
> Pallavi
>
