Ok so if I have a fraction which looks as follows
$$\frac{8π}{N + 1}$$
How could I calculate N on its own?
The above fraction is the mainlobe width formula for a Hamming window and I'm trying to find out how much terms are required (N) for a filter using a Hamming window
solution from someone anonymous (which I do not comprehend)
$$\frac{8π}{N+1} = 0.5 * \frac{\pi}{8} N = 8*16 -1= 127$$
the 0.5 multiplication is just put in there so it only uses half the mainlobe (one side only)
maybe you can help me to understand clearly how this person has done this calculation
I think many of us are having trouble understanding your question, but it seems that you are asking the following: I know that $\frac{8 \pi}{N+1} = \frac{\pi}{16}$. How do I determine the value of $N$?
If that is the question, then this is really a matter of high school algebra.
First, notice that both sides of the equation have a $\pi$ in them, so that can be cancelled.
Next, multiply both sides of the equation by 16.
At this point the equation reads $\frac{128}{N+1} = 1$. From this it follows that $N+1=128$, so $N=127$.
Regarding the "anonynmous solution from someone that you do not understand": Don't ever get help from that person again. He or she seems to know, sort of, how to solve equations, but does not know what an equals sign means; what is written down is a string of operations that amount to gibberish, with the right answer at the end.