The solutions to the equation ez = 1 are the integer multiples of 2πi: :\{ z : e^z = 1 \} = \{ 2k\pi i : k \in \mathbb{Z} \} More generally, if ev = w, then every solution to ez = w can be obtained by adding an integer multiple of 2πi to v: :\{ z : e^z = w \} = \{ v + 2k\pi i : k \in \mathbb{Z} \} Thus the complex exponential function is a periodic function with period 2πi.
This is the most ''physical" choice since it corresponds with our notion of ''negative frequencies". However, we may add any integer multiple of to without changing the sinusoid indexed by.
Because the phase is determined modulo 2 π, visible 2 π discontinuities between pixels may occur which may be removed using unwrapping algorithms that, depending upon the sign of the phase discontinuity between adjacent pixels, either add or subtract an integer multiple of 2 π.
Note that the total number of processes, nhost_world, should be an integer multiple of subworld_size.
For integer values ofs(except whensis an integer multiple of 4), one or possibly two of the solution functions contain logarithmic terms.
Additionally, stable solutions are found that have a fundamental period of an integer multiple of the excitation period.
Constructive interference or intensity maxima are observed on the screen at all positions whose distances from A and B differ by zero or an integer multiple of λ.
And the statement that I'm making is that if I have two discrete-time sinusoidal signals at two different frequencies, and if these frequencies are separated by an integer multiple of 2 pi namely if omega_2 is equal to omega_1 + 2 pi times an integer m when I substitute this into this expression, because of the fact that n is also an integer, I'll have m * n as an integer multiple of 2 pi.
Case 2 ( is an integer multiple of,, ).
It is also an integer multiple of the quantization interval.
Case 1. (is not an integer multiple of ).
