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.
However, if the center frequencies are separated by less than 12 MHz, there is significant power leakage from the 802.15.4 radio.
It follows that if a pair of angular frequencies are separated by less than, then the corresponding peaks appear as a single broader peak (smearing effect).
If the center frequencies are separated by 12 MHz, the interference from the 802.15.4 radio on the 802.11 receiver is still negligible.
According to our findings, an 802.15.4 radio does not interfere with an 802.11b receiver if their center frequencies are separated by at least 17 MHz.
Therefore, two transmitters tuned to channels i and j share the wireless medium (a common frequency range) as long as i and j's center frequencies are separated by less than 22 MHz.
Unlike 802.11, these systems have the benefit of operating in paired spectrum, where transmit and receive frequencies are separated by a guard band relatively large compared to the channel size to prevent self jamming.
When the channel center frequencies of the 802.15.4 and 802.11 radios are separated by at least 17 MHz, the interference power that leaks from the 802.15.4 radio on the 802.11 receiver is 0. If the center frequencies are separated by at least 12 MHz, the interference power from the 802.15.4 radio is still negligible.
In this work, two partials will be considered coincident if their frequencies are separated by less than 5% for frequencies below 500 Hz, and by less than 25 Hz for frequencies above 500 Hz according to tests carried out previously, those values are roughly the thresholds for which traditional techniques to resolve close sinusoids start to fail.
The sounds consisted of four sinusoidal components with frequencies which were separated by one octave.
