Sampling of Positive and Negative Frequencies and Aliasing
When a complex sinusoid is sampled at regular intervals, its frequency becomes indistinguishable from certain other frequencies, including negative ones (referred to as aliasing). The adjacent figure illustrates this effect for several cases. The red indicates 0 Hz (aka DC). Successively higher frequencies are indicated by orange, blue, purple, violet, black, and blue. Note that some frames depict "R" and "I" for the same frequency, and others depict the "I" samples of different frequencies that are aliases of each other.
For instance, the fourth frame (purple and green) compares samples of the imaginary component of the fractional frequency + with those of negative frequency, to illustrate that they are indistinguishable. Or in other words: for integer values of n, representing the sample number. The underlying waveforms are just the imaginary components of: and, where is the sample rate (samples/sec).
Likewise + is indistinguishable from . And (last plot) is indistinguishable from (first plot).
Read more about this topic: Negative Frequency
Famous quotes containing the words positive and/or negative:
“It is easy and dismally enervating to think of opposition as merely perverse or actually evil—far more invigorating to see it as essential for honing the mind, and as a positive good in itself. For the day that moral issues cease to be fought over is the day the word “human” disappears from the race.”
—Jill Tweedie (b. 1936)
“A negative judgment gives you more satisfaction than praise, provided it smacks of jealousy.”
—Jean Baudrillard (b. 1929)