Commitc092c6b

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extra j's

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Original file line number	Diff line number	Diff line change
`@@ -289,10 +289,10 @@ Remember that we tuned the SDR to 100 MHz. So the signal that was at about 97.5`
`289`	`289`	From a mathematical perspective, negative frequencies can be seen by looking at the complex exponential function,:math:`e^{2j\pi f t}`. If we have a negative frequency, we can see that it will be a complex sinusoid that rotates in the opposite direction.
`290`	`290`
`291`	`291`	`..math::`
`292`		`- e^{2j\pi f t} =\cos(2j\pi f t) + j\sin(2j\pi f t)\quad\mathrm{\textcolor{blue}{blue}}`
	`292`	`+ e^{2j\pi f t} =\cos(2\pi f t) + j\sin(2\pi f t)\quad\mathrm{\textcolor{blue}{blue}}`
`293`	`293`
`294`	`294`	`..math::`
`295`		`- e^{2j\pi (-f) t} =\cos(2j\pi f t) - j\sin(2j\pi f t)\quad\mathrm{\textcolor{red}{red}}`
	`295`	`+ e^{2j\pi (-f) t} =\cos(2\pi f t) - j\sin(2\pi f t)\quad\mathrm{\textcolor{red}{red}}`
`296`	`296`
`297`	`297`	`..image::../_images/negative_freq_animation.gif`
`298`	`298`	`:align:center`

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