6 - Fourier Transform 2 - Revision history

Kevin.Starkey at 05:31, 8 November 2009

2009-11-08T05:31:57Z

← Older revision		Revision as of 22:31, 7 November 2009
Line 13:		Line 13:
	(c) Do another property on the Wiki and review a second property		(c) Do another property on the Wiki and review a second property

	(a) to ~~come~~		Find <math>\mathcal{F}\left[e^{j2\pi f_0t}s(t)\right] </math><br>
			First <math>\mathcal{F}\left[e^{j2\pi f_0t}s(t)\right] = \int_{- \infty}^{\infty}e^{j2\pi f_0t}s(t)e^{-j2\pi ft} </math><br>
			or rearranging we get <math> \int_{- \infty}^{\infty}e^{j2\pi f_0t}s(t)e^{-j2\pi ft}dt = \int_{- \infty}^{\infty}s(t)e^{j2\pi t(f_0 -f)}dt</math><br>
			Which leads to <math> \int_{- \infty}^{\infty}s(t)e^{j2\pi t(f_0 -f)}dt = S(f-f_0)</math><br>
			So <math>\mathcal{F}\left[e^{j2\pi f_0t}s(t)\right] = S(f-f_0) </math><br><br>

	~~(b) to come~~

	~~(c)~~		Reviewed Nicks 2nd Fourier transform made comment about one possible error other than that looked good

	i)

	~~ii)~~Reviewed Nicks 2nd Fourier transform made comment about one possible error other than that looked good

2009-11-03T04:59:08Z

← Older revision		Revision as of 21:59, 2 November 2009
Line 1:		Line 1:
	Reviewed Nicks 2nd Fourier transform made comment about one possible error other than that looked good		(a) Show <math> \mathcal{F} \left[ \int_{- \infty}^{t} s(\lambda ) \,d\lambda \right] = \frac{S(f)}{j2 \pi f} \mbox{ if } S(0) = 0 </math>. '''Hint''': <math> S(0) = S(f) \| _{_{f=0}} = \int_{- \infty}^{\infty} s(t)e^{-j2 \pi (f \rightarrow 0)t} \,dt = \int_{- \infty}^{\infty} s(t) \,dt </math>


			<br>
			<br>

			(b) If <math> S(0) \neq 0 </math> can you find <math> \mathcal{F}\left[ \int_{- \infty}^{t} s(\lambda ) \,d\lambda \right] </math> in terms of <math> \displaystyle S(0) </math>?


			<br>
			<br>

			(c) Do another property on the Wiki and review a second property

			(a) to come

			(b) to come

			(c)

			i)

			ii)Reviewed Nicks 2nd Fourier transform made comment about one possible error other than that looked good

2009-11-03T04:50:43Z

New page: Reviewed Nicks 2nd Fourier transform made comment about one possible error other than that looked good

New page

Reviewed Nicks 2nd Fourier transform made comment about one possible error other than that looked good