Chris' Page for HW 4 (Fourier Transforms) - Revision history

ChrisRas at 08:52, 4 November 2007

2007-11-04T08:52:07Z

← Older revision		Revision as of 01:52, 4 November 2007
Line 90:		Line 90:
	<code>		<code>
	clear all		clear all
	</~~all~~>		</code>

			I believe that windowing needs to be added. Suggestions?

ChrisRas at 08:50, 4 November 2007

2007-11-04T08:50:16Z

← Older revision		Revision as of 01:50, 4 November 2007
Line 59:		Line 59:

	[[Image:Example1time.jpg]]		[[Image:Example1time.jpg]]

			Then taking the Fourier Transform via the FFT and plotting

			<code>
			Y = fft(y,512);

			Power = Y .* conj(Y) / 512;

			f = 1000*(0:256)/512;

			figure(2)

			plot(f,Power(1:257))

			title('Frequancy Domain')

			xlabel('f (Hz)')
			</code>

			[[Image:Example1freq.jpg]]

			And if you want to hear it

			<code>
			wavwrite(y,1000,16,'test2.wav')
			</code>

			then

			<code>
			clear all
			</all>

ChrisRas at 08:42, 4 November 2007

2007-11-04T08:42:51Z

← Older revision		Revision as of 01:42, 4 November 2007
Line 29:		Line 29:

	== Examples ==		== Examples ==

			Below is a very basic example based on a Matlab help file.

			The time domain signal is produced by

			<code>
			t = 0:0.001:.1;

			y = sin(2pi50t)+sin(2pi120t) +sin(2pi150t) +sin(2pi310t) +sin(2pi340*t);

			y = 0.2 .* y;
			</code>

			The t matrix represents time vectors and y is the summation of sine functions of various frequencies, then y is redefined as 1/5 the original power.

			Plotted with

			<code>
			figure(1)

			plot(1000*t(1:100),y(1:100))

			title('Time Domain')

			xlabel('t (ms)')
			</code>

			yields

			[[Image:Example1time.jpg]]

ChrisRas at 06:45, 4 November 2007

2007-11-04T06:45:15Z

← Older revision		Revision as of 23:45, 3 November 2007
Line 6:		Line 6:

	The Fourier Transform is detonated by;		The Fourier Transform is detonated by;


	:<math>X(f) = \int_{-\infty}^{\infty} x(t)\ e^{-j \omega t}\,dt, </math>		:<math>X(f) = \int_{-\infty}^{\infty} x(t)\ e^{-j \omega t}\,dt, </math>

ChrisRas at 08:29, 3 November 2007

2007-11-03T08:29:01Z

← Older revision		Revision as of 01:29, 3 November 2007
Line 22:		Line 22:

	: <math>\mathcal{L}\left\{f(t)\right\} =\int_{-\infty}^{\infty} e^{-st} f(t)\,dt.</math>		: <math>\mathcal{L}\left\{f(t)\right\} =\int_{-\infty}^{\infty} e^{-st} f(t)\,dt.</math>

			Setting <math> s=j\omega</math> (<math>\sigma=0</math>) gives the equation

			: <math>\mathcal{L}\left\{f(t)\right\} =\int_{-\infty}^{\infty} e^{-j\omega t} f(t)\,dt.</math>

			which is identical to the Fourier Transform. The same relationship exists between the Inverse Laplace and the Inverse Fourier transforms.

	== Examples ==		== Examples ==

ChrisRas at 08:03, 3 November 2007

2007-11-03T08:03:42Z

@@ Line 5: / Line 5: @@
 == Mathematical Description ==
-:<math>X(f) = \int_{-\infty}^{\infty} x(t)\ e^{-i 2\pi f t}\,dt, </math> &nbsp; for every [[real number]] <math>f.\,</math>
+The Fourier Transform is detonated by;
 == Relation to Laplace Transform ==
 == Examples ==

ChrisRas at 07:27, 3 November 2007

2007-11-03T07:27:06Z

← Older revision		Revision as of 00:27, 3 November 2007
Line 1:		Line 1:
	The Fourier Transform is a process or formula that converts a signal from one domain to another. Often it is used to go between the time domain and the frequency domain.		The Fourier Transform is a process or formula that converts a signal from one domain to another. Often it is used to go between the time domain and the frequency domain.
	Developed by Frenchman, Jean Baptiste Joseph Fourier (1768 - 1830), the Fourier Transform stems from the more general Fourier Analysis, which is the representation of a function with sine and cosine terms.
			Developed by Frenchman, Jean Baptiste Joseph Fourier (1768 - 1830), the Fourier Transform stems from the more general Fourier Analysis, which is the representation of a function with sine and cosine terms. Unlike the Fourier Series the Fourier Transform is capable of representing aperiodic signals.

	== Mathematical Description ==		== Mathematical Description ==

			:<math>X(f) = \int_{-\infty}^{\infty} x(t)\ e^{-i 2\pi f t}\,dt, </math>   for every [[real number]] <math>f.\,</math>

	== Relation to Laplace Transform ==		== Relation to Laplace Transform ==
	== Examples ==		== Examples ==

ChrisRas at 02:08, 3 November 2007

2007-11-03T02:08:02Z

New page

The Fourier Transform is a process or formula that converts a signal from one domain to another. Often it is used to go between the time domain and the frequency domain.
Developed by Frenchman, Jean Baptiste Joseph Fourier (1768 - 1830), the Fourier Transform stems from the more general Fourier Analysis, which is the representation of a function with sine and cosine terms.

== Mathematical Description ==
== Relation to Laplace Transform ==
== Examples ==