HW - Revision history

Jstirn at 04:23, 1 November 2010

2010-11-01T04:23:57Z

← Older revision		Revision as of 21:23, 31 October 2010
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	For this homework assignment I wanted to try and see if I could find a correlation between a dragsters rear tire expansion in comparison to its velocity by using either the method of Laplace transform or the Fourier series. To help me with my model I will me using the Army's dragster for some of my data. If you would like to check it out you can find it at [http://www.goarmy.com/army-racing/nhra-top-fuel/dragster.html].		For this homework assignment I wanted to try and see if I could find a correlation between a dragsters rear tire expansion in comparison to its velocity by using either the method of Laplace transform or the Fourier series. To help me with my model I will me using the Army's dragster for some of my data. If you would like to check it out you can find it at [http://www.goarmy.com/army-racing/nhra-top-fuel/dragster.html]. If you want to watch a video of dragster tires click here : http://www.youtube.com/v/V3yj_OGezWc?version=3


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	y = .075/(Vmax-Vmin) (this is the number of inches that the tire should expand given the current velocity.)		y = .075/(Vmax-Vmin) (this is the number of inches that the tire should expand given the current velocity.)
	~~http://www.youtube.com/v/V3yj_OGezWc?version=3~~

Jstirn at 04:18, 1 November 2010

2010-11-01T04:18:27Z

← Older revision		Revision as of 21:18, 31 October 2010
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	y = .075/(Vmax-Vmin) (this is the number of inches that the tire should expand given the current velocity.)		y = .075/(Vmax-Vmin) (this is the number of inches that the tire should expand given the current velocity.)
	[[<object style="height: 390px; width: 640px"><param name="movie" value="http://www.youtube.com/v/V3yj_OGezWc?version=3"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><embed src="http://www.youtube.com/v/V3yj_OGezWc?version=3~~" type="application/x-shockwave-flash" allowfullscreen="true" allowScriptAccess="always" width="640" height="390"></object>]]~~		http://www.youtube.com/v/V3yj_OGezWc?version=3

Jstirn at 04:16, 1 November 2010

2010-11-01T04:16:17Z

← Older revision		Revision as of 21:16, 31 October 2010
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	For this homework assignment I wanted to try and see if I could find a correlation between a dragsters rear tire expansion in comparison to its velocity. To help me with my model I will me using the Army's dragster for some of my data. If you would like to check it out you can find it at [http://www.goarmy.com/army-racing/nhra-top-fuel/dragster.html].		For this homework assignment I wanted to try and see if I could find a correlation between a dragsters rear tire expansion in comparison to its velocity by using either the method of Laplace transform or the Fourier series. To help me with my model I will me using the Army's dragster for some of my data. If you would like to check it out you can find it at [http://www.goarmy.com/army-racing/nhra-top-fuel/dragster.html].


	'''Data:'''		'''Data:'''
	Outside tire diameter = 36.5" or up to 40.5" due to tire expansion		* Outside tire diameter = 36.5" or up to 40.5" due to tire expansion
	Inside tire diameter = 16"
	Width of tire = 17"		* Inside tire diameter = 16"
	Air pressure in tire = 7 psi
	Volume of Tire = 9.82 ft^3 (you have to add about 1.5ft^3 to account for possible expansion)		* Width of tire = 17"
	Fastest quarter mile time = 4.428 sec
	Fastest quarter mile speed = 337.58		* Air pressure in tire = 7 psi

			* Volume of Tire = 9.82 ft^3 (you have to add about 1.5ft^3 to account for possible expansion)

			* Fastest quarter mile time = 4.428 sec

			* Fastest quarter mile speed = 337.58

			'''Equations:'''
			Volume = [(pi)(R^2)(h)-(pi)(r)(h)]

			y = .075/(Vmax-Vmin) (this is the number of inches that the tire should expand given the current velocity.)
			[[<object style="height: 390px; width: 640px"><param name="movie" value="http://www.youtube.com/v/V3yj_OGezWc?version=3"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><embed src="http://www.youtube.com/v/V3yj_OGezWc?version=3" type="application/x-shockwave-flash" allowfullscreen="true" allowScriptAccess="always" width="640" height="390"></object>]]

Jstirn at 03:21, 1 November 2010

2010-11-01T03:21:08Z

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-*[[Signals and systems|Signals and Systems]]
+For this homework assignment I wanted to try and see if I could find a correlation between a dragsters rear tire expansion in comparison to its velocity. To help me with my model I will me using the Army's dragster for some of my data. If you would like to check it out you can find it at [http://www.goarmy.com/army-racing/nhra-top-fuel/dragster.html].
-==What is a Fourier Transform?==
+'''Data:'''
+Outside tire diameter = 36.5" or up to 40.5" due to tire expansion
+Inside tire diameter = 16"
-<b>Unfortunately, the Fourier Transform isn't a Transform-er. </b>
+Width of tire = 17"
-<br>(This handsome fellow is named Roolbar.)<br>
+Air pressure in tire  = 7 psi
-[[Image:transformer_roolbar.jpg]]<br>
+Volume of Tire = 9.82 ft^3      **(you have to add about 1.5ft^3 to account for possible expansion)**
-<br>Check any of the other pages on this site to find fifty different ways to explain what a Fourier Transform is. If you already know what it is, or you're too lazy to look at the other pages, here's my super trite description: A Fourier Transform is a bunch of sinusoids of different frequencies and time offsets added together create a just about any function you want. Also, you can say that a Fourier Transform is the way of representing a function in the frequency domain instead of the time domain.
+Fastest quarter mile time = 4.428 sec
+Fastest quarter mile speed = 337.58

Rothsa at 17:48, 19 October 2007

2007-10-19T17:48:18Z

← Older revision		Revision as of 10:48, 19 October 2007
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	<br><b> Cooley-Tukey Algorithm </b>		<br><b> Cooley-Tukey Algorithm </b>

	Three popular algorithms are the Cooley Tukey algorithm (radix-r algorithms), the Good-Thomas Algorithm, and the Winograd FFT algorithm. The Cooley Tukey Algorithm Radix-2 algorithm is the simplest and most popular of all. ~~The~~ algorithm separates a given discrete Fourier transform of size <math> N </math> into two equal transform of size <math> N/2 </math> recursively. Here is the definition of the algorithm given on wikipedia's page.		Three popular algorithms are the Cooley Tukey algorithm (radix-r algorithms), the Good-Thomas Algorithm, and the Winograd FFT algorithm. The Cooley Tukey Algorithm Radix-2 algorithm is the simplest and most popular of all. Otherwise known as a "divide and conquer algorithm", Cooley-Tukey separates a given discrete Fourier transform of size <math> N </math> into two equal transform of size <math> N/2 </math> recursively. Here is the definition of the algorithm given on wikipedia's page.
	:<math> X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}</math>		:<math> X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}</math>
	where <math>k</math> is an integer ranging from <math>0</math> to <math>N-1</math>.		where <math>k</math> is an integer ranging from <math>0</math> to <math>N-1</math>.

Rothsa at 17:47, 19 October 2007

2007-10-19T17:47:11Z

← Older revision		Revision as of 10:47, 19 October 2007
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	An intuitive brute force way of computing a Fourier Transform is just adding the function up one at a time starting at n=0 or n=1 like this:		An intuitive brute force way of computing a Fourier Transform is just adding the function up one at a time starting at n=0 or n=1 like this:
	:<math>\sum_{i=m}^n x_i = x_m + x_{m+1} + x_{m+2} +\cdots+ x_{n-1} + x_n. </math>		:<math>\sum_{i=m}^n x_i = x_m + x_{m+1} + x_{m+2} +\cdots+ x_{n-1} + x_n. </math>
	What an FFT does is rearrange the the summation so that you don't compute the transform in sequential order - you group similar elements together and simplify before combining them. This cuts down the adding and multiplying, thus cutting computation time down by about 100 times.		What an FFT does is rearrange the the summation so that you don't compute the transform in sequential order - you group similar elements together and simplify before combining them. This cuts down the adding and multiplying, thus cutting computation time down by about 100 times. The faster computation time makes it a great way to perform analysis for DSP applications like quantum mechanics, linear network analysis, probability, and antenna analysis.

	<br><b> Cooley-Tukey Algorithm </b>		<br><b> Cooley-Tukey Algorithm </b>

Rothsa at 17:43, 19 October 2007

2007-10-19T17:43:47Z

← Older revision		Revision as of 10:43, 19 October 2007
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	<br><b> Cooley-Tukey Algorithm </b>		<br><b> Cooley-Tukey Algorithm </b>

	Three popular algorithms are the Cooley Tukey algorithm (radix-r algorithms), the Good-Thomas Algorithm, and the Winograd FFT algorithm. The Cooley Tukey Algorithm Radix-2 algorithm is the simplest and most popular of all. The algorithm separates a given discrete Fourier transform of size <math> N </math> into two equal transform of size <math> N/2 </math>. Here is the definition of the algorithm given on wikipedia's page.		Three popular algorithms are the Cooley Tukey algorithm (radix-r algorithms), the Good-Thomas Algorithm, and the Winograd FFT algorithm. The Cooley Tukey Algorithm Radix-2 algorithm is the simplest and most popular of all. The algorithm separates a given discrete Fourier transform of size <math> N </math> into two equal transform of size <math> N/2 </math> recursively. Here is the definition of the algorithm given on wikipedia's page.
	:<math> X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}</math>		:<math> X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}</math>
	where <math>k</math> is an integer ranging from <math>0</math> to <math>N-1</math>.		where <math>k</math> is an integer ranging from <math>0</math> to <math>N-1</math>.


	===Related Links===		===Related Links===
	*[[http://en.wikipedia.org/wiki/Fast_Fourier_transform Wikipedia:Fast Fourier Transform]]		*[[http://en.wikipedia.org/wiki/Fast_Fourier_transform Wikipedia:Fast Fourier Transform]]

Rothsa at 17:42, 19 October 2007

2007-10-19T17:42:16Z

← Older revision		Revision as of 10:42, 19 October 2007
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	where <math>k</math> is an integer ranging from <math>0</math> to <math>N-1</math>.		where <math>k</math> is an integer ranging from <math>0</math> to <math>N-1</math>.
	===Related Links===		===Related Links===
			*[[http://en.wikipedia.org/wiki/Fast_Fourier_transform Wikipedia:Fast Fourier Transform]]
	*[[http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm Wikipedia:Cooley-Tukey Algorithm]]		*[[http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm Wikipedia:Cooley-Tukey Algorithm]]
	*[[http://www.relisoft.com/Science/Physics/fft.html Fast Fourier Transforms]]		*[[http://www.relisoft.com/Science/Physics/fft.html Fast Fourier Transforms]]
	*[[http://etd.lib.fsu.edu/theses/available/etd-06262004-162018/unrestricted/Divya_MS_Thesis.pdf FTT's for FPGA's Thesis]]		*[[http://etd.lib.fsu.edu/theses/available/etd-06262004-162018/unrestricted/Divya_MS_Thesis.pdf FTT's for FPGA's Thesis]]

Rothsa at 17:40, 19 October 2007

2007-10-19T17:40:52Z

← Older revision		Revision as of 10:40, 19 October 2007
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	It's an algorithm that can compute the discrete Fourier transform faster than other algorithms. In digital systems, continuous Fourier Transforms are sampled, turning them into discrete Fourier Transforms which then can be computed and manipulated using Digital Signal Processing.		It's an algorithm that can compute the discrete Fourier transform faster than other algorithms. In digital systems, continuous Fourier Transforms are sampled, turning them into discrete Fourier Transforms which then can be computed and manipulated using Digital Signal Processing.

	An intuitive brute force way of computing a Fourier Transform ~~means rearranging~~ the the summation so that you don't compute the transform in sequential order - you group similar elements together and simplify before combining them. This cuts down the adding and multiplying, thus cutting computation time down by about 100 times.		An intuitive brute force way of computing a Fourier Transform is just adding the function up one at a time starting at n=0 or n=1 like this:
			:<math>\sum_{i=m}^n x_i = x_m + x_{m+1} + x_{m+2} +\cdots+ x_{n-1} + x_n. </math>
			What an FFT does is rearrange the the summation so that you don't compute the transform in sequential order - you group similar elements together and simplify before combining them. This cuts down the adding and multiplying, thus cutting computation time down by about 100 times.

	<br><b> Cooley-Tukey Algorithm </b>		<br><b> Cooley-Tukey Algorithm </b>

Rothsa at 17:31, 19 October 2007

2007-10-19T17:31:04Z

← Older revision		Revision as of 10:31, 19 October 2007
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	<br><b> Cooley-Tukey Algorithm </b>		<br><b> Cooley-Tukey Algorithm </b>

	Three popular algorithms are the Cooley Tukey algorithm (radix-r algorithms), the Good-Thomas Algorithm, and the Winograd FFT algorithm. The Cooley Tukey Algorithm Radix-2 algorithm is the simplest and most popular of all. The algorithm separates a given discrete Fourier transform of size <math> N </math> into two equal transform of size <math> N/2 </math>.		Three popular algorithms are the Cooley Tukey algorithm (radix-r algorithms), the Good-Thomas Algorithm, and the Winograd FFT algorithm. The Cooley Tukey Algorithm Radix-2 algorithm is the simplest and most popular of all. The algorithm separates a given discrete Fourier transform of size <math> N </math> into two equal transform of size <math> N/2 </math>. Here is the definition of the algorithm given on wikipedia's page.
	:<math> X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}</math>		:<math> X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}</math>
	where <math>k</math> is an integer ranging from <math>0</math> to <math>N-1</math>.		where <math>k</math> is an integer ranging from <math>0</math> to <math>N-1</math>.
	===Related Links===		===Related Links===
			*[[http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm Wikipedia:Cooley-Tukey Algorithm]]
	*[[http://www.relisoft.com/Science/Physics/fft.html Fast Fourier Transforms]]		*[[http://www.relisoft.com/Science/Physics/fft.html Fast Fourier Transforms]]
	*[[http://etd.lib.fsu.edu/theses/available/etd-06262004-162018/unrestricted/Divya_MS_Thesis.pdf FTT's for FPGA's Thesis]]		*[[http://etd.lib.fsu.edu/theses/available/etd-06262004-162018/unrestricted/Divya_MS_Thesis.pdf FTT's for FPGA's Thesis]]