DFT by harrde - Revision history

Harrde at 07:19, 7 December 2007

2007-12-07T07:19:20Z

← Older revision		Revision as of 00:19, 7 December 2007
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	===Solution===		===Solution===

			MATLAB code and results:
			<pre>
			f = 5; % Sampling freq.
			T = 1/f; % Sampling period
			t = 0:.01:5;
			N2 = 100; % Number of sampling points
			N3 = 30;
			t2 = 0:T:N2*T;
			t3 = 0:T:N3*T;

			x = sin(2pit); % Signal that is sampled
			x2 = sin(2pit2);

			X2 = fft(x2); % DFT of signal

			figure(1) %Original signal with sampling
			plot(t(1:300), x(1:300), 'r')
			hold on
			stem(t2(1:15), x2(1:15));
			hold off;
			xlabel('Time (s)')
			ylabel('x(t)')
			title('Input Signal With Sampling')
			legend('Original signal', 'Sampled signal');

			figure(2) %DFT
			plot(t2/(N2TT),abs(X2))
			xlabel('Frequency (s)')
			ylabel('X(F)')
			title('DFT')

			figure(3) % Shifted DFT
			XS2=fftshift(X2);
			f2=-1/(2T):1/(N2T):1/(2*T);
			plot(f2,abs(XS2))
			xlabel('Frequency (s)')
			ylabel('X(F)')
			title('Shifted DFT')
			</pre>
			[[Image:DH12_1.jpg]]
			[[Image:DH12_2.jpg]]
			[[Image:DH12_3.jpg]]

			===Explaination===
			From the graphs above we see that the DFT is similar to the real Fourier Transform but is only an approximation. The actual Fourier Transform of an input signal with a single frequency F would simply have impulses of infinite height at the positive and negative frequency F. But as seen in this example the DFT only gives impulse like "spikes" that have a height of about 48. Furthermore, without shifting the DFT the "spike" on the left is at the right frequency but the one on the left is not. But as shown, a simple shift takes care of this latter problem.

2007-12-03T01:12:35Z

← Older revision		Revision as of 18:12, 2 December 2007
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	[[User:Harrde\|Back to my page]]		[[User:Harrde\|Back to my page]]

	===Problem Statement==		===Problem Statement===
	Use MATLAB, OCTAVE, or SCILAB to show how the DFT is related to the actual Fourier Transform.		Use MATLAB, OCTAVE, or SCILAB to show how the DFT is related to the actual Fourier Transform.

	===Solution===		===Solution===

2007-12-03T01:12:20Z

← Older revision		Revision as of 18:12, 2 December 2007
Line 1:		Line 1:
	[[User:Harrde\|Back to my page]]		[[User:Harrde\|Back to my page]]

			===Problem Statement==
			Use MATLAB, OCTAVE, or SCILAB to show how the DFT is related to the actual Fourier Transform.

			===Solution===

2007-11-13T01:43:42Z

New page

[[User:Harrde|Back to my page]]