i have doing fourier transform of sine wave. I am given amplitude 5v. but at the fft it not shows the 5v amplitude. so please help me.

f=128;
A=5;
t = 0:1:128;
x= A*sin(2*pi*f*t);
xDFT = fft(x);               % take fourier transform of signal
F=0:64;                          % frequency for fft
subplot(3,1,2);
plot(F,abs(xDFT(1:length(xDFT)/2+1)));

Answer 1

[Azzi Abdelmalek]

First, there is an error in your last line, because length(xDFT)/2 is not always an integer, use instead

Y=abs(xDFT(1:fix(numel(xDFT)/2)+1))
stem(F,Y)

Who told you that a signal and its fft have the same amplitude?

There is another problem, your signal has 128 as a frequency, and you are using 1 as a sample time, this is incorrect. Look at this

t = 0:1:128;
x= A*sin(2*pi*f*t);
plot(t,x)

% Is this a sine wave?

The correct way to do it is to calculate your fft in one period, with an appropriate sample time

f=128; %The frequency 
A=5; % The amplitude
period=1/f; % the period
ts=period/100; % sample time
t = 0:ts:period % vector time
x= A*sin(2*pi*f*t); % your signal
subplot(2,1,1)
plot(t,x)
[wc,w0,a0,ak,bk,c0,ck]=get_harmonics(x,ts)
subplot(2,1,2)
stem(abs(ck))

You can get get_harmonics function from this link

http://www.mathworks.com/matlabcentral/fileexchange/37654-get-harmoniques-of-a-real-signal/content/get_harmonics.m

[Ganesh Vasekar]

first thank you for answer. my friend says amplitude of fft is same as input signal amplitude. It really happen or not.