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This is the FFT I'm using. But two peaks (did not expect the one in the beginning) are occurring and the amplitude is not as specified (expecting a value of 2). Any help is much appreciated!

Amp = 2;
freqHz = 10000;
fsHz = freqHz*2+1;
dt = 1/fsHz;

sine = Amp*sin(2*pi*freqHz*(0:dt:1-dt));

transform = fft(sine,fsHz)/fsHz;
magTransform = abs(transform);

faxis = linspace(0,fsHz/2,fsHz);
plot(faxis,fftshift(magTransform));
xlabel('Frequency')

Output

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  • $\begingroup$ Please clarify what your problem is: how many peaks did you expect (and why) vs how many you're getting; and what amplitude did you expect (and why) vs what you're actually getting. Do not add this information as a comment; rather, edit your question. $\endgroup$
    – MBaz
    Jun 26, 2018 at 17:09
  • $\begingroup$ Please see the picture I've uploaded $\endgroup$
    – mldmnn
    Jun 26, 2018 at 19:00

2 Answers 2

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You need to use complex signal for that. Use this

Amp = 2; freqHz = 10000; fsHz = freqHz*2+1; dt = 1/fsHz; sine = Amp*exp(2i*pi*freqHz*(0:dt:1-dt)); transform = fft(sine,fsHz)/fsHz; magTransform = abs(transform); faxis = linspace(-fsHz/2,fsHz/2,fsHz); plot(faxis,fftshift(magTransform)); xlabel('Frequency')

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The somehow symeetric aspect of the complex DFT might be misleading, so in the past I shared a simple Matlab function FFTR.m for real signals only, that might yield the result you'd expect ($2$ magnitude at peak frequency):

FFRT: FFT for real signals

as long as you don't try bordeline endeavours. That requires a little normalization and a special care at DC and Nyquist. The code could be:

% Signal definition
Amp = 2;
freqHz = 10000;
fsHz = freqHz*2+1;
dt = 1/fsHz;
sine = Amp*sin(2*pi*freqHz*(0:dt:1-dt));

% Graphic part
[fftR,fftAxe] = FFTR(sine',dt);
plot(fftAxe,fftR,'o-');
xlabel('Frequency')
ylabel('Magnitude')
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    $\begingroup$ Thanks! How can I achieve this with the built in function? $\endgroup$
    – mldmnn
    Jun 26, 2018 at 19:02
  • $\begingroup$ Just explore the FFT.m link I gave as a link, and steal the code :) $\endgroup$
    – Laurent Duval
    Jun 26, 2018 at 19:03
  • $\begingroup$ And if you like it, don't hesitate to upvote! $\endgroup$
    – Laurent Duval
    Jun 30, 2018 at 11:38
  • $\begingroup$ Unfortunately my rep is not sufficient :/ $\endgroup$
    – mldmnn
    Jul 1, 2018 at 11:44

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