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Different magnitude values when computing f-domain function by hand and with fft matlab command.

Asked by Ajpaezm on 16 Sep 2016
Hello everyone, I have the following function in time-domain and its correspondent f-domain transform:
With t1 as [0s,8s) and f1 as [-50hz,50hz)
When I plot, I get the following:
Now, I tried using fft command to the time-domain function and see what I got, even if I choose the same t1 and f1 vectors. For my surprise, we have differences when plotting:
Why's that? Is it something about fft command?
Here's how I'm placing the formulas in case you think there's a mistake in there:
s1(t)
s1=(t1-2).*exp(-t1).*heaviside(t1-2);
S1(f)
S1f=(exp(-2*(1+(2*pi*f1*1i)))./((1+(2*pi*f1*1i)).^2));
Can you help me find a reason why is this happening?
Thanks.

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