 # Mathematical Methods - Problems

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% 1.
%
% a) No, since f(t)=0 only for t = 0 (for time limited signals, f(t)= 0 for t
% outside some time interval [t1,t2].
%
% c) Since f(-t) = - t*exp(-2*|-t|) = - t*exp(-2*t) = -f(t).
%
% f) It is not bandlimited since fhat(a) is never = 0 (for band-limited signals
% fhat(a) = 0 for a outside some segment [a1,a2].

% b)

f = @(t) t.*exp(-2.*abs(t));
t = -5:0.01:5;

figure(1);
plot(t,f(t));
xlabel('$t$','interpreter','latex');
ylabel('$f(t)$','interpreter','latex');
title('Signal');

% e)

fhat = @(a) -1i* pi*a ./ (1+pi^2*a.^2).^2;
a = -3:0.01:3;

figure(2);
plot(a,abs(fhat(a)));
xlabel('$\alpha$','interpreter','latex');
ylabel('$|\hat f(a)|$', 'interpreter','latex');
title...
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