Problem 3: Fourier Transform Basics Find the Fourier Transform of the following time-domain signals:
f(t)=\delta (t-2)
, where
\delta (t)
is the Dirac delta function.
f(t)=e^(-2|t|)
, a decaying exponential.
f(t)=cos(2\pi f_(0)t)
, a cosine signal with frequency
f_(0)
. Problem 4: Signal Analysis in the Frequency Domain Consider a signal
x(t)=sin(2\pi t)+sin(4\pi t)
, Find the Fourier Transform of
x(t)
. Plot the magnitude spectrum of
x(f)
. What is the bandwidth of the signal?