APSC 270 / ENGR 361 Practice Examinations
1
School of Engineering
The University of British Columbia
Practice Midterm
1. Find the inverse Fourier transform of:
X( f ) =
1
1
+
a + j2π f a − j2π f
where
exp(−at) × u(t) ⇌
(0.1)
1
a + j2π f
is a Fourier transform pair.
2. Consider an ideal lowpass filter with frequency response:
(
1, | f | < fc
H( f ) =
0, | f | > fc
The filter input is x(t) = exp (−at) × u(t). Determine the energy of the input and output signal.
3. Determine the auto-correlation function of:
x(t) = exp (− j2π f t)
and determine the power spectral density of x(t)
T. Adesina
February 12, 2023