Convolution & LTI systems worksheet with answers

Free printable Convolution & LTI systems worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
x[n]n−1031−12−134h[n]n−10112234

The sequences x[n] = {3, −1, −1} and h[n] = {1, 2} both start at n = 0. Find the sample y[2] of the convolution y[n] = x[n] ∗ h[n].

x[n] = {3, −1, −1}, n = 0…2h[n] = {1, 2}, n = 0…1
y[2] =
2.Easy
x[n]n−10−11−123334h[n]n−101112−334

The sequences x[n] = {−1, −1, 3, 3} and h[n] = {1, 1, −3} both start at n = 0. Find the largest sample ymax of y[n] = x[n] ∗ h[n].

x[n] = {−1, −1, 3, 3}, n = 0…3h[n] = {1, 1, −3}, n = 0…2
ymax =
3.Medium
x(t)t25h(t)t35

The signal x(t) is nonzero only between t = 2 s and t = 5 s, and h(t) only between t = 3 s and t = 5 s. Find the duration D of y(t) = x(t) ∗ h(t).

x: 2 … 5 sh: 3 … 5 s
D = s
4.Medium
x(t)t4h(t)t0.21

A system has the impulse response h(t) = e−5tu(t). The input is a step x(t) = 4·u(t). Find the output y(0.2) at t = 0.2 s.

h(t) = e−5tu(t)x(t) = 4·u(t)t = 0.2 s
y(0.2) =
5.Hard
x(t)t (ms)2.55104

A square wave switches between 4 and 0 with period T = 5 ms (half a period at each level). Find the amplitude c1 of its Fourier component at 200 Hz.

0 … 4T = 5 msf = 200 Hz
c1 =
6.Hard
x(t)t (ms)1020403

A square wave switches between 3 and 0 with period T = 20 ms (half a period at each level). Find the amplitude c7 of its Fourier component at 350 Hz.

0 … 3T = 20 msf = 350 Hz
c7 =

Answer key

  1. 1. y[2] = −3
  2. 2. ymax = 9
  3. 3. D = 5 s
  4. 4. y(0.2) = 0.5057
  5. 5. c1 = 2.546
  6. 6. c7 = 0.2728

Full step-by-step solutions: practise this topic on examproblems.com.