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−10−21−1243345h[n]n−1011−120.534

An FIR filter computes y[n] = x[n] − x[n − 1] + 0.5·x[n − 2]. The input is x[n] = {−2, −1, 4, 3} for n = 0…3 and zero elsewhere. Find the output y[2].

b = {1, −1, 0.5}x[n] = {−2, −1, 4, 3}, n = 0…3
y[2] =
2.Easy
x[n]n−101112131…h[n]n−10−1122−134

A system with the impulse response h[n] = {−1, 2, −1} (n = 0…2) receives the step input x[n] = 1·u[n]. Find the output y[1].

h[n] = {−1, 2, −1}x[n] = 1·u[n]
y[1] =
3.Medium
x(t)t24h(t)t1

The pulse x(t) = 4 for 0 ≤ t < 2 s (zero elsewhere) is applied to a system with h(t) = e−2tu(t). Find the output y(3.5) at t = 3.5 s, after the pulse has ended.

x(t) = 4, 0 ≤ t < 2 sh(t) = e−2tu(t)t = 3.5 s
y(3.5) =
4.Medium
x(t)t10h(t)t1

The input x(t) = 10·e−6tu(t) is applied to a system with h(t) = e−2tu(t). Find the output y(1.5) at t = 1.5 s.

x(t) = 10·e−6tu(t)h(t) = e−2tu(t)t = 1.5 s
y(1.5) =
5.Hard
x(t)t (ms)0.5121−1

A triangle wave rises and falls linearly between −1 and +1 with period T = 1 ms. Find the amplitude c1 of its Fourier component at 1000 Hz.

±1T = 1 msf = 1000 Hz
c1 =
6.Hard
x(t)t (ms)510205−5

A triangle wave rises and falls linearly between −5 and +5 with period T = 10 ms. Find the amplitude c5 of its Fourier component at 500 Hz.

±5T = 10 msf = 500 Hz
c5 =

Answer key

  1. 1. y[2] = 4
  2. 2. y[1] = 1
  3. 3. y(3.5) = 0.09775
  4. 4. y(1.5) = 0.1242
  5. 5. c1 = 0.8106
  6. 6. c5 = 0.1621

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