Practice Convolution Theorem (11.3.6) - Fourier Transform and Properties

Practice: Convolution Theorem

Lesson 11.3.6Fourier Transform and Properties

Practise this section

7 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
5 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What does the convolution of two functions represent?
Show hintHide hint
Think about interactions between two shapes.
Question 2.
What symbol is used to denote convolution?
Show hintHide hint
It's a simple symbol you would recognize.
3Question 3.
What does the Convolution Theorem state?
- Convolution in the time domain results in addition in the frequency domain.
- Convolution in the time domain results in multiplication in the frequency domain.
- Convolution in the time domain results in transformation in the frequency domain.
Show hintHide hint
Think about how operations translate between domains.
4Question 4.
True or False: The function denoted by f(t) * g(t) refers to their addition.
- True
- False
Show hintHide hint
Recall the definitions discussed earlier.
Question 5.
Given two functions f(t) = cos(2πt) and g(t) = u(t), compute the convolution of these two functions.
Show hintHide hint
Setup the integral for convolution and apply Fourier Transform if necessary.
Question 6.
Explain how the Convolution Theorem could be utilized in designing filters for audio signals.
Show hintHide hint
Think about signal processing in terms of frequency components.

3 more questions in this section. Enroll free to practise them all.