The Fourier transform is the primary tool for analyzing signals and signal-processing systems in the frequency domain, especially when signals are sampled or converted from discrete time to continuous time. In this lesson you will learn the definition of the Fourier transform and how to evaluate the corresponding integrals for several common signals. You will also build your intuition for the relationships between time- and frequency-domain descriptions of signals. Developing time- and frequency-domain intuition is an essential skill for the signal-processing practitioner.

## Prerequisites

## Video

## Key Concepts and Screenshots

## Quiz

1. The primary role of the Fourier transform in signal processing is computation of frequency response and the spectral content of signals.True False

2. A signal is defined as . Which is the correct Fourier transform? (Hint: use the result derived in the video.)

a)

b)

c)

d)

e)

3. The Fourier transform of a signal is . Which is the correct time-domain signal? (Hint: use the result derived in the video.)

a)

b)

c)

d)

e)

4. Which of the following signals is likely to have the broadest Fourier transform, that is, whose Fourier transform spans the broadest range of frequencies.

a)

b)

c)

d)

e)

5. The Fourier transform exists for any possible signal.

True False

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