DSP[4] Flashcards
The main drawback of Fourier series is
it is
only applicable to periodic signals
To overcome
this shortcoming, Fourier developed a
mathematical model to transform signals
between time domain to frequency domain &
vice versa, which is called
Fourier Transform
There are
some naturally produced signals such as non-
periodic or aperiodic, which we cannot
represent using Fourier series. To overcome
this shortcoming, Fourier developed a
mathematical model to transform signals
between time domain to frequency domain &
vice versa, which is called
Fourier Transform
The generalization of the complex Fourier
series is known as
Fourier Transform
Signal can be represented using discrete frequencies
Periodic
It is named after Jean Baptiste
Joseph Fourier (1768-1830), a French
mathematician and physicist.
Fourier Analysis
A signal can be either continuous or discrete,
and it can be either periodic or aperiodic.
The combination of these two features
generates the four categories.
- Aperiodic-Continuous
- Periodic-Continuous
- Aperiodic-Discrete
- Periodic-Discrete
These are discrete signals that repeat
themselves in a periodic fashion from
negative to positive infinity is most often
called the Discrete Fourier Transform.
Periodic-Discrete
This type of Fourier transform is
called the Discrete Time Fourier Transform.
Aperiodic-Discrete
This version of the Fourier
transform is called the Fourier Series
Periodic-Continuous
The Fourier Transform for this type
of signal is simply called the Fourier
Transform.
Aperiodic-Continuous
is an equation to
calculate the frequency, amplitude and
phase of each sine wave needed to make up
any given signal
Fourier transform
F(w) is called
Fourier transform
f(t) lives in the ____ and
f(w) lives in the ____
time domain and frequency domain
It is a mapping between domains
Transform
