Fourier transforms with procedures such as Discrete Fourier Transforms and Fast Fourier Transforms

The Discrete Fourier Transform (DFT) converts a signal from:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

The DFT of an N-point sequence produces:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

The computational complexity of direct DFT is:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

The Fast Fourier Transform (FFT) reduces complexity to:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

The fundamental basis functions of DFT are:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Nyquist frequency is defined as:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Aliasing occurs when:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

The inverse DFT (IDFT) is used to:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

The FFT algorithm is based on:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Convolution in time domain corresponds to:
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation