Digital

Why are magnitudes normalised during synthesis (IDFT), not analysis (DFT)?

Why are magnitudes normalised during synthesis (IDFT), not analysis (DFT)?
  1. What is the difference between DFT and IDFT?
  2. Why we use FFT instead of DFT?
  3. What is the purpose of DFT?
  4. What is DFT in digital image processing?

What is the difference between DFT and IDFT?

The DFT allows one to convert a set of digital time samples to its frequency domain representation. In contrast, the IDFT can be used to invert the DFT samples, allowing one to reconstruct the signal samples x(k) directly from its frequency domain form, X(m).

Why we use FFT instead of DFT?

FFT is an implementation of the DFT used for used for fast computation of the DFT. In short, FFT can do everything a DFT does, but more efficiently and much faster than a DFT. It's an efficient way of computing the DFT.

What is the purpose of DFT?

The DFT is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers. Since it deals with a finite amount of data, it can be implemented in computers by numerical algorithms or even dedicated hardware.

What is DFT in digital image processing?

As we are only concerned with digital images, we will restrict this discussion to the Discrete Fourier Transform (DFT). The DFT is the sampled Fourier Transform and therefore does not contain all frequencies forming an image, but only a set of samples which is large enough to fully describe the spatial domain image.

Adding two sine waves results in a low buzz
What do you get when you multiply 2 sine waves of different frequencies together?How does a sine wave produce sound? What do you get when you multip...
Energy or power of exponential summation signal
Is exponential function energy or power signal?How do you know if a signal is energy or power signal?Is exponential signal an energy signal?What is e...
How to get frequency axsis from pythnon CWT
What is the difference between CWT and DWT?How do you calculate CWT in Matlab?What is CWT in signal processing? What is the difference between CWT a...