# Is it possible to Denormalize a matrix of complex numbers?

In this article, FFT and I-FFT are achieved as the following:

FFT steps

process starts with a Bitmap image.

1. Bitmap-image to Integer-image

2. Integer-image to Complex-image

3. Apply Forward-FFT to Complex-image (output: Complex-FFT)

4. Apply Shift to FFT (output: Shifted Complex-FFT)

I-FFT steps

process starts with the FFT (a complex matrix) of an image.

1. Apply Backward FFT to Complex-FFT (output: Complex-image)
2. Complex-image to Integer-image
3. Integer-image to Bitmap-image

Normalization

To display an FFT's Magnitude/Phase, FFT is Normalized and then that normalized matrix of complex numbers is converted to a Bitmap. Without Normalization, I see a complete 'Black' image output.

My Question

As I posted this question, I was thinking about applying an I-FFT in the following process:

1. Obtain the Bitmap-image of a magnitude plot of an FFT.
2. De-normalize the Bitmap-image to obtain the original FFT of the image.
3. Apply I-FFT to the complex matrix and obtain the Complex-image.
4. Convert the Complex-image to Integer-image.
5. Convert the Integer-image to the original Bitmap.

N.B. For some reason, they used,

(1) Bitmap $\Rightarrow$ Integer$\Rightarrow$Complex, and, (2) Complex$\Rightarrow$Integer$\Rightarrow$Bitmap

to obtain the conversion between a Bitmap and its Complex counterpart.

## 1 Answer

Obtain the Bitmap-image of a magnitude plot of an FFT.

De-normalize the Bitmap-image to obtain the original FFT of the image.

This can't work. Preserving only the magnitude throws away half of the information contained in the complex values, and thus, you can't get the original FFT back, ever.