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

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.