# why exponential term neglected in equation? where does that exponential term gone, is this because it is a constant term or it has to do something with stablity?

• Lol really? Imagine it's a vector with length 1, no matter the angle it will always be 1. 😂 – gurghet Nov 4 '17 at 19:45
• @gurghet be nice. – Marcus Müller Nov 4 '17 at 21:43

## 2 Answers

The magnitude of that complex exponential is 1. Recall from complex algebra: any complex number can be expressed as $z = r e^{j \phi}$ where $|z|=r$ is its magnitude and $\arg z = \phi$ is the argument. Using this note that

$$|e^{-j\Omega \lambda}| = 1$$

which is why it "disappeared".

Simply because, when $C$ is a real number, $|e^{jC}|=1$. Here, $C=\Omega\lambda$, apparently real numbers.

Another interpretation is: if you change the phase of a signal (like a mere time-shift), it turns into a constant modulus in the Fourier domain, and provides some invariance, used for instance recently in data classification with Invariant Scattering Convolution Networks.