I am trying to understand pre-emphasis equation.

$$ y[n]=x[n]-\alpha x[n-1]$$

Where $\alpha = 0.95$. My question is what does it mean if $\alpha = 1$?


The pre-emphasis filter is a simple high-pass filter with a monotonically increasing magnitude of its frequency response $H(\omega)$. Its value at DC is $H(0)=1-\alpha$, and its value at Nyquist (i.e., the maximum frequency) is $H(\pi)=1+\alpha$. Consequently, for $\alpha=1$ you get a zero at DC, which means that the filter will totally suppress a constant input signal (which is obvious from looking at the difference equation).

Note that a pre-emphasis with $\alpha=1$ cannot be compensated for because the DC component is lost and can't be recovered. In signal processing terms: there is no stable inverse filter.

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