# how to calculate cross correlation of transient signal?

there.

Let me have a noisy speech signal $y(k)$ as below.

$$y(k) = x(k) + v(k)$$

where, $k$ is the discrete-time index, $x(k)$ is clean speech signal, $v(k)$ is a zero-mean random process, uncorrelated with $x(k)$ e.g. white noise.

If we put into this as a vector form:

$$\textbf{y} (k) = \textbf{x}(k)+\textbf{v}(k)$$

where,

$$\textbf{y}(k) = [y(k) \text{ }\ y(k-1) \text{ }\ ... \text{ }\ y(k-L+1)]^T,$$

$L$ is a length of vector.

If we try to calculate the correlation matrix of size $L \times\ L$, the noisy speech signal can be written as

$$\textbf{R}_y = E[\textbf{y}(k)\textbf{y}^T(k)] = \textbf{R}_x+\textbf{R}_v.$$

Also, $\textbf{R}_x = E[\textbf{x}(k)\textbf{x}^T(k)]$, $\textbf{R}_v = E[\textbf{v}(k)\textbf{v}^T(k)]$.

However, the speech signal is not the stationary signal but the transient signal. This correlation matrix also can be used for calculating MVDR(Minimum Variance Distortionless Response) process.

Here is what I want to know.

Because $\textbf{y}(k)$ is not the stationary signal, I think there is a method for calculating the correlation matrix for transient signal.

How can we calculate the cross-correlation matrix for transient signal?

• Thank you for your comment. Yeah, I tried to calculate the speech signal as transient signal. So I questioned concern this theme. I need to study about quasi-stationary assumption. :) Also, let me summary what you mentioned. If I have one 30 msec frame, $F$. If I have a speech signal which length is $100F$, I have 100 frames if there is no overlap, right? In quasi-stationary assumption, each frame(30 msec signal) is treated as stationary signal? Commented Dec 27, 2013 at 6:39