I am implementing MUSIC algorithm in Verilog, and I need to implement the blocks in following order

$$\text{Input signal}{\longrightarrow}\text{Co-variance/Correlation matrix}{\longrightarrow}\text{EVD}{\longrightarrow}\text{Peak search}$$

But I am confused because some papers refer the second block as correlation and some it as co-variance.

  • 1
    $\begingroup$ Correlation is simply normalized covariance. Follow this link for reference. $\endgroup$
    – havakok
    Commented Apr 29, 2019 at 9:22
  • $\begingroup$ But say for any matrix say A.... I find cov(A) and corr(A) both of them donot produce the same result........... Correct me If I am wrong that I am dividing the output of cov(A) from maximum of the matrix to get it normalized $\endgroup$
    – uzmeed
    Commented Apr 30, 2019 at 4:05
  • $\begingroup$ You should divide covariance by $(\sigma_x \cdot \sigma_y)$ to get the correlation, as in the link I posted. That is not the maximum value. $\endgroup$
    – havakok
    Commented Apr 30, 2019 at 11:19

1 Answer 1


The IEEE signal processing literature deviates somewhat from the terminology used in statistics and actually from itself so your confusion is justified. If $\mathbf{x_k}$ is a vector signal the quantity at sample time $\mathbf{k}$,

$$ \mathbf{R}= \sum_k \mathbf{x_k \, x_k^H} $$

is often called either.

The SP transactions historically focused on application areas like like radar, sonar, speech, audio, telephony, .... where the signal propagates in a way where dc isn’t propagated. The long term time average of amplitude tends to zero.

Music (assumptions) works on 2nd order statistics and is stationary over some interval so implicitly the signal is random. Under these circumstances the average values of the data will be zero. The algorithm is generally used in array processing.

Typically in IEEE SP papers covariance denotes that the mean vector is subtracted out so the correlation (as shown above) of a zero mean signal vector and the covariance is the same thing.

The interesting thing about algorithms that use 2nd order statistics is that they often work well on deterministic signals.

Authors in Kalman Filtering papers are more specific.

In Statistics, the Pearson correlation coefficient is not the same as the usage in array processing.

There are more than a few words that have different but similar meaning, like coherence.

Even in SP, the terms mean, average, and expected value are often used in ways that lead to confusion.


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