![Figure 1: The two sequences for the autocorrelation of x0[n] and x0[n].](https://www.wavewalkerdsp.com/wp-content/uploads/wordpress-popular-posts/5515-featured-125x75.png)
![Figure 3: The complex sinusoid e(j2 pi (2/4) n) only contains energy at X[2].](https://www.wavewalkerdsp.com/wp-content/uploads/wordpress-popular-posts/8136-featured-125x75.png)
![A BPSK signal s[n], real Gaussian noise w[n], and the received signal x[n] = s[n] + w[n] for SNR = 20 dB](https://www.wavewalkerdsp.com/wp-content/uploads/wordpress-popular-posts/15621-featured-125x75.png)
![Figure 2: The complex sinusoid x0[n] = e(j2 pi 0.125 n) plotted in the complex plane.](https://www.wavewalkerdsp.com/wp-content/uploads/wordpress-popular-posts/3104-featured-125x75.png)
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![Figure 1: The two sequences for the autocorrelation of x0[n] and x0[n].](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAABLAQAAAAB12LU4AAAAAnRSTlMAAHaTzTgAAAASSURBVDjLY2AYBaNgFIyCEQcABPsAAZzw+UwAAAAASUVORK5CYII=)
Cross Correlation Explained With Real Signals - Using Euler’s Formula to Derive Sine and Cosine
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![A BPSK signal s[n], real Gaussian noise w[n], and the received signal x[n] = s[n] + w[n] for SNR = 20 dB](https://www.wavewalkerdsp.com/wp-content/uploads/2023/12/HowToComputeSignalToNoiseRatioSNRInSimulation_signalNoiseTimeDomain-300x240.png)
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