# Tag Info

### Replacing "e" in Euler's formula with another number

Say you're interested in $$M^{j2\pi f_0 t}. \tag{1}$$ Note that $$M = e^{\log M},$$ so $(1)$ can be written as \begin{align} M^{j2\pi f_0 t} &= \left( e^{\log M} \right) ^ {j2\pi f_0 t} \\ &= ...
• 13.9k
Accepted

### What would be the variance for complex number?

I will focus on the reason of the factor $1/2$ and leave aside the estimation things. The exact understanding should be : if a scalar Gaussian random variable (rv) is circular symmetric, its real and ...
• 5,780

### Does it make sense to have complex numbers representing real-world audio signals?

So it seems like real-world (discrete) audio signal might have complex values when being represented digitally, No, you misunderstood that. The discrete audio time signal doesn't have non-real ...
• 26.6k
Accepted

• 80.4k
Accepted

### Considering the FFT of Real & Complex Signals

There's nothing wrong here - complex sinusoids like your signal really have only one peak in frequency domain! This is the fundamental idea of why we use the Fourier transform for periodic (even ...
• 26.6k
Accepted

• 2,576

### Are there any real world applications for complex-valued signals or impulse responses?

Software-defined radio (SDR) models real band-pass signals as complex baseband signals. All signals and filters operate on complex numbers.
• 4,721

### Bandwidth with complex sampling

Complex sampling does not "break" Nyquist. IQ quadrature sampling produces twice as many bits per second of information (at the same sample rate for real or complex samples), and the 90 ...
• 34k

Only top scored, non community-wiki answers of a minimum length are eligible