# Tag Info

Accepted

### Periodicity of a constant signal!

As you say, the constant function is periodic. A signal $x(t)$ is said to be periodic with period $p$ or to have a period $p$ if there exists a $p>0$ such that $x(t+p)=x(t)$ for all real numbers $t$...
• 13.8k

### How can a signal be both periodic and random?

Most realistic signals are both random and periodic. For example, you can modulate a harmonic oscillator with a slow enough random signal that moves its frequency around a $\mu_{f}, \sigma_f$. This ...
• 10.1k
Accepted

### Fourier transform artifacts

The cross pattern is typically a border effect, due to the periodicity induced by the standard implementation and hypotheses behind the Fast Fourier transform, when the image lacks periodicity from ...
• 29.9k

### Simple and Effective Method to Estimate the Frequency of a Single Sine Signal in White Noise

I assume the model to be: $$x \left[ n \right] = \sin \left[ 2 \pi \frac{f}{ {f}_{s} } n + \phi \right] + w \left[ n \right]$$ Where $w \left[ n \right]$ is white noise uncorrelated with the ...
• 40.7k

### $2\pi$ periodicity of discrete-time Fourier transform

The argument does not work in continuous time. In discrete time the argument is that $$e^{j\omega n}=e^{j(\omega+2\pi)n},\qquad n\in\mathbb{Z}\tag{1}$$ This is true because by definition $n$ is an ...
• 80.2k

• 80.2k

• 29.9k
Accepted

• 4,105