# Tag Info

Accepted

### The difference between convolution and cross-correlation from a signal-analysis point of view

In signal processing, two problems are common: What is the output of this filter when its input is $x(t)$? The answer is given by $x(t)\ast h(t)$, where $h(t)$ is a signal called the "impulse ...
Accepted

### What are advantages of having higher sampling rate of a signal?

Sampling at a higher frequency will give you more effective number of bits (ENOB), up to the limits of the spurious free dynamic range of the Analog to Digital Converter (ADC) you are using (as well ...
Accepted

### Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?

If the ratio between your sampling frequency and the frequency of your signal is irrational, you will not have a periodic discrete signal. Assuming you have a 1-kHz sine wave and you sample at 3000*...
Accepted

Accepted

### the $L^2$-norm of a signal is also applied as its energy!

Yes, the square of the $L_2$ norm of a signal is also by definition its energy $\mathcal{E}_x$. The concept of signal energy : $$\mathcal{E}_x = \int_{-\infty}^{ \infty } x(t)^2 dt\tag{1}$$ is ...
Accepted

### Does $\cos(bt)\cdot u(t)$ have a Fourier Transform?

The integral doesn't converge in the conventional sense, so you can't solve it with standard methods. Assuming that you know (or can look up) the Fourier transform of the unit step function $u(t)$, it ...

### Analog signal can be discrete time?

This sounds like a confusion in terminology. See http://en.wikipedia.org/wiki/Digitizing Digitization basically involves two steps: Discretization: Sampling the signal at discrete times ...

### $2\pi$ 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 ...

### When does the convolution of $2$ signals equal zero?

Time-domain convolution is frequency-domain multiplication. If at all frequencies at least one of the signals is zero-valued in frequency domain, then the convolution of the two signals will be zero-...

### How to do continuous signal processing (i.e without windowing)?

Yes, it's possible to analyse sound the way ears do. For example, you could compute the DFT of a signal continuously using several Goertzel filters. $$y_k[n] = e^{j2\pi k/N} y_k[n-1] + x[n]$$ ...
### Is the system represented by the equation $y(t) = x(2t)$ time invariant?
From your solution: I followed the following algorithm: $$y(t) =x(2t)$$ $$y_1(t) = x_1(2t)$$ Let $$x_2(t) = x_1(t-t_0) ~~~\text{and}~~~ y_2(t) = x_2(2t)$$ On this following step (time ...