# Tag Info

Accepted

1 vote

### Fourier transform magnitude of the sum of two signals

In general we have $$\big|X_1(f)+X_2(f)\big|\neq \big|X_1(f)\big|+\big|X_2(f)\big|\tag{1}$$ However, the condition $X_1(f)X_2(f)=0$ $\forall f$ implies that for any $f$, either $X_1(f)$ or $X_2(f)$ or ...
1 vote
Accepted

### Why does applying Fourier Transform on point Spread Function yield h(t) which is complex-valued

The Fourier transform doesn't move only from time to frequency (or space etc.), it moves between these domains. The only difference between the Fourier transform and its inverse is a sign in the ...
1 vote

### Difference between DC component and zero frequency component of signal

A brief answer. Rect does NOT contain any DC component = No component at frequency = 0. But the fourier transform does tell there is a DC component at frequency = 0, and the rect function associated ...
1 vote
Accepted

### Is it useful to think of a Fourier Transform as writing out a signal in terms of a basis?

Question 1: Yes. In fact, the Fourier series becomes countable, although infinite, under restriction, say $[0,2\pi]$, with some exceptions. See this: Schauder basis: Relation to fourier series. ...
1 vote
Accepted

### Alternative way to find fourier transform

There are two main strategies to simplify the calculation of the Fourier Transform. Use Fourier Transform properties "Deconstruct" the time domain functions into other functions with easier ...
1 vote

### Alternative way to find fourier transform

With such a simple function it is probably easiest to directly solve the Fourier integral. It's also wise to commit such simple Fourier identities to memory. Another relatively simple method I can ...
1 vote

### Why does multiplying a real signal by a random complex phase term result in "spreading" in the Fourier domain?

I'm not sure I correctly understand what you mean by DC term, but will assume you mean fundamental frequency $f_0$ of some periodic signal, i.e. an unmodulated carrier. So your real-valued signal \$f(x)...

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