Linked Questions

0
votes
4answers
119 views

Negative frequency in the Fourier Transform [duplicate]

Why use this instead of a positive frequency? I asked on the math forum but it just wasn't helpful. I understand the idea of a negative frequency is important in general since many real signals like ...
40
votes
3answers
68k views

Why is the FFT “mirrored”?

If you do an FFT plot of a simple signal, like: t = 0:0.01:1 ; N = max(size(t)); x = 1 + sin( 2*pi*t ) ; y = abs( fft( x ) ) ; stem( N*t, y ) 1Hz sinusoid + DC ...
2
votes
5answers
4k views

What does the exponential term in the Fourier transform mean?

We know that Fourier transform $F(\omega)$ of function $f(t)$ is summation from $-\infty$ to $+\infty$ product of $f(t)$ and $e^{-j \omega t}$: $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^...
9
votes
1answer
11k views

Image processing and the Fourier Transform

I am trying to understand how and why the fourier transform is used in image processing / computer vision. Below is what I have gathered so far. Would my understanding of it be correct? If not, could ...
10
votes
2answers
6k views

How do you handle negative frequencies in the power spectrum of a complex signal?

When we apply the DFT operation on a real signal $x[n]$ to get $X[k]$, then take the square magnitude of the $X[k]$, $\lvert X[k]\rvert^2$, the power spectrum is symmetrical. You can take the ...
3
votes
3answers
1k views

Understanding FFT of an Image

I am having trouble identifying the frequency components of an image, Here i simply generated, 256x256 binary-image. ...
4
votes
1answer
495 views

What is a complex helical sequence?

Matlab says x = hilbert(xr) returns a complex helical sequence, sometimes called the analytic signal, from a real data sequence. How did the name ...
3
votes
2answers
926 views

DFT of real sinusoids - why sum over -$N/2$ to $N/2-1$ as opposed to $0$ to $N-1$?

I'm going through a Coursera course on signal processing, and we're just introduced to DFTs. We are told that if you have a complex sinusoidal signal $x[n]$ where $n=0,1...\ N-1$, its DFT is given ...
0
votes
5answers
200 views

Does negative frequency actually exist or it is just theoretical?

This below questions gives good explanation regarding negative frequency What is the physical significance of negative frequencies? But I have one query Does negative frequency only exist ...
1
vote
1answer
1k views

Spectral Shape and properties [closed]

I started learning audio dsp and the book I am working through is loaded with formulas and most of the time expects the reader to know what the relation is between these functions and why they are ...
0
votes
2answers
1k views

Frequency and phase range of the FFT of an image

I have some questions: 1. What is the horizontal and vertical frequency range (and the steps) of the FFT amplitudes of an image? 2. What is the relevant axes range for the phase image? 3. ...
2
votes
1answer
494 views

What is the role of complex exponential?

What is the role of complex exponential $ e^{jθ} $ in Fourier Transform? Is it different in the continuous and in discrete time domain?
1
vote
3answers
213 views

Can we see the Fourier transform as a filtering operation? [duplicate]

Is the Fourier Transform (FT) a filtering operation? Is it possible to graphically represent this transform? I know that a signal can be represented in the frequency domain, but I want to know if the ...
0
votes
2answers
147 views

Intuitive meaning of complex time domain signal representation (quadrature sampling)

I saw What is the meaning of imaginary values in the time domain?. My question is about I Q samples as recorded from an SDR receiver (e.g. RTL-SDR). My understanding is that we can call these I Q ...
0
votes
1answer
56 views

Negative frequency of a sinusoidal wave on the magnitude spectrum: Physical explanation?

link to the video: Negative frequency Must a cosine function be expressed as two exp functions with opposite frequencies/directions of rotation and half the magnitude/amplitude(1/2), therefore ...