58k 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 ...
3k 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^...
5k 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 ...
9k 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 ...
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. ...
447 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 ...
637 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 ...
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 ...
955 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. ...
What is the role of complex exponential $e^{jθ}$ in Fourier Transform? Is it different in the continuous and in discrete time domain?