# Questions tagged [dft]

The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.

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### What does frequency domain denote in case of images?

I was just learning about the frequency domain in images. I can understand the frequency spectrum in case of waves. It denotes what frequencies are present in a wave. If we draw the frequency ...
59k views

### What is the difference between a Fourier transform and a cosine transform?

In speech recognition, the front end generally does signal processing to allow feature extraction from the audio stream. A discrete Fourier transform (DFT) is applied twice in this process. The first ...
61k 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 ...
12k views

### Is there an algorithm for finding a frequency without DFT or FFT?

I was looking in the Android app store for a guitar tuner. I found a tuner app that claimed it was faster than other apps. It claimed it could find the frequency without using the DFT (I wish I still ...
6k views

### How can I compute a log-spaced power spectrum?

I would like to compute a power spectrum in which the frequencies are logarithmically spaced. In Welch's method there is a trade-off between the frequency resolution of the resulting power spectrum ...
5k views

### Frequency-domain zero padding - special treatment of X[N/2]

Suppose we wish to interpolate a periodic signal with an even number of samples (e.g. N=8) by zero-padding in the frequency domain. Let the DFT X=[A,B,C,D,E,F,G,H] ...
7k views

### Why are magnitudes normalised during synthesis (IDFT), not analysis (DFT)?

In most examples and FFT code that I've seen, the output (frequency magnitudes) of the forward DFT operation is scaled by N -- i.e. instead of giving you the magnitude of each frequency bin, it gives ...
5k views

### What are some of the differences between DFT and FFT that make FFT so fast?

I'm trying to understand FFTs, here's what I have so far: In order to find the magnitude of frequencies in a waveform, one must probe for them by multiplying the wave by the frequency they are ...
1k views

### DFT with geometrically-spaced bins?

The traditional Discrete Fourier Transform (DFT) and its cousin, the FFT, produce bins that are spaced equally. In other words, you get something like the first 10 hertz in the first bin, 10.1 through ...
16k views

### When to use the DTFT vs the DFT (and their inverses) in analysis?

In many of my readings, whenever some author speaks about working in the frequency (transform) domain (of a digital signal), they often times take the DFT, or the DTFT, (and of course their ...
14k views

### How to demodulate an AFSK signal in software

I am trying to transmit binary data from one device to another over an audio channel (speaker/mic). I use AFSK (Audio Frequency Shift Keying) as in Packet Radio, with $1200 \text{ Baud}$ and two ...
609 views

### How to efficiently calculate only the low coefficients of a zero-padded FFT

I've got an algorithm that zero pads a sequence to 4N, does an FFT, and only uses the lowest frequency N points out of the generated 4N. This seems like a lot of wasted work, any ideas how this can ...
2k views

### Could a DCT be used for an audio magnitude spectrum rather than DFT?

From what I understand, the DCT has half the bin size as a DFT of the same size N. The DFT also includes phase information, but often this is not needed when only the magnitude spectrum is desired. ...
11k views

### Why do we say that “zero-padding doesn't really increase frequency resolution”

Here is a sinusoid of frequency f = 236.4 Hz (it is 10 milliseconds long; it has N=441 points at sampling rate ...
27k views

### Discrete Fourier Transform: What is the DC Term really?

I am currently toying around with the Discrete Fourier Transform (DFT) in Matlab to extract features from images. I like to fully understand the concepts that I use. I have read several explanations, ...
4k views

### Z-transform of a downsampler

In this paper or multirate filtering, the author establishes the following mathematical relationship. Let $y_D$ be the output of a downsampler such that $$y_D[n] = x[Mn]$$ where $M$ is the ...
11k views

### When should I calculate PSD instead of plain FFT magnitude spectrum?

I have a thirty-second speech signal that was sampled at 44.1 kHz. Now, I would like to show what frequencies the speech has. However, I'm not sure what would be the best way to do that. It seems ...
3k views

### How does subpixel image shifting using DFT really work?

I am trying to assess the quality of several image interpolation methods for an application that involves generating subpixel-shifted images. I thought I could compare the results of a subpixel shift ...
4k views

### STFT and DWT (Wavelets)

STFT can be successfully used on sound data (with a .wav soundfile for example) in order to do some frequency-domain modifications (example : noise removal). With ...
9k views

### Real discrete Fourier transform

I am trying to understand the real DFT and the DFT and why the distinction exists. From what I know so far the DFT uses $e^{i2\pi kn/N}$ for basis vectors and gives the representation x[n]=\sum_{k=...
2k views

### Why do I have frequency leakage in DFT after zero padding if frequency resolution is fine?

Let's consider this example: Fs=1000; Ns=500; t=0:1/Fs:(Ns-1)*1/Fs; f1=10; f2=400; x=5+5*sin(2*pi*f1*t)+2*sin(2*pi*f2*t); X=fft(x); In this scenario, frequency ...
15k views

### What is normalized frequency

I am working on DSP and finding difficulty to understand the term Normalized frequency often used with DFT & DTFT. What is normalized frequency in DSP ? and how it is different from analog ...
1k views

### DFT - Removing window effect in spectral domain with convolution

I was thinking about the DFT windowing subject and a thought came to my mind. A DFT will yield the spectrum of a signal convoluted with spectrum of the window used, therefore having a main lobes and ...
11k views

### Why does the DFT assume the transformed signal is periodic?

In many signal processing books, it is claimed that the DFT assumes the transformed signal to be periodic (and that this is the reason why spectral leakage for example may occur). Now, if you look at ...
3k views

### Artifacts in FFT

I recently realized that FFT's aren't perfect. Meaning if I take a signal and then take it's FFT, and then do an inverse FFT, the resulting output isn't exactly the same as the input. Here's an image ...
2k views

### Log-Polar DFT Based Scale-Invariant Image Registration

I'm trying to do image registration using phase correlation as described in the Reddy Chatterji paper. In my case, the images may be scaled and translated relative to each other. The algorithm for ...