# 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 ...
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### 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 ...
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### What happens when N increases in N-point DFT [duplicate]

I am curious about DFT, and I wrote a simple MATLAB code to test what happens when $N$ increases. I took a rectangular signal with length $L=15$, an then found th DFT of 16, 32 and 64 points. I looked ...
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### 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 ...
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### How to get Fourier coefficients to draw any shape using DFT?

I'm teaching myself about Fourier Series and the DFT and trying to draw a stylised $\pi$ symbol by fourier epicycles as detailed by Mathologer on youtube (from 18:39 onwards), and the excellent ...
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There are many question related to the zero padding a time domain signal to get more frequency bins after performing Fourier transform. As I understand this process is equivalent to trigonometric ...
284 views

### Using fourier coefficients to reconstruct data in matlab

When doing a discrete fourier transform on some data using matlab's fft function, its output is a set of fourier coefficients but I was wondering how do I go about converting these into an and bn so I ...
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 ...
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### What is the meaning of the DFT? [duplicate]

Possible Duplicate: Real Discrete Fourier Transform What is the most lucid, intuitive explanation for the various FTs - CFT, DFT, DTFT and the Fourier Series? Discrete-time Fourier transform ...
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### Number of DFT (FFT) Points Required for a Specific Frequency Resolution for an Oversampled Signal

I have a bandpass signal centered at 2 MHz and bandwidth of 50 kHz (the signal frequency varies from 2 MHz - 25 kHz to 2 MHz + 25 kHz). This signal is being sampled at 10 MHz. I want a frequency ...
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### 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 ...
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### Should the phase coefficients of the DFT of a real, even input signal all be zero?

The phase coefficients of a real, even input signals should all apparently be $0$ or a multiple of $\pi$. That's a property of the DFT I've learned about in the Audio Signal processing course on ...
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### Time scaling in DFT?

Let $x[n]$ be a real signal whose length $N$ is even. Let $y[n]=x[2n]+jx[2n+1]$ a signal whose length is $M=\frac{N}{2}$. $X[k]$ for $k=0,...,N-1$ and $Y[k]$ for $k=0,...,M-1$ are the respective DFTs ...
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### 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 ...
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### 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=...
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### 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 ...
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 ...
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### Failed to implement Goertzel algorithm in Python

After some questioning on stackoverflow, I tried to implement a Goertzel algorithm in Python. But it doesn't work : https://gist.github.com/4128537 ...
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### 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 ...
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### 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. ...
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### Frequency resolution and timestep in DFT

I am learning DFT and I am not sure I understand it correctly. I am just going to write out the process of DFT and I am asking you to tell me if I am thinking the right way. Suppose we have a signal ...
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### A system that perfoms Fourier Transform operation - is it an LTI system?

If a system takes input as the time domain signal and outputs the frequency domain signal, is such a system an LTI system? For if the input time domain signal can be represented as a linear ...
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### Hermitian symmetry in OFDM systems

I am trying to understand the usage of Hermitian symmetry in OFDM systems and have a couple of questions regarding this. What is the reason of using the Hermitian symmetry in OFDM? How can we arrange ...
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### 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 ...
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### 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 ...
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### 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 ...