# 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.

816 questions
Filter by
Sorted by
Tagged with
36 views

### Why does a longer observation time improve DFT resolution, but repeating a signal does not?

As was proven here: https://math.stackexchange.com/questions/228614/why-doesnt-repeating-a-signal-give-rise-to-a-finer-resolution-of-dft-fft repeating a certain sequence does not improve DFT frequency ...
37 views

61 views

### Why do the DTFT and FFT give me completely different results for magnitude at a specific frequency?

I am trying to write a program to compute the magnitude and phase of a specific, non-integer frequency component (i.e. given a sampled finite signal of length $N$, I want to know the magnitude and ...
44 views

### What is the correct length for obtaining a true linear convolution from DFT?

In the linear convolution of two equal length sequences M and N, the length of the output is length(A)+length(B)-1, and if we apply the DFT property of converting convolution into multiplication, the ...
135 views

### In the context of DFT, Where Does the Nyquist Frequency Sample Belong In a Double Sided Frequency Spectrum (Positive / Negative Side)?

If we have an even number of data points $N$, after DFT in MATLAB, the output has the order: $$(\text{DC}, f_1, f_2, \ldots, f_{N/2-1}, f_\text{Nyq}, -f_{N/2-1}, -f_{N/2-2}, \ldots, -f_1)$$ For real ...
25 views

### Properly stagger an FFT? How to handle output data (Have highs weigh as much as lows?)

I'm new to audio processing so I'm mostly running into problems with not being able to properly google something. Sorry. Basically I want to create something like an equalizer (just visually without ...
174 views

### The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples

Given a signal $\left\{ x [ 0 ], x [ 1 ], ..., x [ N - 1 ] \right\}$ what would be the correct way to downsample it in the frequency domain (Sinc interpolation)?
83 views

### Difference between $\tt fft$ and $\tt dftmtx$ in MATLAB

I have the following MATLAB code: ...
64 views

153 views

### Multiplying the imaginary part of DFT with a linear ramp to get a derivative

I am trying to understand the statement in a relatively old publication from 1970s, when Fourier transforms found applications in chemical analysis. The author quotes the derivative theorem citing ...
27 views

### How to successfully resolve multiple pulsation frequencies in the FFT?

I am dealing with signals that in both extreme cases can have: a) Non-overlapping monochromatic pulsation-like events at different points within a time series. b) Overlapping pulsations at multiple ...
30 views

### Find Magnitude of a DFT signal using a Blackman window

Hi I've been given a signal made of a series of cosines. I have taken the DFT of the signal using a rectangular window (blue), hamming window (red) and a Blackman window (black). I have identified two ...
82 views

### Do symmetric discrete signals have zero phase?

I generated a Hanning window having an even symmetry: where for even-sampled case we either take "left" and "right" to include or exclude the center sample. I was surprised to ...
229 views

### Interpreting N in DFT as the Number of Points vs. Number of Intervals

The "N" is DFT is understood to be the number of data points in a given sequence or in other words the length of the sequence. We recently have had discussions here Indexing in DFT (from an ...
120 views

### Why Is the Total Time Equal to $N \cdot {T}_{s}$ and Not $\left( N - 1 \right) \cdot {T}_{s}$ In the Context of DFT?

In the definitions of the DFT DFT $$X(j)=\sum_{k=0}^{N-1} x(k) \exp \left(-i 2 \pi\left(\frac{j}{N}\right) k\right)$$ Let us say, if we have $10$ points, $N=10$, each sampled at $0.2$ seconds, why ...
44 views

### Indexing in DFT (from an old paper)

There is a nice paper on explaining DFT from the 1960s in IEEE A guided tour of the fast Fourier transform. The author uses the following definitions of DFT DFT  X(j)=\sum_{k=0}^{N-1} x(k) \exp \...
58 views

### How to remove the modulation before doing frequency offset estimation?

To use DFT/FFT (or maximum likelihood) method to estimate the frequency offset introduced by the channel, we need to remove the modulation on the received data samples in the front. If the unknown ...
2k views

### Applying DFT twice does not actually reverse an array. Instead, the first element stays in place while the rest of the array is reversed. Why?

I've heard a million times that applying DFT twice will result in a reversed array, but that is not what actually happens. Instead, the first element remains where it was, and the rest of the elements ...
49 views

### How to detect resonance with DFT

In the last paragraph of this article, the author gives an example of the DFT of a song and his window's resonant frequency. As he points out (and it is a bit intuitive), if he listens to this song, ...
96 views

### Why should the last point be excluded when performing a least-squares fit of a periodic discrete time signal?

I fitted the function: f(t)=A_o+A_1 cos(wt)+B_1 sin(wt) to the following periodic discrete signal: ...
67 views

### Linear convolution in the DFT domain

Let's say I have 2 sequences a and b in the time domain. Both are length N. A and B are the DFT of a and b. If I do a circular convolution of A and B in freq domain (A o B), then the IDFT of the ...
119 views

### Why DFT is used for approximating CTFT when you can approximate CTFT-integral itself?

I was using MATLAB for approximating FTs. Why DFT is used if we can approximate the transform-integration using summation.
53 views

### Discrete Fourier style transform with non-sinusoidal/arbitrary waveform components

A discrete Fourier transform will produce frequency samples sufficient to recreate the original time sampled signal from sinusoidal waveforms. That works great as long as the original signal is ...
While Analyzing the DFT Plot for a signal with N samples, say we find a peak in the magnitude of the DFT plot at index $k$, this implies that our signal has a high amount of similarity with an ...