# 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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### LED image phase projection

Say you have a goal image G with a phase called phase G. Can you physically construct and project phase G, or is phase not something physical? Like, can you set up an array of LEDs to project the ...
378 views

### Mathematically, why is there a tradeoff between main lobe width and sidelobe level when we apply a window?

This answer says that there is a tradeoff between SLL (sidelobe level) and BW (main lobe width). I am able to verify this and I understand that we cannot have our cake and eat it too, but why is there ...
1 vote
86 views

### IFFT return complex values in Matlab

I've been experimenting with the frequency sampling method for designing FIR filters. I created a low-pass filter that has a linear transition band. However, when I performed an IFFT on the frequency ...
1 vote
45 views

### Signal response amplitude depends on the time interval in simulation

I have already tried to look for an answer, but I do not find existing answers satisfactory. I am interested in the absolute value of the response function of a damped oscillator (or any time series). ...
44 views

### Getting the magnitude and phase of a single specific frequency from an audio signal

Assuming I only care to calculate the magnitude and phase of ONE single frequency from a signal, how can I get this information without calculating anything else? For example I want to come up with an ...
21 views

### Constant Q transform where you keep the window size constant (so Q is no longer constant)?

I've been working on implementing a constant Q transform to try and detect musical notes within an audio signal and I came across an issue. When trying to detect low frequencies the constant Q ...
2k views

### Does Zero Padding Distort the Spectrum of a Signal?

It's said to "sample the DTFT", revealing what "DFT fails to see". And I fail to see how this sampling isn't distortion. The "spectrum" aims to provide the sinusoidal ...
440 views

### Why does the frequency sampling method for FIR filter design operate in this manner?

I'm studying FIR filter design and it's time for the frequency sampling method, my teacher said that to use this method you need to follow the following steps: Sample the periodic frequency response ...
37 views

### Are integer multiples of a frequency in an FFT necessarily in phase?

I performed a FFT on a signal and the most prominent frequency at about 0.5 cycles/time only makes up about 6% of the total frequency distribution, which is pretty low for my purposes, so I was ...
112 views

### Unwindowed STFT of sine, closed form solution and insights (sliding FFT)

I seek to calculate, mathematically, the unwindowed Short-Time Fourier Transform of $$\cos(2\pi f t + \phi)$$ i.e. any arbitrary real-valued sine: any frequency, duration, phase shift, and number of ...
80 views

### Effect of sampling rate and duration on discrete parameters of sine (spectrum)?

The DFT of $$\cos(2\pi f t + \phi)$$ peaks at $k=\pm f$ if $t = \frac{1}{N}[0, 1, ..., N - 1]$ (for integer $f$, & within Nyquist). What about other $t$? What if we double the sampling rate or ...
188 views

### Finding Discrete Fourier Transform (DFT) for different DFT size

$N$ is an even integer, $x[n]$ is a finite length signal over the interval $n \in [0,N-1]$, and $X[k]$ is the $N$-point DFT of $x[n]$. Analytically find the DFT of sequence below in terms of $X[k]$. ...
1k views

### Why doesnt DFT Padding cause sinc like features

I'm new to the land of DSP so any incorrect terms please let me know. It seems padding the time domain signal can make the magnitude spectrum look 'nicer', the fact it doesn't gain any more useful ...
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### Is it possible to compute a 2D-FFT if the input size is not a power of 2? [duplicate]

Let us suppose to have an image with size $28\times28$, and that we want to apply a 2D-FFT without any padding operation. Does exist any algorithm which allows to perform the 2D-DFT calculation with ...
1 vote
74 views

### Expression for DFT of linear 2D ramp

One dimensional solution is in “Expression for discrete fourier transform of linear ramp“ I need two-dimensional for image processing. We have function f(x,y) = $a_1 \cdot x + a_2 \cdot y$, My ...
90 views

### fast spherical filter: interpolation

Here is the minimum working examples of fast spherical filter in c++ The reference paper is Fast Spherical Filter There is a bug in the implementation where the ...
1 vote
45 views

### Generating new random phases for DFT of 2d uniform distributed noise image changes image distribution

My goal is to produce a new random noise image from two already existing noise images. For that I take the absolute values of one image and the angles (phases) from another image in Fourier Space and ...
183 views

### Why are my frequency bins oscillating?

I am working on a personal project that maps bass notes to colors in real-time. However, I'm encountering some issues with oscillations in my frequency bins. I visualized my frequency bins to ...
119 views

### What is the difference between the DFS (Discrete Fourier Series) and DTFS (Discrete-Time Fourier Series)

I'm looking at two different books written by Oppenheim. In Discrete-Time Signal Processing (source 1) he defines the DFS to be: where, $W_N=e^{-j(2\pi/N)kn}$ , while in Signals and Systems (source 2)...
227 views

### Can time aliasing cause peaks?

For the following I use the terms “time domain signal” and “frequency domain signal” as a Fourier Transform pair. The question is for generalized cases of continuous-time signals that once sampled in ...
125 views

### The Discrete Fourier Transform (DFT) decomposes any signal into four orthogonal signal components

Let $F=\frac{1}{\sqrt{n}}(w^{kl})_{k,l=0}^{n-1}$ be the discrete Fourier matrix of size $n$ where $w=\exp^{-\frac{2\pi i}{n}}$. It is a well-known that $F_n^4 = I_n$ where $I_n$ represents the ...
1 vote
193 views

### Constraints on choosing the frequency axis when Fourier transforming non-uniformly sampled data?

Does anyone have a reference that specifically discusses choosing the frequency scale for a simple 1D data for non-uniformly sampled time-domain data when performing the discrete Fourier transform. In ...
2k views

### Understanding LPC for Formant Estimation

I went through the Matlab tutorial on Formant Estimation using LPC Coefficients. Though I vaguely understand the details, it's not entirely clear why we need to do this. From http://person2.sol.lu.se/...
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### Why are these excess frequency components in my FFT spectrum? [duplicate]

I am experimenting with digital signal processing and I took the FFT of a sinusoid in Matlab. I got the frequency components that I expected to be present but there are two excess spikes that mirror ...
1 vote
129 views

### What are the *undesirable* effects of windowing in Fourier space?

My goal is to split a periodic signal into two (or more) signals. The first signal would contain the low-frequency information, and the later signals, the higher-frequency information. These signals ...
108 views

### How are subcarrier symbols modulated into an analog OFDM signal?

I am currently researching about OFDM models (formulae) that show how the individual data symbols (eg., QAM symbols) are converted to OFDM symbols and how the OFDM symbols are turned into an analog ...
1 vote
176 views

### Is it feasible to implement analog-style spectrum analyzer and sliding DFT as visualizations in music players?

The real-time constant-Q transform are possible using sliding DFT (sDFT) because unlike FFT, sDFT can have arbitrary frequency scale and variable per-bin window size, and of course, the realtime CQT ...
1 vote