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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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Generate a Time Series from Power Spectral Density Python

I am trying to generate a time series from a defined PSD function, however i tried to do this in python , with the following steps: Define the Power Spectral Density Define the time parameters Define ...
zouatine mohamed's user avatar
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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 ...
arecibo_april's user avatar
3 votes
1 answer
382 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 ...
RajaKrishnappa's user avatar
1 vote
2 answers
149 views

Why is reconstruction of window function from its DFT difficult/noisy when the sidelobes of DFT are higher?

I am able to use the DFT and IDFT formulae to get the DFT of a window and reconstruct it but only if the sidelobes is very low (or the main lobe is narrow) as shown in the image below: Why does this ...
RajaKrishnappa's user avatar
1 vote
2 answers
89 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 ...
minghierid's user avatar
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2 answers
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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 ...
tjwrona's user avatar
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1 answer
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 ...
tjwrona's user avatar
  • 327
2 votes
5 answers
449 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 ...
minghierid's user avatar
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1 answer
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 ...
Data2Dollars's user avatar
1 vote
1 answer
47 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). ...
Andris Erglis's user avatar
2 votes
2 answers
194 views

Differences in PSD for windowed vs non-windowed spectra

For a non-windowed spectrum, this article gives this equation for the power spectrum $$\text{PS}(k)=\frac{1}{N^2}|X(k)|^2$$ and this for the power spectrum density $$\text{PSD}(k)=\frac{N}{f_s}\text{...
RF Shenanigans's user avatar
10 votes
3 answers
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 ...
George kirby's user avatar
0 votes
1 answer
84 views

What's Nyquist frequency in DFT?

I'm currently studying digital signal processing at university but I can't figure out what the Nyquist frequency means in the DFT coefficients, I know what the Nyquist frequency is in the sampling ...
minghierid's user avatar
2 votes
1 answer
107 views

How signal generation affect its spectrum

Im trying to get dft of hanning window. Im trying different methods of generating the same signal, yet im resulting with such different graph of signal spectrum. ...
user8464651's user avatar
0 votes
1 answer
54 views

Non-uniform FFT

I'm looking for a form of a FFT where the samples in the frequency-domain don't represent uniform spaced frequencies. What I would like to get is a frequency-domain with samples that are unevenly ...
wimalopaan's user avatar
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0 answers
42 views

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 ...
Giorgio Bianchi's user avatar
4 votes
1 answer
53 views

Show that the similarity between a signal at an analysis frequency with a phase offset with a reference signal is $\frac{N}{2}\text{cos}(\phi)$

I'm reading Brian McFee's excellent book Digital Signals Theory. He presents the DFT as a measure of similarity $S$ between a digital signal $x[n]$ with $N$ samples and a set of reference signals $y_m[...
NickleDave's user avatar
1 vote
2 answers
96 views

DFT Matrix Oversampled In Frequency?

Edit 2: I am trying to replicate results from this paper Compressed Sensing with Coherent and Redundant Dictionaries. On page 3 the "oversampled DFT" is mentioned as an example of an "...
coult099's user avatar
1 vote
0 answers
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 ...
Jaksl's user avatar
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2 votes
2 answers
124 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)...
eball's user avatar
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4 votes
2 answers
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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 ...
Alex Larson's user avatar
2 votes
0 answers
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 ...
ABB's user avatar
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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 ...
Michael's user avatar
1 vote
1 answer
195 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 ...
AChem's user avatar
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1 vote
2 answers
79 views

do closer peaks Leak more to each other (spectral leakage in FFT)

I am familiar with the spectral leakage problem in FFT due to a rectangle window for a sin signal giving two peaks that leak to each other. My question is will the leakage to the frequency bins near ...
babzzz's user avatar
  • 11
0 votes
1 answer
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 ...
jomegaA's user avatar
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1 vote
1 answer
46 views

Trying to understand significant loss caused by OpenCV's inverse DFT

I'm quite a novice on computing Discrete Fourier Transforms with OpenCV, and I've been attempting to compute the DFT, and computing the inverse of the DFT using the latter as the input. Judging from ...
edition's user avatar
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0 votes
2 answers
98 views

How to show that these two factors are related to frequency interpolation and extrapolation respectively

Consider two sequences $x[n]$ and $y[n]$ being simultaneously sampled from a real-world signal. Let $x[n]$ be a sequence of length $N$ sampled for duration of $T_x$ at rate $f_x$ $n = 0, ..., N-1$ ...
auckydocky's user avatar
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1 answer
138 views

What is wrong with this sinc interpolation? (Zero padding in frequency domain)

I'm trying to pad $N=16$ zeros to the DFT of a $16$ point sinewave, but something is wrong either with my code or with my method. The method is this : I create a new $32$ point DFT where $F'(0),...,F'(...
In the blind's user avatar
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1 answer
93 views

Does the length of DFT points (duration of a signal) affect the "amplitude" of the power spectral density?

For example, performing a DFT on a 10-second-long and 20-second-long signal with the same sampling frequencies will change the "amplitude" of the power spectral density (PSD) at each ...
Tom's user avatar
  • 3
1 vote
1 answer
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 ...
user572780's user avatar
6 votes
1 answer
1k views

Bandwidth of an entire song

My question has to do with the difference between the frequencies of a single note, and the frequencies of an entire song. If I have a 5 second signal of the form: $x(t)=\sin(8\pi t)$, here is the ...
Levi's user avatar
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1 vote
1 answer
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How To Calculate Length Of Sequences And A Suitable N?

I have been struggling to understand how to calculate the length of a sequence and also the minimal N to choose in order to avoid aliasing. Most sources tell me to take the (last non-zero value - ...
Sugi's user avatar
  • 11
2 votes
1 answer
153 views

Correcting noise floor of DFT sampled signal

As mentioned in the slide below (full slides located here, starting at PDF page 29), the apparent noise floor on a DFT plot depends on the number of sample points $N$ used to calculate the DFT. The ...
Halleff's user avatar
  • 347
1 vote
1 answer
46 views

Summation interchange in DFT/FFT

Let $x(n)$ be a sequence of length $N = LM, n = 0,\dots,N-1$.$N$ and $M$ are integers. The Discrete Fourier Transform (DFT) of $x(n)$ is given by $X(k) = \sum_{n = 0}^{N-1}x(n)W^{nk}_N$ where $W_N = e^...
Vinod's user avatar
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2 votes
2 answers
477 views

Question about zero padding example in Lyons book on Understanding DSP

I have been reading "Understanding Digital Signal Processing" by Richard Lyons and I find the example in Section 3.11 on zero-padding a little confusing. Incidentally IMHO this is the best ...
gschro's user avatar
  • 103
2 votes
2 answers
100 views

Signal power depending on FFT bin size

I have read the following quote from a different post: If the noise is white (spread evenly across frequency), then the power will be distributed equally to each bin, and as we increase the number of ...
Processor48's user avatar
0 votes
1 answer
45 views

How to interpret this DFT of a sequence which is symmetric

The input sequence is spherical harmonic function of certain degree ...
jomegaA's user avatar
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0 votes
1 answer
23 views

Discrete Frequency representation for central frequency/ discretize up-converted signal in time and frequency

I want to analyze a signal after up-conversion in discrete time and frequency, for example: Let's assume a continuous up-converted signal is: $$e^{j2\pi ft} \cdot e^{j2\pi f_c t} = e^{j 2 \pi (f+fc) t}...
user70521's user avatar
2 votes
1 answer
111 views

Reconstructing the original signal from its DFT

Hi I am a newbie to signal processing and I am trying to better understand how inverse DFT works under the hood. Consider this signal and its DFT: (Source) For the sake of this post, let's assume ...
John Davies's user avatar
6 votes
2 answers
180 views

Discrete Fourier Transform of the Gaussian

Cross-posted from here I encountered the following question in a Digital Image Processing examination: Find the 2D DFT of $\frac{1}{2 \pi \sigma^2} e^{-\frac{(x - x_0)^2 + (y - y_0)^2}{2 \sigma^2}}$ ...
kaddy's user avatar
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0 answers
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Driving bandpass DSM with tone close to full-scale - stability issue?

I am experimenting with Dr. Schreier's DSM toolbox for MATLAB. I stumbled over a strange phenomenon when having a look at a bandpass DSM in demo-script 2. If I increased the amplitude of the test-tone ...
MisterFilter's user avatar
1 vote
0 answers
25 views

please help me solve the question which proving X[N-k] is the complex conjugate of X[k] [closed]

Show for the DFT that if all x[n] are real, then X[N - k] is the complex conjugate of X[k] for k > 0. (i.e. if X[k] is a + bi, then X[N - k] is a - bi)
Reece's user avatar
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0 votes
0 answers
18 views

How to derivate the DFT of the time-domain samples?

I am currently reading a paper titled 'Channel Estimation and Data Detection for Insufficient Cyclic Prefix MIMO-OFDM' published in IEEE Transactions on Vehicular Technology. As you can see below, the ...
David's user avatar
  • 1
2 votes
1 answer
190 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 $X[k]$. ...
nexxterp's user avatar
1 vote
0 answers
65 views

Is `fft` always the best choice?

I hope this is the right place to ask this question since it is partially a note which might help others. Until recently, I always used the fft-algorithm ...
TheIdealis's user avatar
1 vote
1 answer
158 views

What's the distribution of the DFT of a real-valued, zero-mean, normally distributed random vector?

Suppose $X$ is a real-valued N-dimensional Gaussian vector, $X \sim \mathcal{N}(\mathbf{0}, C_X)$. The discrete Fourier transform can be obtained by left-multiplying with the unitary DFT matrix, i.e. $...
DangerousTim's user avatar
1 vote
0 answers
81 views

Insight behind DCT-III (Type 3)

Following the sketch from Wikipedia 1, I am able to carry out DCT-II with DFT by manipulating the input signal: ...
diegor's user avatar
  • 181
5 votes
2 answers
475 views

FFT: Sinewave frequency displacement when zero-padding

I am creating a signal consisting of a single-cycle sine wave in Python. This signal has 32 samples. I am using a sampling rate Fs of 48 kHz so the signal's frequency is 1500 Hz. The signal looks like ...
Dani S.'s user avatar
  • 53
0 votes
1 answer
84 views

Why dft sine plot is so strange

Why does my dft plot of $\sin(x)$ look so strange? It goes to negative and then inverts closer to the edge. ...
Alexander's user avatar

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