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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3answers
61 views

DFT coefficients meaning?

What "are" they? What's a sensible way to interpret the coefficients (and what isn't)? To pose specifics: DFT coefficients describe the frequencies present in a signal They describe the ...
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DC Value of DFT

I came across this question and I've been pretty confused if its a trick question or I'm just wrong. Having a signal x[n] with 6 samples, it's DFT has values (6,3+j,0,0,0,3-j), what is the DC ...
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Why does DFT have only $N$ components?

Why does the DFT have only $N$ components in it? I can see that after N components the frequency component is periodic and repeats with the same values but that does not seem to explain why we can ...
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Why does time-domain convolution correspond to frequency-domain multiplication? (visual)

I seek a visual explanation of this. I've already seen the maths, and can derive the proofs - they amount to nill for an intuitive understanding. Any amount of math is welcome, as long as serving to ...
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Is the DCT prone to spectral leakage like the DFT?

My understanding is that the DCT assumes the input to be an even periodic signal. This avoids the discontinuity that can occur in the periodic extension assumed by the DFT (see image). Does this lack ...
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Morlet wavelet: DFT vs Fourier Transform

I find what seem to be contradictions between the two. "Morlet" defined here, and its Fourier Transform (FT) below it. DFT's imaginary component zeroes with large ...
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5answers
312 views

DFT derivative property?

Does it have one? The continuous variant does, $f'(t) \rightarrow j \omega F(\omega)$ - but $jkX[k]$ definitely isn't it for DFT. To find it there must be a useful simplification of $\text{DFT}(x[n] - ...
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Why does sampling chirp at peak frequency yield correct frequency response?

Followup; setting Fs = bandWidth in accepted answer's code yields the "correct" frequency response of an LFM chirp: constant magnitude, parabolic phase. ...
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Does chirp have constant magnitude frequency response?

Pg. 223 claims so, yet my results via DFT differ: Is the textbook wrong? My attempted explanations: (code) DFT vs DTFT: "frequency response" is computed via latter. Still, DFT should ...
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1answer
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Applying fourier transform twice (DSP course)

I stumbled upon a question in a DSP course (coursera) which I don't understand, shown below is a screenshot of the question and answer. The part which I don't understand is circled. Why is it equal ...
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The impact on the frequency of adding zero samples and non zero samples

Can someone give me a brief explanation of what is going on in here? I struggle to understand the full differences between the impact on the frequency of added zero samples and adding samples which ...
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Fourier coefficients of images?

For a continuous function $f$, it is well-known that the decay of $f$'s Fourier coefficients $\hat f_n$ is related to the differentiability of $f$. Some examples: for a smooth periodic function $f$, ...
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Discrete Fourier Transform on images using OpenCV

I applied DFT on an edge image (attached both). I expected the output image to not have very low frequencies (~0).[Refer this link for more info] But the output I got consisted of low and high ...
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Why does dot product return zero at non-harmonic frequency

If I understand correctly, dot product between two sinusoids should return zero if they are orthogonal. Since dot product is at the heart of the DFT, we can only clearly compare the frequencies that ...
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Wasn't Wikipedia errata on DFT/Trigonometric interpolation polynomial

https://en.wikipedia.org/wiki/Discrete_Fourier_transform "Trigonometric interpolation polynomial" Section. Shouldn't the middle term in the second line be? $$ \cdots + X_{[(N-1)/2]} e^{i\ ( ...
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Does it make sense to express a given FT from 0 to 1 as a convolution?

I'm learning about Fourier transform, and was asked whether the following FT can be expressed as a convolution: $$X[k] = \sum\limits_{n=0}^{N=1} x[n]e^{-i\frac{2\pi}{N}kn}$$ There are two things I don'...
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How does a receiver compensate for signals with lower RSSI to achieve the same magnitudes in the frequency domain constellation?

Is the RSSI that is measured during a 802.11 preamble for instance used to scale the amplitudes of complex time signal samples acquired at the receiver so that it translates using DFT to the same ...
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2answers
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Why could window function help to get more accurate specific frequency amplitude?

In order to calculate amplitude of sinusoidal signal at a frequency around 60 Hz (but may be not 60 Hz), window function is adopted while using DFT. hk is the coefficient of window function and Kdc ...
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Amplitude after Fourier transform

How to obtain the correct amplitude after the numerical Fourier transform of a signal? Example: consider an exponential decaying wave $y(x)=e^{-x}\sin(100\pi x)$ with Fourier transform $y_f(x_f)$ ...
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What could cause fast Fourier transform to give complex conjugate of the intended result?

I have 2 real time series $x(t)$ and $y(t)$, after fft it should become $\tilde{X}(f)$ and $\tilde{Y}(f)$. Then I need to normalize $\tilde{X}(f)$ with $\tilde{Y}(f)$ : $\tilde{X}(f)/\tilde{Y}(f)=\...
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Finding PHASE between two sinusoids with FFT/DFT (ArduinoFFT w/ C)

I am having trouble finding a known phase between two data sets, lets call them data set 11 and data set 12. I am obtaining a sample size of 1024 samples, at a sampling rate of 500kHz with a total ...
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1answer
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Find signal power in a band by integrating the PSD in a frequency band (and zeroing the out-of-band DFT bins)

I know that directly zero DFT bins outside a frequency band has the side effect of introducing ringing, as this post says Why is it a bad idea to filter by zeroing out FFT bins?. But what about ...
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1answer
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Sparse Inverse Fourier Transforms

I'm looking to compute an IDFT but my input is very sparse: Example: IDFT length: 7,408,800 (complex floats) Sparsity: 96.61% to 99.99% I found this Sparse FFT website but it looks like the library ...
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Determine a sequence whose N point DFT is given without computing inverse

For example, I'm given a sequence x(n) = { 3, 5, 1, 4, -3, 5, -2, -2, 4 } whose 9 point DFT is X[k]. Without computing IDFT, i need to find the sequence y(n) whose 9 point DFT is given by $Y[k] = (-1)^...
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Why is my time domain interpolation via zero-padding in frequency domain wrong?

Since the process can be applied in either domain to increase the sampling rate in the other domain, I am trying to apply zero-padding in frequency space to recover a 'cleaner' interpolated signal in ...
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1answer
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FFT shows systematic deviations from analytical result

I am calculating the numerical Fourier transform of an exponential decay exp(-|t|) and compare it to the analytically calculated result, a Lorentzian. I find that the numerically calculated spectrum ...
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DFT exercise in the book Understanding digital signal processing 3 Ed

I am trying to solve exercises from the book Understanding digital signal processing 3 Ed - Richard Lyons. I will repeat the question as it is in the book: 3.3 We want to calculate an N-point DFT ...
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Get displacement from acceleration with DFT

I looked at the already existing topics: here, here or matlab code, finally here I tried to create my python code but it is not working : ...
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2answers
344 views

What is hidden in DFT below frequency resolution?

Setting: signal sampling rate 1000Hz, DFT 1s 1000 samples. This yields frequency resolution 1Hz. I know, this is the limit of meaningful frequency and when I want to read 0.5Hz then either sampling ...
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Phase Spectrum in Fourier Transform

Probably a simple question to answer. I have been trying to use the fft function in MATLAB and have been succesful to get the amplitude spectrum of a known signal. But when working out the phase ...
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1answer
46 views

What is the purpose of dividing an audio signal into segments and analysis each segment?

I read bunch of materials for extracting feature from audio signal and they all tell me to break signal into segments, why don't we analyze all the audio signal? I don't know what are the advantages ...
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How does DCT decorrelate images?

I've read in multiple places that DCT decorrelates Toeplitz matrices and images usually have Toeplitz structure. Can you explain with an example how DCT decorrelates a Toeplitz matrix? Example for DFT:...
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Frequencies of complex exponentials in Discrete Fourier Transform

What I understand is that using DFT, we are representing a given discrete signal using a basis of complex exponentials of different harmonic frequencies. If I am taking 16 point DFT of a signal ...
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1answer
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Mulitplication in Frequency Domain as a Similarity Measure of Audio Clips

I have an audio clip and I copy a 256-point part satarting at 10th second. Then I create a 256-point frame on the original clip. At every itreation, I calculate the DFT of the frame, multiply it with ...
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Welch's method, no windowing function

I'm trying to pick a method to increase the bin-width on several discrete Fourier transforms I'm incorporating into some scientific analysis code. I have several questions about how this could work ...
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Phase of signals in real and complex DFT

I have been reading chapter 8 - The Discrete Fourier Transform of the book The Scientist and Engineer's Guide to Digital Signal Processing and chapter 12 - Discrete Fourier transform of the book ...
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Question on N point DTFT - Fourier transform

I have been trying to use the logic that both X and Y should have same Z transform, but according to the definition, Y is not anti causal.
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1answer
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Radix-2 vs Radix-4 FFT

What are the differences between radix-2 FFT and radix-4 FFT, Are the only differences following two: In case of radix-2 $N$ is a number that is a power of 2 and in case of radix-4 $N$ is a number ...
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1answer
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confusion understanding FFT butterfly diagram?where are 12 , two input butterflies?

https://www.alwayslearn.com/DFT%20and%20FFT%20Tutorial/DFTandFFT_FFT_Butterfly_8_Input.html I was reading above link and then i came across a confusing sentence, i highlighted it in attached ...
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Continuous frequency vs discrete frequency? [closed]

I have understood idea of discrete time and continuous time but I am feeling difficult to comprehend this idea in regard to frequency. As for example the DFT output is discrete and the DTFT output ...
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1answer
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FFT question as it relates to Neural Networks / Supervised Learning Models

So I've been researching wavelet transforms and FFT. I want to feed wavelet transforms of a 1D signal in time into a neural net and train against a target variable at each time step. The idea being ...
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2answers
134 views

Duality Property for DFT

I was watching a youtube video for the duality property for continuous time Fourier transforms, which shows that if Fourier transform of $x(t)$ is $X(\omega)$ then Fourier transform of $X(t)$ is $2\pi ...
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1answer
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FFT Multiple Response for time T

I want to do a fft spectral decomposition of a dataset, but the data has more than one sample for every time t. The data goes from the discrete years 1998 to 2010, each year has 20-30 points. Every ...
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How to interpret the window size and FFT size while performing FFT? [closed]

I have a discrete signal of length 98,000 samples and I am supposed to a FFT of the discrete signal with certain window size and FFT size. Can someone help me explain what is meant by the window and ...
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1answer
89 views

DFT symmetry vs DFT duality in Richard Lyons' “Understanding DSP”

I am reading Richard lyons, understanding dsp, chap 3. Article 3.2 is about property of dft symmetry but any where in this chapter, i am unable to find discussion about dft duality property I want ...
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1answer
59 views

Response of a system using DFT

Let's say that we have two sequences, input sequence $x(n) = [0121]$ and impulse response of a given system $h(n) = [0, 1, -1, 1]$. I need to find response of this system to given input sequence. ...
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Inverse DCT via DFT formula deduction

Context I am reading this book Discrete Cosine Transform [...]. K.R. Rao and P.YIP. 1990. Given That From Equation (2.4.11.a) $$ X^{C(2)}(m) = \left ( \frac{2}{...
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Why can we have non-integer frequency bins in FFT?

I am studying DFT/FFT and I'm very confused about one thing. I read online that the frequencies we can sample with DFT must be integer (Why does the frequency in the DFT have to be an integer?). Later ...
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1answer
53 views

Prove the following DFT for a periodic sinc sequence or ideal lowpass filter

I need to prove the following DFT for a periodic 𝑠𝑖𝑛𝑐 sequence or ideal lowpass filter: $\sqrt{\frac{p}{m}}\frac{sinc(\frac{\pi np}{m})}{sinc(\frac{\pi p}{m})} \stackrel{DFT}{\longleftrightarrow} ...
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Confusion regarding DFT calculation?

I am studying Richard lyon chap3 , article "Understanding the DFT equation " But i am bit confused how x(n) is calculated specially x(0) and x(1) because apparently x(n) is calculated by plugging ...

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