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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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How to Know which signal is likely sampled from spectrogarm

I know that x(t) =( 2 pi f t ) And the sampling rate is 1000 and y axis is normalized How can i use these information to know each signal in the spectrogram graph
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how can i find the value of inverse dft

i have dt signal x[n]={6.29,8.11,-7.46,8.26,2.64,-8.04,-4.43,0.93,-9.29} give the function value of 1) sum of k=0 to 9 X[k] 2) sum X[k]exp^(-j 3 pi k/5) of from k=0 to 9 ) sum |X[k]| of from k=...
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Is there a name for the result of summing the bins of an FFT?

Is there a name for the result of summing the bins of a DFT? I don't mean to sum the squares of the bins, but to simply add the magnitude of the frequency bins together to get a single result. Is ...
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21 views

Finding n Amplitudes by DFT, what is correct normalization

Please forgive me if this has already been asked. Let us assume an example with $x(t) = \sum_{i=1}^N A_i \sin(2\pi f_i t) $ under a given sampling frequency $f_s$, frequencies $\omega_i$ and ...
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In case of Complex DFT spectrum, why the x axis range from N/2 to N point mean a negative frequency?

When we transform a complex signal into frequency signal by using a complex DFT, The range from N/2 to N point on the X axis of the spectrum mean a negative frequency... But i cant understand why ...
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54 views

Proving that the IDTFT is the inverse of the DTFT?

The DTFT is given by: $$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty}x[n]e^{-j\omega n}$$ The IDTFT is given by: $$x[n]=\frac{1}{2\pi}\int_{0}^{2\pi}X(e^{j\omega})e^{j\omega n}d\omega$$ I have been ...
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33 views

DFT of a series of RC exponentials

Context: I'm trying use matlab to apply a single-pole filter to a time-domain ramp waveform that is generated by a sequence of time-shifted "RC steps" that are added together. The time domain voltage ...
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24 views

Frequency Resolution Problem

Im trying to tackle the following problem while still not having a firm idea on what "frequency resolution" means : Suppose we sample a continuous time signal with sampling period Ts = 1/2000, and ...
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24 views

DFT sample point k < N has negative frequency

(From: Schaum's DSP outline, 2nd edition, page 254, problem 6.35) A signal $x_a(t)$ that is bandlimited to 10 kHz is sampled with a sampling frequency of $f_s = 20$ kHz. The DFT of N=1000 samples of ...
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70 views

Why is this recursive DFT algorithm not equivalent to this iterative method?

Edit 1/30 - Taking @Fat32's edits into account, it seems like there is still an issue with the scale of the frequency axis. While version 2 correctly identifies the response at 1 HZ, version 1 seems ...
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34 views

DFT zero-padding of signals starting before n=0

If a signal starts before n=0, what part of the signal should be used to compute DFT after zero-padding? For example, x(n) = {1, 2, 3, 4, 5}, where x(-2) = 1 and x(0) = 3. If this signal is zero-...
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41 views

time downsampling vs. frequency downsampling [closed]

$x[n]_M$ is a finite length sequence of length M. if: $$ y = x[nN]_M \tag{1} $$ is called downsampling in the time-domain. then what do you call the process of converting going from a M-point ...
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31 views

DFT product of sinusoids

(From Shaums DSP outline, 2nd edition, page 248, problem 6.21) Book says, evaluate the Sum: $$ S = \sum^{N-1}_{n=0} \Bigg( x_1[n] \ x^{*}_2[n] \Bigg) $$ when: $$ \begin{aligned} x_1[n] = \cos\left(...
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Estimators for improved spectral subtraction of noise

Real zero-mean Gaussian white noise, independent of a clean signal $x$ and of known variance is added to $x$ producing a noisy signal $y.$ Discrete Fourier transform (DFT) $Y$ of the noisy signal is ...
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44 views

downsampling DFT with aliasing

(Schuam's DSP Outline, 2nd edition, problem 6.11(c), page 241). Is there a DFT down-sampling property that looks something like this: Given $x[\![n]\!]_M$ we want to downsample from M to N to obtain ...
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36 views

DFT conjugate of $X^*[k]$, how to prove its formula in terms of $x^*[n]$?

Trying to prove that: $$ X^{*}[k] = \sum^{N-1}_{n=0} x^{*}\left((N-n)\right)_N\ W_N^{nk} $$ Where: $$((x))_N \text{ = x modulus N}$$ $$W_{N}^{nk} = e^{-j\ 2\pi / N}$$ So I start out with ...
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1answer
54 views

Why do DFT frequency buckets need to be divided by sample period?

edit: This is my first post in this community. I'm sure that my downvoter had a good reason to do so, but could someone please comment and tell me how I can better format my question? -- I have a ...
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24 views

Calculating phase of DFT sinewave?

I have been attempting to make a basic, slow, DFT in Matlab and have noticed peculiar behavior that I don't understand. I have been trying to plot the phase of a 100Hz sinewave captured at 250kHz ...
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22 views

Voice classification

I'm working to prepare research article for my project. While preparing for it, I've gone through the topics like Gaussian mixture model and Fourier transform for voice classification problems. I've ...
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1answer
36 views

What's the difference between “Discrete Fourier Series” and “Discrete Fourier Transform”? [duplicate]

I look at the equations for DFS (Discrete Fourier Series) and DFT (Discrete Fourier transform) and the only difference I notice is that one has a squiggle above the letter and the other doesn't. The ...
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30 views

Amplitude and Phase spectrum of a signal [closed]

Please help me to solve this question.
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18 views

Is it customary to use the period as coefficient when sampling the impulse response?

I have an analog, continuous impulse response $$h_a(t)=u(t)\cdot\sum_{n=1}^4A_ne^{s_nt}$$, and by sampling it with the usual method I get $$h[n]=\Delta th_a(n\Delta t).$$ Now, that $\Delta t$ is a bit ...
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Performing inverse DFT after taking conjugate of the result of DFT

The following is a question I got in my school assignment. Pick an image and follow the operations Multiply image by (−1)x+y. Compute the DFT. Take the complex conjugate of the ...
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1answer
16 views

performing FFT on Voltage measurments to get Z(f)

I have a csv file containing measurments a system's step response when the step is current and the output is the voltage. output looks something like this and the it's evenly sampled provided I know ...
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1answer
41 views

Performing DFT twice on an image. Why am I getting an inverted image? [duplicate]

I was asked to perform DFT on an image twice as a part of my school assignment. Why am I getting a blurry inverted image when I perform DFT on an image twice? Sorry, I'm new to image processing and ...
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1answer
42 views

Autocorrelation sequence in terms of Fourier transform of the underlying signal

Let $x(n)$ be a sequence of length $N$, which is zero outside the interval $(0,N-1)$. Let $X(k), k=0,1,\cdots,N-1$ be the FFT coefficients of $x(n)$, that is, $X(k)=\sum_{n=0}^{N-1}x(n) \exp\left( -\...
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1answer
32 views

Compute the two-dimensional DFT

Compute the two-dimensional DFT [4x4] for the following 4x4 image $ \begin{matrix} 0.5 & 0.5 & 0.5 & 0.5 \\ 0.5 & 0.5 & 0.5 & 0.5\\ 0.5 & 0.5 & 0.5 & 0.5\\ ...
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1answer
48 views

Fourier like spectral analysis with uneven intervals and redesigned DFT matrix

I intended to use a discrete Fourier transform (DFT) on a time series sampled at uneven intervals. What I did was to calculate a DFT matrix where the elements are the values at the uneven locations ...
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32 views

Lowpass-filter necessary before DFT?

I'm trying to distinguish eletrical engines by the magnetic field they create. I have no idea whether this is a smart idea, it's possible at all, whatsoever. However it brought me to a basic question ...
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63 views

Applying DFT to OFDM signals above Nyquist rate

Consider an OFDM signal which has $N=8$ subcarriers and is band-limited to $[-B/2,B/2]$, $\sum_k x_k e^{j2\pi kf_0t}$ where $f_0=\frac{B}{N}$. For this case the Nyquist rate is $2\times B/2=B$, i.e., ...
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How to increase resolution of FFT?

I have an input signal in the ( 0 - 20 kHz ) frequency range . When i sample this signal maximum sampling frequency is around 40 kHz . When i calculate the FFT using 1024 points i got resolution of ...
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DFT: Zeroing frequency bins resulting in strange values at the end of my signal [duplicate]

I have an issue with my DFT. I think that I got how to fix it, but I lack the intuition on why there was a problem, and why my solution fixes it. I have to apply DFT to a noisy signal. The second ...
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1answer
39 views

Are there frequency detection methods that are subject to less latency than the Goertzel algorithm?

I am trying to detect oscillations in a small range around 1.5Hz as early as possible. I am currently using the Goertzel algorithm with bins 1.0Hz, 1.2Hz,..., 1.8Hz, and 2.0Hz; with block size N = 500 ...
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2answers
152 views

Symmetry and periodicity of frequency-shifted discrete Fourier transform

The unitary discrete Fourier transform (DFT) of a sequence of numbers $x_n$ to $X_k,$ with integer $0 \le n < N$ and $0 \le k < N,$ can be defined as: $$X_k = \frac{1}{\sqrt{N}} \sum_{n=0}^{N-1}...
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1answer
56 views

How to make DFT in matlab without FFT [duplicate]

Does anyone have a algorithm for DFT without FFT function in matlab? and second question is how can I make zero padding in this algorithm?
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2answers
152 views

What is the DFT of DFT of discrete signal [duplicate]

What is the discrete fourier transform of the discrete fourier transform of any discrete time signal. Is result same signal? How?
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2answers
89 views

Calculating N-point DFT of a signal based on another signal's DFT

Recently I have asked this answer. Now I would like to know a little bit more about expressing N-point DFT's of signals in terms of one another. Having N-point DFT X(k) of a certain signal x(n), ...
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2answers
151 views

Result of conjugate symmetry property of DFT

I know one of the properties of DFT for real-valued time series is conjugate symmetry. But what does it imply? In the textbook it says that for a DFT of the length M, this makes M/2-1 spectral ...
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1answer
21 views

Shifting and phase difference

Assume we have a series v[k] of length M=16. It's shifted to the right in a circular manner by k0=2 samples. Which phase difference between the DFT spectrum of the original signal and that of the ...
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2answers
41 views

Fourier-Analysis of Stationary Random Signals

Let's say we have discrete-time stationary random signals with Gaussian PDF of mean value 0 and variance 1, whose individual signal values are uncorrelated. For such a signal, how can we determine ...
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1answer
68 views

Limitation on the shift theorem of DFT due to frequency resolution?

The shift theorem states that shifting a sine wave in time domain by t is equivalent to multiplying the corresponding DFT coefficient of the signal by a complex exponential e^(-jwt). Described by the ...
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0answers
32 views

How to sample a transfer function (angular spectrum) in the frequency domain?

I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given ...
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1answer
140 views

Expressing 2N point DFT in terms of N point DFT

I have a problem with expressing odd samples of X2 in terms of X1. I understand that the resulting DFT will be more precise in terms of expressing the exact spectrum of signal x[n], due to more ...
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1answer
38 views

IDFT of $Y[k]=2X[k]$ for even $k$

If the 16-point DFTs of $x[n]$ and $y[n]$ are given as $Y[k]=\begin{cases}2X[k], & k=0,2,4,...,14 \\ 0, & k=1,3,5,...,15\end{cases}$, where $x[n],y[n]=0, \forall n<0, n>15$, how can I ...
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1answer
28 views

Inverse DFT in terms of original signals for product of two DFTs

Given $x[n]$ and $h[n]$ that are zero for $n<0$ and $n>15$, their linear convolution being $y[n]=x[n]*h[n]$ and their discrete time Fourier transforms are $X(e^{j\omega})$ and $H(e^{j\omega})$, ...
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52 views

IDFT of upsampling in frequency domain

Suppose I have a discrete time signal $x[n]$ of length 32 and I take it's 32 point DFT $X[k]$. Then I upsample this by a factor of 2 to get $Y[k]=X[k/2]$ and then take 64 point IDFT to get $y[n]$. ...
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1answer
51 views

Quite confused with Fourier Analysis results

So I'm meant to show how the DFT can find the frequencies, and respective amplitudes, associated to some data. And I have this data set from the curve $$ f(t) = 1 + 2\cos(2\pi t) + 4\cos(4\pi t) $$ ...
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1answer
50 views

Evaluate DFT-downsampler-upsampler-IDFT block diagram

I am trying to solve the above question. I am not sure how to proceed. I know the formula for 64 point DFT of $x[n]$. $X[k]=\sum_{n=0}^{63} x[n] e^{-j2\pi nk/64}$ But how can I find $R[k]$ and $Y[k]...
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1answer
69 views

Is possible reach the DFT if I have the DTFT?

My teacher told me that DFT is DTFT sampled, i.e.: $$X[k] = X(e^{j \omega})\Bigg|_{\omega = \frac{2\pi k}{N}}$$ But, if I have the sine $$ x[n] = \sin(\omega_0 n) $$ the DTFT is: $$X(e^{j \...
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1answer
120 views

Calculating the first derivative of an image using DFT

I need to calculate the first derivative of a greyscale image (a 2D array) using a DFT function I built (which works). Unfortunately, the results don't seem to be correct. In the fourier domain, the ...