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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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DFT Question, Im stuck [on hold]

Im giving the function of $x(t)=\sin(\omega_0t)\text{rect}\big(\tfrac tT\big)$. The sample rate is $f_\text{s} = \tfrac{1}{T_\text{s}}$. I need to make DFT to this. I said: $$x[n]=x(nT_\text{s})=\...
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16 views

What are the best algorithms used for sound denoising in dsp

I thought of doing sound denoising depending on processing using wavelets, however my professor strongly stated that wavelets are not suitable for harmonics, and sounds as far as I know is mostly ...
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122 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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20 views

How to calculate accurate frequency components with minimal spectral leakage?

I need to find an accurate frequency response of a signal. As an example, I have taken 2 signals, a 10 Hz signal and a 10.1 Hz signal with a sampling frequency of 1000 Hz and a length of 1000 samples....
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55 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
41 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
18 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
38 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
56 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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20 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
35 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
34 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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1answer
22 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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21 views

Variation or alternative to DFT that does not assume periodic signal

I am considering a pretty standard case of a signal: Finite duration, scalar real valued with equi-distant samples. The signal has a dominant single frequency, and corrupted with roughly gaussian ...
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1answer
50 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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48 views

Discrete Fourier Transform: Can't get the correct amplitude in frequency domain

I've gone through this link. I've generated a signal using two sine waves, one with an amplitude of 1000 and with a frequency of ...
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1answer
49 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
66 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
110 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 ...
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1answer
55 views

Ambiguity in the IFFT process in OFDM

I am still trying to iron out some ambiguities in my understanding of the IFFT component of OFDM modulation schemes. So here we have a QAM symbol $s_0$ being multiplied with the subcarrier for that ...
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1answer
55 views

What Is the Point of Doing the Zero Padding? [duplicate]

What are the advantages and disadvantages of doing Zero-padding, in particular the case of speech signals?
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1answer
27 views

DFT of sum of sinusoids with random zeroed samples

I have a noisy signal consists of sum of sinusoids, I had a situation where some of the time domain samples are zeroed randomly. The following figure shows the DFT before and after zeroing, the number ...
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26 views

Unexpected behaviour when using a Hamming window during FFT

I'm trying to get a smooth signal in the frequency domain of a pressure signal I've computed using a Hamming window. This is the code I'm using: ...
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1answer
31 views

Advantage of using DFT and IDFT hardware for modulation

I am doing a course in communications and while discussing multicaruer modulation to break down a signal into smaller bandwidths (for BW to be less than coherence bandwidth), there was mention of ...
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1answer
76 views

What determines the accuracy of the phase result in a DFT bin?

What are the factors that affect the accuracy and precision for the phase that is given by the DFT? Just thinking medium-hard about this, it occurs to me that it must have something to do with the ...
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1answer
30 views

problem finding 16 point DFT using two 8 point FFT (Divide and combine algorithm) MATLAB [closed]

Write MATLAB code that determines and plot the N-point Discrete Fourier Transform of x[n] defined by the following equations: x[n]=0.5*pi*n n=0:16 Compute and plot 16-point DFT using two 8-...
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2answers
85 views

Plot the spectrum and n-point DFT

$x_a(t) = \cos(2\pi f_a t)$ was sampled with sampling period $T_s$. Plot the { spectrum | $N$-point DFT } of $x[n]$ ($f_a$, $T_s$ or $f_s$ given, $N$ given - whole number of periods or not). Anyone ...
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1answer
41 views

Calculate a DFT of a simple finite signal {+1, −1, +1, . . .})

Hey i was wondering whether approach presented in this video (6:10) is a good approach to solve this task. Cause it seems kinda tricky and i was wondering whether it can be done faster.
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2answers
105 views

Choosing sampling frequency and base interval to eliminate leakage

I'm studying for an exam and have some trouble with an exercise. So I have a continuous-time signal that is $$s(t)=\sin(2\pi f_{s1} t) + \sin(2\pi f_{s2}t)$$ with $f_{s1} = 1.4\text{ kHz}$ and $f_{s2}...
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2answers
67 views

How to do DFT of this signal

I am trying to get $X[k]$ when $x[n]$ is equal to $$x[n] = \cos\left(\tfrac{\pi}{4}n-\tfrac{\pi}{4}\right)$$ I'm using this equation: $$X[k] = \sum_{n=0}^{N-1}x[n]e^{-j \frac{2 \pi}{N}kn}$$ but ...
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1answer
22 views

DFT as an Orthogonal Basis Change

In one of the homeworks that I am dealing with for Linear Systems course, I have encountered with such a statement: Consider $\mathbb{C}^N$ the vector space of N dimensional complex vectors. We can ...
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27 views

“Image Processing” [closed]

I'm an Italian student. I'm studying Gnu Radio and I would like to upload a photo, can I upload it with "file image source" or other blocks? I need to make FFT of an a image. -> image 2D Thank you ...
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1answer
72 views

Basic confusion about the DFT and convolution

I am learning DSP (with Digital Images) and I have some elementary confusion about the convolution between two discrete periodic signals. Specifically, I have learnt that when filtering an image, we ...
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1answer
45 views

Relationship between the IDFT of a sampled DTFT and its discrete-time domain signal

Suppose we are given an input signal s[m,n] with DTFT $S(\omega_1, \omega_2)$. We sample it at $\omega_1 = \frac{2 \pi k}{256}$ and $\omega_2 = \frac{2 \pi l}{256}$ to get a 256 point DFT S[k,l]. ...
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71 views

Why is my DFT/FFT always 90° out of phase?

I'm doing an FFT using Python and Numpy on one machine, and C# on another. I'm using some dummy data that mimics how I'll eventually be gathering data from sensors in the C#/UWP application. The two ...
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25 views

Obtain Original Signal Values From DFT

Hello, Trying to solve a Discrete Fourier Transform problem in Excel 2016. I have run the DFT and obtained the Amplitude and Phase Angle values as shown in the attached screenshot. Wondering how I go ...
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1answer
71 views

Why a DFT of two sinusoids is very noisy even with frequency sampling 5 times higher?

I've set up this case to try to understand DFT implementing a real case in Excel Frame Size $\;\color{blue}{(T = 5 \; s})$ Time Sampling $\;\color{blue}{(T_S = 0.1 \; s})$ Block Size $\;\color{blue}{(...
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1answer
66 views

If my sampling rate is not high enough to capture all frequencies, can I accurately capture low frequencies?

Let us say that my sampling rate is 1000 Hz. This enables me to accurately capture every frequency in the 0-500 Hz range according to the Sampling Theorem using a DFT. However, there are higher ...
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1answer
49 views

Comparison of Linear Convolution and N point DFT

I am studying Discrete Fourier Transform currently and I have a doubt in that. Consider two sequences {1,2,3,4} and {0,1,0,0}. When I convolve them linearly, I get this {0,1,2,3,4,0,0}. However, if I ...
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3answers
70 views

Maximum Magnitude Deviation between DFT and DTFT

Let $x[n]$ be a finite-length discrete-time signal with length $N$. The continuous DTFT $X(\omega)$ is then $$ X(\omega) = \sum_{n = 0}^{N-1} x[n] e^{-j \omega n}. $$ The length-$N$ DFT of $x[n]$ is $...
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47 views

Create a frequency spectrum from a sequence of event times

I have a sequence of event times with non-uniform intervals between events and I'd like to get a frequency spectrum from these data alone. I imagine I could create a waveform that peaks at these times ...
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1answer
63 views

zero padding shifting signal peak?

I am trying to find the fundamental frequency of a low-frequency signal. I need an estimate that is precise to .01 Hz based on only a few cycles, so I'm trying to code up a fft in Python. The signal ...
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2answers
67 views

Relating phase difference in a signal with its frequency

I have a 134 point complex signal. Using MATLAB, I have observed that the phase difference between any two adjacent samples of this signal is 2 radians i.e. the phase increases linearly from 0 to 268 ...
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101 views

Acceleration time series to velocity conversion using DFTs

I have 1000 Hz time series data for acceleration (512 data points), which I want to convert to velocity. I am trying to use the omega arithmetic method to achieve this. Following are the steps I am ...
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2answers
153 views

FFT vs DFT Run Time Comparison (Complexity Analysis) in MATLAB

So we were given an assignment to plot the time taken by the FFT algorithm by MATLAB and a DFT algorithm written by me in MATLAB.G The expected output should have been the DFT algorithm following the ...
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2answers
284 views

How to get around the circular shift property of Discrete Fourier Transform?

I understand that when we introduce a linear time shift using DFT on a finite sequence, the algorithm assumes that the signal repeats itself outside of the given range. Here is an example explaining ...
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1answer
67 views

What's wrong with my Goertzel algorithm implementation?

I've implemented Goertzel algorithm, now very simply in Python. But I cannot obtain the correct answer it's supposed to produce for a single DTF frequency. here is my code in Python: ...
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1answer
240 views

Computation of the Inverse DCT (IDCT) Using DCT Or IFFT

Is there a way to compute the inverse discrete cosine transform (type-2) by leveraging either a DCT, FFT, or IFFT algorithm? I have seen ways to compute the DCT using FFTs, and I've seen ways to ...
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2answers
76 views

Goertzel algorithm produces incorrect phase

I've implemented Goertzel algorithm according to the Wikipedia page (https://en.wikipedia.org/wiki/Goertzel_algorithm) and another page (http://www.mstarlabs.com/dsp/goertzel/goertzel.html), which are ...