The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in the frequency and time domains. DFT requires an input function which is discrete and non-zero, such as a sampling from an analogue audio signal.

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MATLAB implementation of modified DFT filterbank

I'm currently researching DFT filterbanks with near perfect reconstruction and ran across the MDFT (modified discrete fourier transform) filterbank in a paper by Karp and Fliege "Modified DFT Filter ...
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26 views

Limit of DFT from zero to N-1:

Why do we take the limit of DFT from 0 to N-1? If signal exists from let say -5 to 8. Then what will be the limit and how will we calculate DFT?
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8 views

DFT of 2d matrix only along one direction [on hold]

I have a 100 X 800 matrix. I want to do a DFT along each row. That is, for each of the 100 rows, I want to do a DFT of the 800 elements. How do I go about this (in FORTRAN) .
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29 views

DFT independent variable as fraction of sampling rate

When the frequency domain's independent variable is labeled as a fraction of the sampling rate, the values along the horizontal axis always run between $0$ and $0.5$, since discrete data can only ...
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21 views

When working with DFT of a real sinusoid why is the discrete time input taken over -N/2 to N/2, as opposed to 0 to N?

I know that when we take the input from 0 to N, the frequency component in the mth bin is the same as that in the N-mth bin, and when we take it from -N/2 to N/2 then the mth bin value is same as -mth ...
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Filter design using inverse dft

How do I get the cut-off frequency? A filter is needed to recover $x_2(n)$ from the signal: $$x(n) = x_1(n) + x_2(n) + x_3(n)$$ where: $x_1(n) = \sin(0.5n)$ $x_2(n) = \sin(1.4n)$ ...
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31 views

2D FFT vs 2 Pass 1D FTT

We know that the 2D FFT can be performed by taking the FT along the rows and then taking the FT along the columns. I'm wondering how theoretical performance compares to the direct 2D FT case, which ...
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33 views

DFT of a pressure signal from space domain to wavenumber domain

When I do the DFT of the following signal: I get the following DFT which doesn't capture any peaks at all: Why is this? I'm not really able to identify what the error is?
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29 views

Size obtained by applying Linear convolution

We know that applying a filter on an image is called correlation or convolution depending on the filter angle. In Gonzalez I have read that we can apply linear convolution on an image. Here I have a ...
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1answer
131 views

Cooley-Tukey Implementation of FFT in Matlab

For my course I need to implement a 30 point Cooley-Tukey DFT by transforming it into a 5x6 matrix. I have tried to implement using the following Matlab code: ...
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2answers
60 views

Purpose of Phase Information

I am learning Fourier Transform from many days but till now I am not able to understand what does phase angle image show us or tell us? They say that MAGNITUDE tells "how much" of a certain frequency ...
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1answer
32 views

Frequency of the wave in frequency domain

If we have a 1-dimensional wave in time domain, it can be represented in frequency domain with x axis indicating the frequency of the wave and y axis indicating amplitude/magnitude of the wave. But ...
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1answer
56 views

Explain Shift property of DFT

Please check the link What effect does a delay in the time domain have in the frequency domain? Here it is said that if you delay your input signal by D samples, then each complex value in ...
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2answers
42 views

What is a translation property in DFT

Hi someone please explain me the translation property of DFT. I am not able to understand it neither from Gonzalez nor from internet. I have done extensive study on this but not able to get it. Really ...
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1answer
59 views

What is the significance of the DFT in SC-FDMA systems?

Long term evolution (LTE) systems use single-carrier frequency division multiplex (SC-FDMA) in the uplink. In such a system, there is a DFT block and a sub carrier mapping block before the IFFT block. ...
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1answer
84 views

Recursive version of DFT as presented in Cooley-Tukey paper

The seminal paper of Cooley and Tukey provides an iterative method for computing the DFT for a sequence of length $N$. Specifically, they mention a method which utilizes the fact that $N$ can be ...
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1answer
22 views

Determining effect of powers of DFT matrix conjugate on input without multiplying

Suppose I have a DFT matrix $F$ of dimensions $N \times N$ where $N$ is a power of $2$. I convert it into a unitary matrix $\displaystyle U = \frac{F}{\sqrt{N}}$ and compute $S = U^* U^* $. $S$ ...
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22 views

Variation in Signal Power in Mimo system

I am exploring methods for reducing computations required by MUSIC (Multiple Signal Classification) Algorithm. Most of the computational power is spent on calculating SVD. My approach is to take ...
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54 views

Incorrect Frequency results when using Multiple Signal Classification (MUSIC)

I am using MUSIC (Multiple Signal Classification) to determine Direction Of Arrival (DOA) and frequency of signals impinging on an Antenna Array. I am using a function ...
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1answer
37 views

Interpreting magnitude of DFT results

I'm working on creating a simple program to render spectrograms like this one. In this plot, the X-axis is time, the Y-axis is frequency, and the color represents the magnitude of the DFT at that ...
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74 views

Autocorrelation and FFT : avoid zero-padding

Some posts evocate the computation of convolution or cross-correlation using FFT and zero-padding the temporal signal. I want to compute the autocorrelation of a 3D array using FFTW (2 dimensions are ...
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43 views

Instantaneous power estimation by discrete hilbert transform - how far does it smooth?

In my research area, instantaneous power in a specific frequency band is commonly estimated by the following procedure: Apply a bandpass filter on the raw signal (e.g. 80-90Hz bandpass). Estimate ...
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44 views

Multiply filter kernel by sine

1)Suppose that we have low-pass filter with cf equal to 0.1. How frequency response would look like if I multiply filter kernel by sine with frequency say 0.3? How this is related to converting ...
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2answers
106 views

please give the reason why every notation for DFT is valid?

$X$ represents sample in frequency domain and $x$ represents samples in time domain. NOTATION 1 $ X[k] = \sum\limits_{n=0}^{N-1} x[n] \ e^{-j \frac{2\pi}{N} n k} $ $ x[n] = \frac{1}{N} ...
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2answers
120 views

About frequency resolution [duplicate]

The frequency resolution of DFT is $\Delta f = \frac{1}{T_{0}} = \frac{1}{NT} = \frac{f_{s}}{N}$ where $f_{s}$ is sampling frequency, $T_{0}$ is sampling time, $N$ is number samples, and $T$ is the ...
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153 views

Why does the DFT assume the transformed signal is periodic?

In many signal processing books, it is claimed that the DFT assumes the transformed signal to be periodic (and that this is the reason why spectral leakage for example may occur). Now, if you look at ...
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100 views

Difference between convolution and multiplication of freq. response and freq. spectrum

Suppose I have impulse response like [1/25,2/25,3/25,4/25,5/25,4/25,3/25,2/25,1/25]. I did convolution with 600 samples of test signal (it seems that I did some filtering). Then I calculated the ...
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1answer
63 views

Basics of waveform, how to define the zero point

Audio is a sequence of waveforms which have peaks, troughs, 0, just like below. How to define the x axis (y = 0) in the picture, how to choose the 0 point in the waveform since there are so many ...
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3answers
507 views

disadvantages of FFT, it can not extract enough frequencies without enough samples

Let's say sampling rate is $Fs = 44\mathtt{kHz}$, now I have $N = 2048$ samples, then I can get $N/2 + 1 = 1025$ frequencies. I'm confused by Matlab's FFT documentation that says the frequencies are ...
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60 views

Using Fourier Transform on Gyroscope

The original idea is to calculate distance from accelerometer input. However, accelerometer reading also contains the gravitational values, thus to remove gravity, I tried using Gyroscope. The idea ...
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1answer
59 views

Exercise related to frequency resolution and SNR

I'm studying a book aboud dsp and trying to make excercises. Here is one I'm interested in: A scientist acquires 65,536 samples from an experiment at a sampling rate of 1 MHz. He knows that the ...
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1answer
76 views

Writing a Discrete Fourier Transform program

I would like to write a DFT program using FFT. This is actually used for very large matrix-vector multiplication (10^8 * 10^8), which is simplified to a vector-to-vector convolution, and further ...
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2answers
151 views

Using Goertzel Algorithm in under-sampling

I plan to calculate a signal's phase using Goertzel Algorithm. I have 2 signals coming to microcontroller's ADC. Need to measure the phase difference between them. Signals are 15MHz sinusoids. Sample ...
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1answer
54 views

image 2-d real cepstrum with DFT ? ifftshift needed?

this is my testing image,it is taken from this paper: I tried to transform it into its real cepstrum domain with this simple matlab code: cepstrum_img=ifft2(log(1+abs(fft2(img(:,:,1))))); ...
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113 views

Extraction of fundamental signal information-Fourier full cycle algorithm

After filtering my noisy input signal using an anti-aliasing and FIR filter, I now wish to get the basic signal information (peak voltage and impedance; $R$ and $X$) from the pre-filtered as well as ...
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1answer
89 views

Simple questions related to dft

I'm reading a book about dsp and doing some exercises. Here is question that confused me: A peak appears at index number 19 when a 256 point DFT is taken of a signal 1) What is the frequency of the ...
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44 views

Calculating Energy Spectral Density from Magnitude and Phase data

I'm trying to do a program that can judge whether 2 audio files have the same pronunciation or not by comparing the frequency of them with each other. The first step, finding the magnitude and phase ...
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2answers
66 views

Signal Resolution

I have a question. Suppose we have a signal $x(n)$, length (samples) $N=400$ which have been sampled with $f_s=8000 \mathtt{Hz}$. Also suppose $X(k)$ - the DFT transform of this signal. How many ...
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1answer
95 views

Uncertainty, time-bandwidth product, harmonics

For a signal that is not corrupted with noise, how is the time-bandwidth product affecting the uncertainty or error introduced when extracting the fundamental frequency ? I mean, instead of choosing ...
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1answer
61 views

Understanding IIR , Low Pass, High Pass, Chebyshev, Elliptic Filter? [closed]

I see these terms everyday in every lecture, I do read stuff from wikipedia, follow lecture notes, study solved exercises. All in all I do have a rough idea about these, I know a little from ...
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1answer
50 views

Applying Discrete Filters

I have an exercise in DSP. I learnt about discrete filter but I don't know how to apply it to produce an output from an input signal. Please guide me to do this: Assume fundamental sample time is ...
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1answer
133 views

Time domain distortion vs Harmonics

I have a periodic time domain sensor signal sampled at $500 \text{ Hz}$ whose amplitude spectrum I compute and obtain. From the periodicity of the signal, I was expecting the fundamental frequency to ...
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1answer
62 views

Polarity inversion in frequency domain (polar coordinates)

I don't fully grasp how polarity inversion is performed in the polar coordinates of frequency domain. The frequency components of the signal do not change, so the amplitude part is going to stay ...
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2answers
120 views

Hermitian symmetry in OFDM systems

I am trying to understand the usage of Hermitian symmetry in OFDM systems and have a couple of questions regarding this. What is the reason of using the Hermitian symmetry in OFDM? How can we ...
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2answers
88 views

Reason of circular conv in OFDM

In OFDM system, after IFFT a CP is added at the beginning of the OFDM symbol by copying it from the end of the symbol.My question is that with CP why we use cyclic convolution instead of linear ...
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1answer
72 views

Determining power of white noise component of an incomplete time signal

I want to determine the power of the noise component of a time dependend signal x(t) (similar to picture below) With constant sampling rate I use Parceval's Therorem and calculate the standard ...
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1answer
169 views

Why can't DFT be used when samples are not equally spaced in time?

I found the following comment here The DTFT can be used when the samples are not equally spaced in time, the DFT cannot My initial thought was that this had to do with periodicity of the basis ...
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42 views

how to sample sine wave to 4 points dft output

sinusoid x(t)=1+sin(2*pi *500) sampling rate :1000 samples/s Can I have 4 points DFT output with the above data.
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125 views

Autocorrelation Function and Power Spectrum

My aim is to determine the power spectrum of a signal of finite duration using Its autocorrelation function Performing FFT directly on the time-domain data The function is defined as follows in ...
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2answers
205 views

Magnitude Spectrum, different magnitudes same amplitude

When the following code is written,the resulting magnitude spectrum shows magnitude values represented by two peaks is different even though they have the same amplitude. why is that? a fast reply ...