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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What is the limit of zero padding?

I have a intensity profile in energy i.e., the X axis is the energy from A to B (both positive). The Y axis is intensity. It has N (~1300) data points within the range. Now in order to get the signal ...
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14 views

IDFT of H(z) sampled in N values

If a have a causal IIR filter described by $H(z)$ and I sample it in $N$ equispaced values around the unit circle, I get a DFT of $N$ points. That DFT corresponds to $h[n]$ truncated in $n=N-1$ or to ...
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54 views

Time scaling in DFT?

Let $x[n]$ be a real signal whose length $N$ is even. Let $y[n]=x[2n]+jx[2n+1]$ a signal whose length is $M=\frac{N}{2}$. $X[k]$ for $k=0,...,N-1$ and $Y[k]$ for $k=0,...,M-1$ are the respective ...
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1answer
31 views

Analysis of a LTI system using DFT

Consider an LTI system $$H(z)=1-\frac{1}{2}z^{-1}+\frac{3}{4}z^{-2}$$ Let $x[n]=(\frac{1}{3})^n\cdot u[n]$ be the input signal. It is desired to determine the output for $n=0,1...,N_a$. To ...
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28 views

What's the IDFT of this sequence?

Let $x[n]=0$ for $n<0$ and $n>63$. If $X[k]$ is its 64-point DFT and $X[32]=1$ while $X[k]$ is $0$ for any other value of $k$, what sequence is $x[n]$? I used the definition of IDFT and I got ...
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1answer
28 views

DFT of a cosine/sine wave?

I'm seeing everywhere that the DFT of a sinusoid (i.e. a sine that has been windowed with a rectangular window) are just two deltas. What I don't understand is why the DFT is not the convolution of ...
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25 views

Applying Filter to Complex Data

I have data being streamed in the time domain, I would like to use a transfer function for a low pass filter in order to filter the data. I use DFT to get the data to the frequency domain, in the form ...
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58 views

Determine sequence's value from equally null circular convolution DFT

can anyone help with this exercise from my Signal Processing exam? The text is: Given two sequences xand y whose supports are ...
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2answers
82 views

How to realize DFT6 with 3 DFT2 blocks?

Is it possible to realize DFT of 6 samples by using 3 DFT2 blocks? For example if had 2 * N samples by one step of decimation in frequency or time is possible to reduce DFT(2N) to 2 * DFT(N). So if we ...
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1answer
51 views

Why is the DFT used for spectrograms rather than the DCT?

Related to Could a DCT be used for an audio magnitude spectrum rather than DFT?, but more on the (audio) spectrogram side of things I've been reading about the DCT (such as from here) and it ...
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49 views

Sampling H(z) to get DFT

Suppose that I have a $H(z)$ and I sample it to get a DFT of 15 values. Let's call this DFT $H_{1}[k]$. Then, suppose I antitransform $H(z)$ and grab the first 10 values of the sequence, and then I ...
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50 views

Find the output signal using only DFT

The problem goes as follows: Assume that there is a stable system defined as $$H(z)=\frac{1}{1-\frac{3}{4}z^{-1}+\frac{1}{8}z^{-2}}$$ The output of the system is $y[n]$ and it is desired to find ...
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2answers
73 views

Relationship between z-transform and DFT

I'm studying for a Signals Processing exam and came across an exercise that I'm finding pretty difficult to solve. It says: Asume there is a signal $x[n]$ of length $N$. Its ...
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1answer
70 views

DFT normalization for amplitude estimation

After an interesting recent answer, I'm doing some research on proper DFT normalization for sinusoidal peak estimation. It's clear that to get the correct amplitude from DFT peaks we need to normalize ...
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1answer
79 views

Relation between sawtooth Fourier coefficients and its DFT

I'm having some trouble with understanding the DFT of a sawtooth single period signal and its relation with sawtooth Fourier coefficients. Let's say I have a signal $$ s(t) = \frac{At}{T} - ...
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1answer
39 views

Oversampled polyphase filter banks

i would a confirm of this: with polyphase structure is possible only design a filter bank with a INTEGER oversampling ratio? For non-integer i've seen the weighted overlap-add metod, is right? thanks ...
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3answers
54 views

Formulas of the Fourier transform family

It has annoyed me that there doesn't seem to be a source online where the complete complex Fourier transform family is presented with every variable defined. The lack of definitions can be a nuisance ...
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59 views

Accuracy of IFFT(FFT(X)) unit transformation

I want to use FFTs to do seriously accurate interpolation on band-limited data. To do that, I need to get a handle on the fundamental accuracy of the FFT() and IFFT() algorithms available. My idea ...
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40 views

Trouble understanding discrete Fourier Transform

In the paper Calculation of a constant Q spectral transform - J.C.Brown it is mentioned The conventional linear frequency representation given by the discrete Fourier transform gives rise to a ...
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2answers
71 views

Inverse Sliding DFT

From paper: Bradford R., Dobson R., ffitch J. - Sliding is Smoother than jumping In chapter 6 - Signal Reconstruction, the inverse of the sliding DFT can be achieved by this formula: ...
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74 views

Log-Polar DFT Based Scale-Invariant Image Registration

I'm trying to do image registration using phase correlation as described in the Reddy Chatterji paper. In my case, the images may be scaled and translated relative to each other. The algorithm for ...
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2answers
43 views

Studying spectral leakage due to DFT length and frequency resolution

I guess this is a pretty basic question, but I am kinda stuck... So if I am remembering the DSP theory correctly, spectral leakage can occur when we take "inappropriate" combinations of the following: ...
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1answer
63 views

Performed the Danielson-Lanczos shuffling for FFT, but I don't know what to do next

I'm writing an audio analysis program and need to do some FFT to frames of the data. I've got some code (rather verbose so I'll leave out the details) that successfully performs the shuffling of the ...
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26 views

Sign of DC Component obtained from FFT differs with the sign of Mean of the signal, Does the sign really matter?

I've been working on 3-axis accelerometer data to predict the gesture of an user. Lot of literature pointed me to consider Frequency domain features for my problem and i'm using Mean of the ...
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24 views

How to get cofficients in DFT?

In my recent study of signal processing I came to know that we can compress images/signal using DFT/DCT. If we consider the lossy compression of audio or any image then it follows the same steps: ...
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13 views

Digital low-pass filters: why not just zero out the dft? [duplicate]

Say I want to LP-filter $s[n]$. This is done by $s*\ell[n]$ where $\ell$ is some fancy low-pass filter. What I kind of don't get is why we can't just transform the signal obtaining $S[k]$ and then ...
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1answer
65 views

Calculating original signal from Discerete Fourier Transform

I am trying to calculate the original equation using a DFT. I start with a equation, generate values from this equation and then get the dft of these values. The aim is to generate the original ...
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1answer
83 views

Power spectrum estimate from FFT

I'm plotting the FFT power-spectrum of a signal in MATLAB. I uploaded the 8000 samples time-series signal in a text file here: http://wikisend.com/download/896484/signal.txt I'm using the following ...
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2answers
46 views

DFT provides coherent integration?

I read from material that coherent integration can be provided by DFT. But it doesn't give further explanation on this remark. As far as I know, coherent integration is the summation of discrete ...
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1answer
168 views

FIR filter design and implementation - sample rate and number of taps

I have been designing and using IIR filters to process audio for a while now but want to design some FIR filters for delay equalization. I have done some preliminary work using the following approach: ...
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1answer
62 views

Minimum number of data points needed for a DFT to avoid spectrum leakage?

Let $x(t) = 0.4 + 0.5 \cos (2 \pi f_1 t) + 2 \cos (2\pi f_2 t) + \sin(2 \pi f_2 t) + 1.5 \cos(2\pi f_3 t)$ where $f_1 = 3 kHz, f_2 = 5 kHz, f_3 = 8 kHz$. If $x[n]$ is obtained by sampling $x(t)$ with ...
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23 views

Event Based Sampling - DFT

I'm familiar with traditional time based sampling - analog waveform(s) sampled at some rate (according to Nyquist) and then running a DFT. But, what about event based sampling. I've recently come ...
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84 views

“Flanging” in frequency domain?

Flanging is defined as a mix of two identical signals where one signal is delayed in time by a small and gradually changing period, around 10-20 milliseconds. Since delay in the time domain is ...
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1answer
44 views

Why DFT exact for periodic signals?

I have in my course notes: $$ \sum_{k=0}^{N-1}y(k)e^{-j\omega_nk}\approx\sum_{k=-\infty}^{\infty}y(k)e^{-j\omega_nk} $$ Where the $\approx$ for some reason becomes $=$ when $y(k)$ is periodic. Could ...
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56 views

Short VHF pulse detection from SDR

I need to detect a short (10ms) VHF pulse that occurs every 1.5s at a specific frequency (e.g., 150.20 MHz). I have an SDR that support IQ sample rates up to 10MSPS but due to computing constraints ...
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16 views

Designing 2D DFT filter that works with cycle per degree

Here is my question regarding 2d dft. I know how to do 2d-dft and convolution and filtering. However, I still have a basic question. Maybe I have not understand the concept, and that's why I don't ...
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1answer
128 views

Phase measurement

I have a problem with phase measuring. I'm acquiring two signal with a USRP (complex signals) with a coherent generator and I want to measure the phase different between them.. One is at 150Mhz and ...
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1answer
50 views

Use of FFT to compute frequency response [duplicate]

Is there an algo that uses fft to compute the frequency response of an FIR? Currently I follow the textbook method of evaluating the $z$ transform at $e^{-j\omega}$ for $\omega$ running from $0$ to ...
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57 views

Why does filtering the same discrete dataset while choosing different sampling rates yield different results?

If I have a two-dimensional discrete dataset (one space, one time), and I create subsets of this dataset by "sampling" (although the original dataset isn't continuous) it at different rates, should I ...
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36 views

the DFT of a periodic signal represented by a fourier series

If I have a signal represented by a Fourier series(like in the photo), which is sampled with $T_s$: $$x[n]=x(t=nT_s) = \sum_{m=-\infty}^{\infty}a[m]e^{j2\pi m(nT_s)/T_0} $$ How do I find its DFT? I ...
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1answer
61 views

DFT for audio classification - signals of different lengths

If I have a set of signals each with $n$ points, I can take the DFT of each and then use the resulting frequency domain vectors as features for some classification algorithm. If the signals are ...
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1answer
28 views

Frequency of DFT term

I've been wrestling with this question for way too long. I appreciate any insight you can offer. Thanks. "If the 9 point sample sequence x(n) represents a time domain signal sampled at 48 kHz, what ...
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2answers
73 views

Beginner question on aperiodic samples and DFT behavior

I have a strongly aperiodic signal and I get weird artifacts after running a fft, using a low-pass filter, and then doing an inverse fft. I believe the artifacts are due to the way the signal is ...
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1answer
55 views

what is the preffered data and FFT length for blackman harris window for improving Accuracy due to ENBW Consideration of window?

for Rectangular window if data length is 1K then FFT Length Should be 1K FFT only because ENBW of rectangualr window is 1.0 but for Minimum 4-Sanple BlackmannHarris window is 2.0. so for improving ...
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1answer
58 views

DFT: Basis functions and Significance of dividing frequency by Sample length

A time domain signal can be decomposed into sinusoids which are based on basis functions. For a N sampled input, a cosine basis function is defined as: $$C_k[i] = \cos\left[\dfrac{2\pi k ...
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3answers
60 views

Using FFT as a channeliser

This article mentions that the DFT/FFT can be used as a channeliser in a similar way to a filterbank. I get how the DFT filters into spectral bins, but its output is in the frequency domain, i.e. ...
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107 views

DFT sinusoid's fundamental frequency, intuitively

I am trying to understand, intuitively, the mapping of a sinusoidal signal's fundamental frequency from time domain to frequency domain using $\textrm{DFT}$ formula. Given the time domain samples ...
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2answers
208 views

What are the alternatives to FFT for computing high-resolution tone power levels?

I have a system where there's a transceiver which transmits tones on specific frequencies (about 260kHz) and a receiver which is supposed to recognize those tones. The transmitted tones are of low ...
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1answer
185 views

How to calculate resolution of DFT with Hamming/Hann window?

The frequency resolution of a DFT with a rectangular window of size $N$ is given by $f_s/N$. However, when using other window functions like a Hamming or Hanning window the resolution gets worse. How ...
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1answer
146 views

Difference between 2D-DFT's and 1D-DFT's of linearized matrices

I have recently left the safe and easy MATLAB environment and begun to use CUDA-C/C++ for image processing. Since CUDA doesn't allow 2D arrays to be passed into kernels I am now used to linearizing ...