# Questions tagged [fft]

The fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse.

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### Intuition for sidelobes in FFT

I was wondering if there's a intuitive way to understand why sidelobes appear when performing an FFT on a signal of fixed length?
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### Calculate the difference of the magnitude of discrete fourier transform - help inimplementing the formula

I have a time-series of length N generated by the following equation: ...
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### Zero-padding or Interpolation in 3D FFT

I'm trying to perform a FFT of a 3D regular grid and then compute the bin average (in spherical shell bins) of the Fourier transformed grid. The problem is that the resulted vector is very noisy as I'...
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### Flipping of x axis values when the Fourier Transform is compared to the FFT

EDITED 3-Jun-20 I have a lorentzian lineshape $$f(z) = \frac{1+iz}{R(1+z^2)} \qquad (1)$$ where $$z=\frac{-2\pi(f - F0)}{R} \qquad (2)$$ and $R$ is the decay rate, $f$ is the frequency, $F0$ ...
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### PSD Accelerometer and Gyroscope

I used Xsens IMU and collected 1 Hour static data for accelerometer and gyroscope. I used the pwelch analysis in matlab to calculate the onsided PSD. The plots looks the following: How do I ...
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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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### Pitch shifting with bins creating large feedback

I am attempting to create a pitch correction algorithm. I started by performing a test. The test goes as such: Get WAV file Split it into bins of size n (512 in my case) Shift each bin by 2 semitones ...
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### Cross power spectral density (CPSD) comparison between signals

I want to compare various signals with Matlab's CPSD to identify shared frequency components. (If there's a better method, I would like to know!) I have 3 signals, A, B, and C. B is pure noise while ...
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### Python tool for time-frequency analysis

I am trying to perform time-frequency analyses using the PyWavelets (pywt) toolkit for python. My ultimate goal is to perform time-frequency analyses for EEG signals but I am starting with something ...
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### Why does the frequency in fft plot of the baseband modulated signal isn't changing at the receiver

I have designed a transceiver system for cellular frequencies(800MHz). On the receiver side, I have converted the band signal to baseband signal through digital mixing. I have added the Inphase and Q ...
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### How to extract the Freezing Index from Accelerometer data?

I'm working on a project to detect Freezing of Gait episodes for Parkinson's Disease patients, and according to this paper and other ones, extracting the freezing index which is "The power in the “...
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### How to calculate FMCW Radar Chirp STFT?

I have received signal from FMCW Radar which is of the shape [128x64] = [Number of samples per chirp x Number of chirps per cycle] and i want to calculate the stft i am calculating it with stft ...
137 views

### Inverse FFT of complex exponential with time delay - window leakage?

I am working in MATLAB with a frequency domain signal that is a sum of complex exponentials, e.g. $X(\omega) = \sum_i e^{-j\omega t_i}$ where $t_i > 0$ $\forall$ $i$ I expect the output to ...
312 views

### Spectral Subtraction python implementation error

I am trying to implement Spectral subtraction in python. I am new to DSP. I used this article as reference and below code is what I can come up with. Of course I did not get the expected output. I ...
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### Inverse FFT - Synch the Phase

Is there any way to synchronize phase of output of inverse DFT in each buffer? When I send the output of inverse DFT to the ...
91 views

### Strategy / Method for Implementation of the Fastest 1D Linear Convolution / Correlation

I am after the method and its implementation of the fastest convolution of 1d signals: $$y \left[ n \right] = \left( x \ast h \right) \left[ n \right]$$ Where $\ast$ is the linear convolution ...
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### On the simplification using trigonometric functions

Assume I have a matrix $D$ whose its entries are as below : Where $A$ and $B$ can be written using using the trigonometric functions for (1) as: My question, Is it possible to simplify (1) more? ...
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### FFT of a variable-frequency signal

I'm writing a software that read engine rpm during acceleration, using a recorded audio. To do that, I divide the record in small time-steps, and for each one I do an FFT, to know the rpm in that ...
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### fft of a signal in the space at a fixed time

I have to do a fft of a signal in the space at a fixed time. I have always done fft of signals in time, so this is strane for me. In particular I have some difficulties in defining the Nyquist ...
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### Construct IFFT from only the major frequencies of an input signal?

I have data which when plotted looks like the green line in the below image. The data is from the walking-motion of a reinforcement-learning-model in a simulation and therefore the values do not ...
70 views

### 64 point FFT Hamming window interpolated to 720-point sequences

Can someone here explain the meaning of, 64 point FFT Hamming window interpolated to 720-point sequences and its inverse? 720 point is from 0 to $2 \pi$ or (0 to 720 degree). I get the 64 point ...
476 views

### Efficient calculation of correlation function every $N^{\rm th}$ point

I would like to calculate a long correlation function of length say, 1e6 points. I have a prior knowledge that the correlation peak will be in point k*1000. Is there an efficient way to apply this ...
732 views

### $1/n$ octave complex smoothing

An excellent answer to this post explains how to do $1/n$ octave energy smoothing and mentions complex smoothing can be done as well, but it's tricky business because of phase wrapping. How is phase ...
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### WOLA vs Simple Hamming Window on signal before FFT

Im working on a project in which I should FFT a signal coming into my FPGA from ADC. I want my FFT to show the peak values as clear as possible without the side lobes. The solution should be straight ...
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### Relationship of input-outputs in Hartley transformation based on few elements in a vector

This question is related also to that question HERE, but with further details and another issue I need to solve. Assuming we have a vector $X = [x_0,x_1,\ldots,x_N]$, its Hartley transformation is ...
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### Windowed N-point FFT

In the previous question, Smoothing in frequency domain and impulse reponse of the filter in time-domain I guess I have made a mistake in-terms for applying windowing to FFT. After reading "...
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### How can I insert message bits into the frequency spectrum of an audio signal using Matlab?

I have been trying to use the DSSS spread spectrum technique for audio steganography in MATLAB. I multiplied the PN sequence with the message bits. Now I want to insert this spread message into a ...