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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349 views

Why MATLAB fft cos makes imaginary parts?

The cos fourier transform has no imaginary parts, but in this code it has imaginary parts that little big. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(7); fs=128; t=-4*pi:1/fs:4*pi-1/fs;...
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218 views

FFT amplitude vs IQ amplitude

I'm very new to digital signal processing, so please let me know if my question doesn't make sense. I calculated the amplitudes (using the formula : $10 \log_{10}(i^2 + q^2)$) for some IQ data ...
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2answers
401 views

Ifft through Matrix multiplication

I am still new to MATLAB, so apologies if I sound lazy to you. I am attempting to model a transformation as a set of matrix operations. I start with a vector, up-sample it by $U$ (up-sampling rate), ...
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1answer
150 views

Understand Inverse DFT (FFT)

I was reading this article to understand the fft https://jackschaedler.github.io/circles-sines-signals/dft_walkthrough.html I understand that the fft takes a block (256 or 512) of the signal, ...
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2answers
112 views

Radix2 fft - zero padding output size

With zeros padding the FFT radix2 has different input size than output. How to deal with that? I see two solutions but not sure which one is better/appropriate. Maybe you know some other and better ...
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1answer
906 views

Numpy fft2 frequency shift

I don't understand how to make frequency shift in fft2 or higher dimensions. Could anyone explain it, please? import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import ...
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3answers
307 views

Deconvolution Using Complex Division in The Frequency Domain

Consider these two signals: a = [1 1 0 0 0 0 0 0] b = [1 0 1 0 0 0 0 0] their convolution is c = a * b = [1 1 1 1 0 0 0 0] ...
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1answer
50 views

Meaning of a formula about transient frequency bins

I'm trying to understand the following formula in this paper: Sadly, the paper does not define most of the symbols it is using, so my guesses so far are: $T_{tr}$ refers to the sampling interval i....
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1answer
46 views

Complex FFT reversing

I've succeeded to compute complex FFT of a data array of interleaved values using the arm_cfft_f32() API of the CMSIS DSP library for Cortex-M4, and got in the same array the FFT results as frequency ...
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1answer
31 views

Non-decaying Harmonics in Vibration Signal

I am analyzing vibration data collected by an accelerometer positioned in a stamp press machine. The fundamental frequency is around 10 Hz. The problem here is that when I take the FFT of the data I ...
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1answer
49 views

FFT for distance-limited sum of pairwise products

I have a sequence of fixed length $N$ input arrays ($x_0$, $x_1$, ..., $x_{n-1}$), and my goal is to compute output arrays as such: $$d_{00}[l] = \sum_{i = 0}^{N - l} x_0[i]x_0[i + l]$$ $$d_{01}[l] = ...
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2answers
57 views

What to do for the right FFT in Matlab (two peaks and incorrect amplitude)?

This is the FFT I'm using. But two peaks (did not expect the one in the beginning) are occurring and the amplitude is not as specified (expecting a value of 2). Any help is much appreciated! ...
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1answer
59 views

Harmonics in Quantal Histogram

I'm studying what I believe to be a system that produces a (noisy) quantal response (i.e. there should be a minimum increment of response). To do this, I've plotted a histogram of some ~6000 amplitude ...
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1answer
143 views

THD: estimation using periodogram or fft?

I want to estimate the THD of a voltage signal (output from a frequency inverter). At the begining, I need to estimate the power of the signal at frequency domain. To doing so, I should use a ...
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2answers
233 views

How to assess perceptual volume from FFT

So far I could estimate signal volume from FFT using amplitude information, then adding all amplitudes together and divide this number by the number of frequencies. But I think this method does not ...
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1answer
754 views

Checking for VHF pulse with SDR and python

So I have a small NooElec Software Defined Radio and I've got it working well with my Raspberry Pi using GQRX as a controller and to visualize the SDR output. My goal though is to use a python script ...
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4answers
1k views

Why does the frequency in the DFT have to be an integer?

I don't know why the result of DFT and FFT in MATLAB like below images.. fs=128; t=0:1/fs:1-1/fs; x=cos(2*pi*3.5*t); X=fft(x); N=length(x); n=0:N-1; f=fs*n/N; plot(f,abs(X)/N); If I set the ...
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75 views

Making longer a time domain signal by adding values on its frequency domain. What am I doing wrong?

Background Here's the thing: using software for Finite Element Acoustic Simulation I got the dataset of frequency response from a room; software works by solving the wave equation in the interval $`[...
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1answer
163 views

How to interpret the signal in frequency domain

I'm having difficulties understanding some basics regarding FFT. I was hoping you could answer a few questions I have. These questions will probably seem silly to you, sorry for that. I'm a complete ...
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128 views

Correctly scaling Power Spectrum and Correlation Function of Galaxies from Mock Catalogues

I'm currently writing a code to compute the two-point correlation function of a set of galaxies. As I work with a loooot of galaxies, it was suggested to me not to do it in real space, but to compute ...
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3answers
2k views

Correct method for processing FFT in realtime

I am attempting to build a 'live' FFT for continuous analysis of an audio signal. I am relatively new to this, but have attempted the full thing, and then updating the graph at 20Hz refresh rate. My ...
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2answers
52 views

Why the angle of a real signal in frequency is continuous?

This original signal is shown below (time domain): It is a real signal. According to the signal processing theory, the form part of the angle is conjugate to that of the latter part. That is, $\...
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149 views

Auto-correlation function, an inverse problem

$x[n]$ is a complex function $n=0,1,2,\cdots,L-1 $ we assume $x[n]$ is periodic in its index: $x[n+L]=x[n]$ Its auto-correlation function $C[n]$ is uniquely defined as: $$ C[n]=\sum_{i=0}^{L-1} x[i+...
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78 views

non-negative FFT spectrum, subtlety

definations $x(t)$ is a function of time. Physically, it can be voltage, displacement, magnetization and so on. It can be real, complex, vectors or more fancy numbers. $C(t)$ is the auto correlation ...
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2answers
69 views

How to detect a long signal inside an even longer one?

I'm trying to detect a long pattern inside a long recorded audio. In order to do so I am implementing a matched filter in time by performing a FIR filtering using the coefficients of my pattern ...
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1answer
405 views

extracting ultra accurate phase and frequency with FFT with real world data

I was doing some experiments in Matlab, and write this code to experiment with it. I want to know if it's possible to extract accurate within -+0.01° phase info from samples of an ADC, the matlab FFT ...
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52 views

which is the relationship between domains (x and k) in FFT?

I need to plot an escalar field f(x,y) in an interval xv= (xmin,xmax) in Nx steps and ...
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1answer
106 views

Precompute parts of an FFT on streamed data inputs

I've implemented Radix-2 & Radix-4, DIT & DIF variants of the cooley-tukey FFT algorithm and they perform well on test data. Now for a project, my algorithms will be applied to a real-time ...
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86 views

How does this Odd stacking DFT work?

I have just read on page 3 of this paper: https://www.onsemi.com/site/pdf/Filtering_Hearing_Ai.pdf That an "odd stacking" DFT can be created, essentially sacrificing the DC and Nyquist bands to ...
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1answer
113 views

Remove Frequency Range

I got a signal and I would like to remove a specific frequency range. I am a frequency noob, so I will explain it by images: I have a frequency filter (butter bandpass): I have a signal and it's ...
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2answers
119 views

How to implement discretized CWT with FFT?

I tried to make circular convolution (correlation actually because it is easier to understand for me) look like the Continuous Wavelet Transform (CWT) but got stuck because the conjugation was on the ...
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1answer
116 views

Measuring Amplitude of sound wave FFT

Please, pardon my ignorance. This may be a simple question, but I am still unable to explain what is happening. I am using a turtlebot to listen to sound emitted from a stationary sound source. My ...
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4answers
847 views

DFT (FFT) of a Real Even Function Doesn't Yield Real Only DFT Signal

There are a lot of similar questions already, but I can't find one answering this problem. I used the following MATLAB code to perform the FFT on a Lorentzian input signal ...
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1answer
62 views

Improvement of SNR by sampling different number of cycles using FFT of a fixed length singal

My question relates to Fourier transform of signals with different lengths in time but the same fixed length of the digitized signal with different sampling rates. Specifically, how does the number ...
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3answers
214 views

Decreasing Sample Rate in DFT (FFT) for Audio Analysis

I'm working with audio data analysis through FFT algorithm. My example audio is a sine wave at 440 Hz and 44100 Hz sampling rate. FFT methods in programming, like ...
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2answers
13k views

Apply Low pass Butterworth filter in Python

I want to use a low pass Butterworth filter on my data but on applying the filter I don't get the intended signal. Here is the dummy code: Signal A: ...
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1answer
170 views

Measuring acoustic phase difference between two receivers

I am trying to measure the acoustic phase difference between two sensors 30cm apart each other. The sampling frequency is 20kHz, and my interest frequency is about 1700 Hz. The below is how I ...
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1answer
611 views

Scale FFT frequency range for a bars graph

I'm trying to show frequency spectrum for audio data as a bars graph using FFT. If I have data for a sine wave at 440 Hz and with sampling rate 44100 Hz and analyze its first 1024 samples I get an ...
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1answer
100 views

In a periodogram, why is the modulus squared of the DFT taken rather than the DFT itself? [duplicate]

Why can't you just take the DFT itself? And how accurate is this method in spectral density estimation? Are there cases in which it is very accurate?
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1answer
264 views

How to shift FFT spectrum by half a bin?

I am trying to find a way to shift the outputs of the FFT (any algorithm implementation, currently using radix-2) by half a bin with the same bandwidth. To put it another way, say you have a 512pt ...
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1answer
190 views

Morphing between two FFTs

I'm a musician and I'm making a script that takes a wave file and snaps each of its frequencies from the fourier transforms to the nearest musical harmonic. Thanks to help from another question I ...
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1answer
269 views

FFT - preferred way of tone detection

I am using FFT to detect certain frequencies (DTMF). I can clearly see the frequencies in the spectrum. Is there a preferred / optimal way to decide if a certain frequency is present or not by looking ...
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1answer
175 views

Band energy and Parseval theorem

In Python, I consider a dummy signal as follows: fs = 512 sig = np.random.standard_normal((fs,)) sig corresponds to 1s of ...
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1answer
202 views

Wavelet transform and FFT using to extract feature power bands with EEG signals

I am using 5 channels [ fz , cz , c3 , c4 , pz] to detect drowsiness of driver My First Question is, what is the right input to get feature power band ( Theta , alpha , gamma , beta ) to wavelet ...
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1answer
255 views

Windowing a signal for FFT

I am actually working on a project involving the cross-correlation of two signals. My cross-correlation code is working fine, but I suspect that I should apply a window to my data set in order to ...
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1answer
44 views

How to Calculate the number of DFTs taken in a STFT

Given variables of window size (W), overlap (O), and length of the Signal (S) (in my case, length of a song) and I am trying to determine an equation that gives me the number of DFTs that would be ...
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1answer
172 views

Phase Modulation and Intermodulation Anomaly ? (Spectrum plots inside - **Updated**)

I have a MATLAB script for modelling a two tone signal (a sum of two sinusoids) going through a non linear transfer function (such as an amplifier). The amplitude of a signal is amplified non linearly,...
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1answer
61 views

psd of an ac voltage signal

In an lab class experiment who's subject of interest was Johnson's noise I measured the ac voltage of a battery. Now I wish to find the psd of the measurement and show that it is constant. 1.Is such ...
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1answer
176 views

Arbitrary Phase FIR design using FFT

I want to design a digital FIR filter to cancel the phase of an analog Butterworth filter (i.e. the phase is smooth) i.e. the filter has unity gain with just an inverted phase component. The ...
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2answers
162 views

Adding phase to a signal that has multiple frequencies

An amplifier changes the phase at different amplitudes of asignal. I am using amplifier data in a MATLAB model. I have constructed a signal that is a sum of sinusoids of different frequencies with ...