# 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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41 views

### Measuring group delay through a linear phase filter

I'm having a difficult time wrapping my head around a phase/ group delay problem and it corresponding to where you start sampling so I built up a system to test some of these issues. The system passes ...
230 views

### How do I find the peak frequency of a wav file in python?

I am fairly new to python and signal processing and I was given a task to record audio for 'x' seconds and then find the peak frequency in the audio file. So far I have successfully implemented the ...
64 views

### Why would FFT interpolation using zero-padding undershoot the true frequency of a single tone sinusoid?

Why would FFT interpolation by zero-padding or using the Chirp Z-Transform produce a maximum at a bin that corresponds to a frequency less than the input frequency of a single tone sinusoid? I am ...
30 views

### Is fft2 in MATLAB unitary? Some differences happen

I meet a problem when implementing fft2 in MATLAB. The question is I try to simulate the realistic measurements $Y = |FCXF^H|^2$ - the intensity of Fourier domain of object $X$, where $F$ denotes ...
52 views

### What measurement errors occur in an inteferogram?

This question is bordering on physics, but it is the signal side that I am interested in so I hope this is the correct forum. I am very familiar with instrumental noise sources in CCD based ...
46 views

### Normalizing FFT after recording with Pyaudio

I have a USB microphone that has a 24 bit ADC, however, Pyaudio doesn't allow for 24 bit encoding so I used 16 bit. I hope this is not an issue. Having said that, I hope to make sure I'm applying the ...
163 views

### Filter length in a Filtered-OFDM system

In a filtered-OFDM system, lets say we have the following parameters: ...
401 views

### Decimation and Upsampling

I'm currently trying to understand decimation and possible ways to retrieve back the original signal. If the signal of supposed frequency $X$ Hz was decimated by a factor of four, would there be $4$ ...
64 views

### Is the value of a frequency bin of a DFT-output the average of the 'real' frequency values within that bin's range?

I am wondering whether the value of a frequency bin with a certain resolution is the average of the fourier transform values of the 'real' frequencies within that bin's range.
211 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,...
98 views

### Half Window Functions and Formulas

I am looking at implementing different window functions in an application I am making. I have found the formulas for all major symmetrical windows, however I would like to implement half windows. ...
48 views

### Approximating Lorentzian Fourier transform with FFT

I have a Lorentzian frequency distribution $F(w) = \frac{1+iz}{1+z^2}$ Where $z = \frac{w-\Omega}{R}$ With $\Omega$ being the peak frequency and R the decay constant. I know that analytically ...
40 views

### Does FFT magnitude of a sound drop to 1/10 of its value if sound level is decreased by 20dB?

I understand decibel = 20 * log (magnitude/reference value). To truly appreciate the meaning of this, if I have a single frequency tone that corresponds to a certain FFT magnitude shown on a PC that's ...
25k 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: ...
47 views

### Scaling issue after doing manipulations in FFT

I have two filters which must apply (in series) to same input data $x[n]$ e.g of length 256 (real time asio input buffers). One filter is e.g. an impulse response $h_1[n]$ of a speaker and other one ...
210 views

### Using fourier coefficients to reconstruct data in matlab

When doing a discrete fourier transform on some data using matlab's fft function, its output is a set of fourier coefficients but I was wondering how do I go about converting these into an and bn so I ...
7k views

### Logarithmic fourier transform(LFT) on audio signal

I am trying to analyze the musics as possible as precisely. Of course I tried FFT, but got some problems. I found low frequencies have very low resolution than human's hearing. I tried very long time ...
70 views

### Is frequency resolution (“bin size” inverse) always directly proportional to sampling duration (window length)?

I am new to DSP and signal processing in general (digital or analogue). In implementing an FFT/Goertzel I have noticed that the resolution ("bin size" inverse) is directly proportional to the sampling ...
109 views

### Is it possible to approximate given skewness and kurtosis values using an IFFT?

I have time domain data for a signal that behaves randomly but has non-random (non-Gaussian?) skewness and kurtosis values of ~0.9 and ~7.4, respectively. The FFT of the signal shows that it's not ...
39 views

### For a 20 MHz channel, with 1200 usable subcarriers(18 MHz occupied), what should be the size of the FFT on the transmitter before IFFT is applied?

I am trying to simulate the SC-FDMA transmission and I read H Myung's paper and research on the topic but I am not sure exactly on what should be the size of FFT at the transmitter. For a 20 MHz ...
20 views

### Using KNN for audio classification based on FFT

I need to classify whether a product sound "good" and "bad" based on FFT of its audio recording. The FFT magnitudes are shown for frequencies from 0 to 7khz, with a frequency resolution of 5 hz, so ...
49 views

### Why autocorrelation can be more efficiently calculated using the fft

Can anyone explain why autocorrelation can be more efficiently calculated using the fft ?
69 views

### Is the FFT magnitudes of multiple audio sources additive?

Is the FFT magnitude of two audio signals when played together the sum of their individual FFT magnitudes across frequency bins? Note I'm talking only about the magnitude, ignoring phase. For ...
65 views

### Analyzing a signal that contains frequency content at Fs/2 doesn't seem to work unless there is a phase shift

I am trying to write a basic program that samples a 4 kHz sinewave at a sampling rate of 8 kHz and takes the FFT of the signal and plots it. From everything I have read, as long as the signal you are ...
30 views

### Discrete vs Continuous Power Spectrum Analysis

Let's suppose we have a time signal of watt units which in the frequency domain transforms into a sinc-like spectrum. The amplitude of that spectrum will likely be also of watt units. In order to find ...
462 views

### 1D convolution and deconvolution using FFT

The task: there is some original signal, and there is some response function. I need to convolve them using FFT and then do deconvolution to restore original signal. The task graphical illustration ( ...
106 views

### fft function in R vs spec function from 'seewave' package? They don't give a similar frequency spectra

I understand that spec will give me the frequency and the corresponding amplitude of that component, whereas fft will compute the DFT of the signal and throw the complex numbers for each component ...
60 views

### How can I graph the amplitude for a given frequency window over time?

I have simple audio files of single plucked notes from a guitar: I want to graph the amplitude of each partials over time, rather than just have this color-coded "dB" intensity graphing I have here. ...
49 views

### ACF expression using FFT method

It is known that the ACF of a 2D digital image can be obtained by computing the inverse Fourier transform ...
91 views

### How can I “smooth” square wave/pulse data to remove/reduce harmonics?

First, I have reviewed close-match questions, but can't find something that seems to match what I'm looking for. Also, it's been 30 years since college, so forgive me for forgetting stuff.. :) I am ...
61 views

### What's the difference between calculating the FFT of a constant sound for 5 seconds versus every 1 second and taking the average?

I'm interested in learning the frequency spectrum of a constant sound. However, there is background noise. My plan is to record the sound for 1 second, take the FFT, and then doing this 5 times and ...
121 views

### SNR computation in frequency domain with scipy.fftpack.fft

I have a noisy time series (gaussian coloured noise) to which I add a signal. I call the sum of noise+signal a segment. In the picture you can see an instance: I want to compute the signal-to-noise ...
37 views

### How to remove sum and difference terms while computing frequency from fft?

I am currently operating in vhf band AND trying to detect frequencies using Fast Fourier transform thresholding method. While detection of multiple frequencies , i received spurs(May not appropriate ...
79 views

### How to group similar patterns together that are shifted along the x axis?

I have a set of time series plots that are shifted along the x-axis. I am looking for an algorithm using which I can group them together. My end goal is to average them. While reviewing the ...
789 views

### Clarification on defining FFT bin sizes

When reconstructing the frequency domain for an FFT, what is the most self-consistent way to do this -- i.e. how is it best to define the bin width, $\Delta f$? For example, previously I thought it a ...
195 views

### Understanding the phase in DFT

Although using regularly the FFT algorithm to compute DFTs, I don't really understand how the phase part works. e.g. in Matlab: ...
38 views

### (FFT) Is it good practice to ignore each bin's phase when characterizing a signal

I have been recently working with the FFT and realized that each frequency within a bin corresponds to a phase. I understand why a phase that corresponds to each frequency is needed because it allows ...
5k views

### How to Average Complex Responses (and Justification)?

I am developing software that calculates the response of a system by comparing the FFT of input and output signals. The input and output signals are divided into windows and, for each window, the ...
129 views

### Power and Energy of an Audio file

I have a question about calculating the power and Energy of an audio recording. I have imported a waveform of an audio recording in WAV format into Matlab and then calculated the energy and power in ...
32 views

### What does imaginary Component of a bin's phase in the Fourier Transform mean?

I have been recently working with the FFT and realized that each frequency within a bin corresponds to a phase. This concept I have no problem with because if you wanted to construct the summation of ...
23 views

### psd in matlab, problem with the coefficient $\frac{1}{2\pi}$

Using the fft to mimic the Fourier Transform I have this question. The definition that I use for the PSD $S(f)$ is: $S(f)=\frac{1}{2\pi}\int_{\infty}^{\infty}exp(-i\tau2\pi f)r(\tau)d\tau$ where r(t)...
27 views

### Classifier for detecting abnormal noise using FFT

As a simple machine learning application for quality evaluation, I want to detect abnormal sound in a product. A good product would make a signature humming sound, a bad product might make noises due ...
41 views

### Unexpected frequency components found in Periodogram

I am trying to make sense of Digital Signal Processing with the help of R language. So, the issue came up when I tried to create a periodogram for a simple sine wave. The regular periodogram shows 2 ...
1k views

### Convolution and windowing using a buffer - how do I do overlap add?

I'm reading chunks of audio signal (1024 samples) using a buffer, applying a Hanning window, doing an FFT on it, then reading an Impulse Response, doing its FFT and then multiplying the two (...
53 views

### Is the sum of all FFT bins from Audacity equal to RMS amplitude?

Say I open an audio segment with Audacity. Then I perform a size 4096+ FFT with a rectangular window. The program outputs bin magnitude values in dB. If I add them all together like this: sum = 10*...
29 views

### how to cut off frequencies above 10 Hz with Welch method

This is the first time I have worked with any code so I am rather unfamiliar with all the lingo and processes involved. I am trying to convert a signal to the frequency domain and want to find the ...
60 views

### The DC bin of an FFT should be the mean of all the other bins in the spectrum, why does the FFT produce 0?

I am experimenting a bit with FFT's. From what I have read the first bin of an FFT is called the DC bin -- that is it is the mean of the other components in the FFT. I have also read that it should be ...
32 views

### Should you scale the FFT bins by $1/N$ where $N$ is the number of points in a transient signal?

I am going over the following tutorial. In section 2.1 the author says To calculate the $N$ point FFT the Matlab algorithm 1 can be used. Here, after taking the FFT, its magnitude is calculated ...