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# 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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225 views

### Creating an array whose DFT is all whole numbers

I'm working on a simple FFT implementation and currently running some unit tests. Long floating point numbers in C and assembly become very hard to keep track of, and this whole thing is error prone. ...
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### Removing drift from integration of accelerometer data

I am trying to get a positional data from the accelerometer data using the following steps: Re-zero the accelerometer value Removing mean from accelerometer value First integration of accelerometer ...
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### Non Uniform FFT / DFT with FFTW?

Can FFTW perform the FFT on data which is not uniform in time? I can't seem to find a straight-forward answer to this question anywhere online.
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### PSD estimate using FFT - scaling and units

I know that similar questions have already been asked – I have read the answers, yet I am still not sure if I understand the topic properly at some points. I want to use FFT to calculate PSD ...
564 views

### Mapping the value of a sample in a 2-D DFT to cycles/pixel

If I have an image and its 2-D DFT of that image, what is the mapping between the value of the DFT at (u,v), and the frequency in the spatial domain in the x and y components, in cycles/pixel? I want ...
462 views

### What is a Phase Delay filter?

I'm looking at a job spec, detailed below. I'm perplexed as to what is being asked for. Could someone offer a basic understanding of this material? I can imagine a solution may involve performing ...
634 views

### High Level Process, Calculating Cepstrum When You Only Have Spectrum

I am not a DSP expert, so I would like someone to check my thought process: I have a text file representing the spectrum (calculated by some FFT hardware), and I'd like to calculate a cepstrum. I'm ...
4k views

### Best way to resample a signal (image)?

I have an original image $\ I(x_i,y_j)$ where $\ x_i = i*\Delta x, 0<= i < n_i$ and $\ y_j = j*\Delta y, 0<= j < n_j$ I am trying to implement a function that resamples the image ...
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### FFT, How to decide if there is a signal among noise?

I have sets of data of different deep sky objects. My job is to check for any periodicity. I use IDL to run an FFT and wavelet methods to check for a signal. To test my code I ran the IDL built in ...
214 views

### Is there a “first” Fourier transform?

Every time I've read "first Fourier transform", I've assumed it to be a misspelling of the fast Fourier transform. Recently though, I saw the term in both the title and keywords of an article from a ...
241 views

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### Is it possible to do single vehicle tracking using Fourier transform?

I am working on a project in image processing which is based on importance of phase only reconstruction of a signal obtained using Fourier transform.For more information about phase only ...
3k views

### OFDM transmitter bandwidth

Theory Suppose an OFDM transmitter with four subcarriers is implemented using the structure shown below. If the serial data input rate is 40 bps, each parallel stream will run at 10 bps. ...
1k views

### How to Apply Window Functions in Frequency Domain?

I am trying to apply a window function to smooth my signal and finally obtain the peaks of the signal. Yet, for spectral leakage I apply window function in time domain. After taking the Fourier ...
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### Effect of sampling interval length and Gaussian noise on the frequency-spectrum

Suppose you have a signal $s(t)$, corrupted by Gaussian noise of $\eta(t)$ with zero mean and standard deviation $\sigma$. So that the measured signal is $f(t)=s(t)+\eta(t)$. I now want to calculate ...
366 views

### Is $O (N \log N)$ FFT speed the fastest we can ever attain?

I am wondering about whether or not there is a theoretical limit as to the speed at which we can compute a DFT. We all know that the FFT executes in $O (N \log N)$ time. However, is this a lower bound ...
6k views

### How to Remove the Periodic Oscillations from a Signal

The task that I have is to remove the annual and semiannual oscillation from a set of temperature measurements, taken over several years, by means of least squares method. I found the method ...
57 views

### Transform Length and event duration

Does the length of a Fourier Transform affect the ability to discern a small event in the data? This is a tricky question to ask, let me clarify. I don't care about when the event happened and I don'...
420 views

### 2D Convolution in MATLAB Causes Artifacts (Boundary Issues)

I`m trying to do a 2D fast convolution in Matlab of large matrices. If I use FFT version based on convolution theorem ( https://en.wikipedia.org/wiki/Convolution_theorem ), there are some artefacts in ...
277 views

### Why isn't the Hartley Transform more widely used?

I was doing a bit of research on FFT and I came across this paper. According to it, computing the Fourier Transform using FHT is significantly faster than other methods, even for complex data. Yet, ...
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### Speech Recognition - Project Idea

Wondering if someone could offer me any advice or help. Sorry if this question is too broad or anything. I'm wanting to complete an algorithm in basic Speech analysis. The algorithm will detect ...
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### How to build a program that gives you on the fly the chords of the song while listening to it?

I am trying to think how can I program a SW that can recognize Chords on the fly. since I know nothing about music, Can I assume that the chords are orthogonal and unique? I guess I can since it is ...
740 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 ...
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### Zero-pad before or after windowing for FFT

What's the correct way. Should I zero-pad a signal before or after applying a windowing function?
$x[n]$ 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+...