Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

1,645 questions
Filter by
Sorted by
Tagged with
1k views

What should the amplitude be when plotting 1-sided Amplitude Spectrum?

I have a continuous signal x(t) such that $x(t)=12cos(6\pi t)+6cos(24\pi t)+3cos(30 \pi t)$ and is asked to sketch a 1-sided Amplitude Spectrum of the signal x(t) if sampled above the minimum ...
1k views

Analysing 2500 frequencies using FFT with an input vector of 2048 samples?

I am currently reading the paper A Highly Robust Audio Fingerprinting System and on page 4 one can read about the technical parameters they use: Sampling rate of 5000 Hz, frames of 2048 samples as ...
1k views

Sense of zeropadding in a time domain

I have the task related to Radon transform which contains a subtask which uses resampling by means of DFT. Let's consider the non-periodical discretized signal (Fig.1) (for example the string of ...
12k views

How do I create a frequency vs time plot?

I'm a chemical engineer, not an EE, so this is a bit difficult. I'm trying to figure out how to take amplitude vs time data and transform it into frequency vs time. My first instinct is to slice my ...
1k views

Correlation filter output range normalization

I'm developing correlation filters based image recognition. I implemented MACE correlation filter in matlab: training code: ...
321 views

Channel Vocoder producing output with “click” sounds

I'm trying to make a channel vocoder that takes two inputs, one a frequency rich carrier (a musical sound) and the other a modulator (vocals). Applying operations involved in the channel vocoder ...
10k views

Conceptually, how does a Fourier transform differ from an autocorrelation?

I realize the two are derived using different algorithms, and the units are different, but from a conceptual standpoint of the information they provide how do they differ? I'm thinking here about the ...
5k views

FFT with asymmetric windowing?

Common non-rectangular window functions all seem to be symmetric. Is there ever a case when one would want to use a non-symmetric window function before an FFT? (Say if the data on one side of the ...
19k views

What is the sparse Fourier transform?

MIT has been making a bit of noise lately about a new algorithm that is touted as a faster Fourier transform that works on particular kinds of signals, for instance: "Faster fourier transform named ...
593 views

Books that explain DSP well to those not directly in engineering?

I do work with computer graphics and am dipping my toes into ray tracing. That field involves a good number of the subjects covered in DSP (Fourier transform, time vs frequency space, etc) but I was ...
417 views

How to generalise the Fourier transform?

The Fourier transform takes a signal and splits it into a series of sine and cosine waves. I am told that it's supposed to be possible to split a signal into some other set of functions. My question ...
307 views

How to calculate the gain in a bivariate fft in R?

In Statistica gain is defined as follows: Gain. The gain value is computed by dividing the cross-amplitude value by the spectrum density estimates for one of the two series in the analysis. ...
843 views

Solving a Convolution Problem of a 1D Signal

I'm finding in trouble trying to resolve this exercise. I have to calculate the convolution of this signal: $$y(t)=e^{-kt}u(t)\frac{\sin\left(\dfrac{{\pi}t}{10}\right)}{({\pi}t)}$$ where $u(t)$ is ...
4k views

Real-Time Human Pitch Detection

I'm trying to implement a singing game that will analise raw mic input and tell the player how good is he singing. That needs to be done in real-time. I've come across a lot of threads asking the ...
258 views

plotting phase of a signal adding delay

I'm trying to plot the phase of this signal $s(f)=A^2T^2sinc^2(Tf)e^{-(j\pi Tf)}$ How can I plot manually this signal?I have to follow some particular rules?I have problems with the delay. Edit ...
452 views

631 views

How to combine a rotation matrix and a stretch matrix into a single matrix for easy Fourier Transform

For full disclosure, this is related to homework. I have to find the Fourier Transform of a function that I've boiled down to the following. I have a function $f(x,y)$ that I can think of as another ...
8k views

5k views

What is the most lucid, intuitive explanation for the various FTs - CFT, DFT, DTFT and the Fourier Series?

Even after having studied these for quite sometime, I tend to forget (if I'm out of touch for a while) how they are related to each other and what each stands for (since they have such similar ...
238 views

Deriving 2-D discrete Fourier transforms

I have a problem in DFT. It was one of my past-year exam papers questions. Question: Let $F(u,v)$ be the 2-D Fourier transform of a 2-D continuous function $f(x,y)$. Derive in terms of $F(:,:)$ ...
2k views

Whats the optimal window function to use for analyzing real-time data samples?

Say you wanted to run a X point FFT on the last X audio samples that were played. The problem being, using a normal hann window function would place emphasis on the "middle" of the audio sample. ...
4k views

Harmonic Product Spectrum limitations in pitch detection

I've made a pitch detection algorithm using HPS and I'm facing a problem. I'm a beginner with signal processing and this site helped me before, so I though I should ask. For higher pitches ( ...
4k views

Choices of convention and notation for the Fourier transform?

The definitions of the Fourier transform and inverse Fourier transform I learned in college were $$F(j\omega) = \int_{-\infty}^{\infty} f(t) e^{-j\omega t}\ dt$$  f(t)=\frac{1}{2\pi}\int_{-\...
5k views

Using the Inverse Filter to Correct a Spatially Convolved Image (Deconvolution)

As part of a homework assignment, we are implementing the Inverse Filter. Degrade an image then recover with an Inverse Filter. I convolve the image in the spatial domain with a 5x5 box filter. I FFT ...
6k views

How to get coefficients for sine/cosine function from complex FFT?

I'm working on a control system that measures the movement of a vibrating robot arm. Because there is some deadtime, I need to look into the future of the somewhat noisy signal. My idea was to use the ...
53k views

What effect does a delay in the time domain have in the frequency domain?

If I have a signal that is time limited, say a sinusoid that only lasts for $T$ seconds, and I take the FFT of that signal, I see the frequency response. In the example this would be a spike at the ...
11k views

Tips for improving pitch detection

I'm working on a simple web app that allows the user to tune his/her guitar. I'm a real beginner in signal processing, so please don't judge me too harshly if my question is inappropriate. So, I ...
9k views

RMS calculation in frequency domain after windowing

I can calculate RMS in frequency domain as derived from Parseval's Theorem. But what if I have applied a windowing function before doing the FFT (in my case a Hann window)?. Now the RMS values are ...
440 views

Am I handling offline FFT correctly?

I need some help clarifying FFTs and what they represent. I have a buffer containing compressed audio. Due to limitations, I can't handle the full uncompressed audio but can decompress small segments ...
557 views

Recognizing math functions within songs

I'm new to DSP, and just discovered this StackExchange, so apologies if this isn't the right place to post this question. Is there a resource that describes genres in a more mathematical terms? For ...
5k views

Complex conjugate and IFFT

I asked a question over on stack overflow. I'm having a slight problem however. As suggested by Paul R I am mirroring my lower $n/2$ bins into the upper $n/2$ bins. I have a few questions however. ...
12k views

How do I optimize the window lengths in STFT?

I have many EEG signals and I want to analyze them using linear methods such as STFT (Short Time Fourier Transform). In STFT , How can I optimize the analysis window length, to reflect the frequency ...
195 views

Is it possible for a signal to be represented by *both* sinusoidal *and* rectangular/triangular Fourier transforms?

A signal might have both continuous and discrete parts (where the "discrete" parts are regions where a sinusoidal Fourier transform would be subject to unnecessary Gibbs Noise). So I would think that ...
524 views

In Fourier transforms, can momentum space be analogized to frequency, and position space be analogized to wavelength?

We know that in quantum mechanics, momentum space is the fourier transform of position space (and vice versa) And also, in time-series analysis, that frequency (of cycles) is the fourier transform of ...
1k views

How do you measure “detail” of a signal?

I have an image and I would like to measure the amount of detail in it. Another way to look at it is to measure how blurry an image is. One way is to analyse the high frequency components in the ...