Questions tagged [fourier-transform]

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

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How does causality (i.e. unit step) affect the DTFT of a sine or cosine wave?

Tables of common Discrete-Time Fourier Transform pairs list the transform of a sine wave: $ \sin(\omega_0\ n) $ and its transform: $ -j\pi\ [d( \omega\ - \omega_0\ ) - d( \omega\ + \omega_0\ )] $ ...
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WAV encoding problem

When processing wav files, I encounter this problem: the what I extract PCM from a 8-bit encoded .wav file, I got a sequence of integers. However, when verifying my implementation with ...
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How to 'interpret' the Fourier Transform (specifically, of a convolution kernel)

As part of a homework assignment, I had to take the Fourier transform of the kernel I was using to convolve a signal. The kernel was a constant rectangular function, that was 1 within the square $(-1,...
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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 ...
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How does shift and scaling inside of a function affect its Fourier Transform?

The properties aren't entirely clear to me, sorry for the basic question. I know the Fourier Transform of one function. Say, $\text{rect}(x,y) \Leftrightarrow \frac{\sin \pi u}{\pi u} \frac{\sin \...
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Discrete-time Fourier transform

I am a junior high school student who has a general fascination for electronics, programming, and the like. Recently, I have been learning about signal processing. Unfortunately, I haven't done much ...
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Basic question about trigonometric series and transforms thereof

I would like to know the relation between the parameters $\{\omega_k,A_k\;|\;k\in\mathbb{Z}\}$ of a series $\sum_kA_ksin(\omega_kx)$ and a related series, for example, $\sum_kA_k^2sin^2(\omega_kx)$. ...
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Find h[n] using DTFT properties

Using the DTFT property, find h[n] of a system where: Is it an FIR or IIR system?
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Calculating smoothed derivative of a signal by using difference with larger step=convolving with rectangular window

I have a signal sampled at $\Delta t: fi(ti=i\Delta t)$ where i = 0..n-1. I want to find the first derivative of the signal: f'(t). My first thought was to estimate this by a central difference: $f&#...
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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 ...
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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 $F(:,:)$ ...
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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. ...
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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 ( ...
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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_{-\...
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Using the Inverse Filter to Correct a Spatially Convolved Image

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 ...
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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 ...
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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 ...
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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 don't judge too hard if my question is inappropriate. So, I managed to get ...
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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 ...
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1answer
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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Why is the Fourier transform so important?

Everyone discusses the Fourier transform when discussing signal processing. Why is it so important to signal processing and what does it tell us about the signal? Does it only apply to digital signal ...