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

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Energy calculation in frequency domain

I was just wondering... The formula I learned to calculate the energy of the signal is expressed in the time domain: $E_x^{\text{time}} = \sum_{n=-\infty}^{\infty} |x[n]|^2 $ Then, what does the ...
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40 views

Discrete Time Fourier Transform to Frequency Domain

I failed to do this question on the exam and finding it very difficult, I would be glad if you can help me solve it. How shall I start?
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37 views

Find significant frequencies in a spectrum [on hold]

Are there any proven methods to select the few really important frequencies in a spectrum, without losing too much? My goal is to reduce computation time, for some heavy algorithm. What I tried so far ...
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50 views

Do signals with a Fourier transform with discontinuities or zero amplitude (in some frequencies) have Laplace transform?

I am reading a book on Laplace transform, and in the section on the convergence of Laplace transform for various signals the following theorem is stated, without any proof : If a signal's Fourier ...
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45 views

Removing periodic noise from image using Fourier transform

I'm trying to get rid of some periodic flicker noise through post-processing of the recorded images. The reason for these artifacts is that the electronic rolling shutter of the camera reads each line ...
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1answer
70 views

Fourier transform possible on non-rectangular part of an image

Dear Signal Processing readers, I want to introduce 'noise' into parts of images. Until now, I worked with rectangluar images for a similar purpose and did the following, using (inverse) Fourier ...
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30 views

Fourier descriptors: trying to classify objects

Describing my background: I have around 33 items labeled. For example, 3 pictures of the contour of a basil plant, 4 pictures of the contour of earphones, 7 of a mug, etcetera. I'm trying to ...
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1answer
28 views

Filtering Passband Signals using Complex Baseband Filtering

So I'm given a pass band filter with specific transfer function $H_p(f)$, I want to implement this via baseband processing. I already know how to take the input signal $u(t)$ and process it such that ...
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26 views

How to narrow the frequency band of a wavelet

I have a ricker wavelet with a dominant frequency of 15 Hz. The fourier transform shows its frequency band is almost to 50 Hz. How can I narrow the frequency band of this 15 Hz ricker wavelet? I ...
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86 views

Psudocode implementation of true envelope

I am trying to implement the algorithm described in this paper, I'll quote the relevant portion: http://recherche.ircam.fr/equipes/analyse-synthese/roebel/paper/trueenv_dafx2005.pdf Let $V_i(k)$ ...
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1answer
69 views

Conceptual question on FFT/IFFT (IFFT existence)

I was reading "Discrete and continuous Fourier transforms: analysis, applications and fast algorithms" written by E.Chu and, at some point, I found something that I could not completly understand. ...
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70 views

Using only positive frequencies in fourier domain, How will it affect the ifft?

I am going to do some kind of transformation and transform a data to another domain, and again back to the first domain. For this, I take a fourier transform of the data and separate the positive part ...
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58 views

Normalization purpose in signal processing

What is the purpose of normalizing the signal? If we have two signals on hand, how is it used when comparing these two signals?
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56 views

Converting raw I/Q to dB

I am getting I/Q data from a software-defined radio. I want to do some stuff on signals in the data, but only if it exceeds a certain range. What is the general procedure to get dB (dBm, or ...
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0answers
32 views

Spectral method for correct first derivative?

I'm trying to take the first derivative of a non-peroidic function. I'm getting a good result for periodic signals, but a bad result on a ramp like signal. How do I get an accurate 1st derivative ...
2
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1answer
70 views

Implications of $X( -j\omega ) = X^*(j\omega)$

What are the implications of: If $x(t)$ is real and $x(-t) = x^*(t)$, then $X(-j\omega) = X^*(j\omega)$ and $X(j\omega)$ is real. I am trying to understand it and I would like to research it ...
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41 views

Fourier series qn determine the fourier series coefficients

Can someone please help me with this Fourier series question: Determine the Fourier series coefficients of $x(t)$ given as $x(t) = > \cos4t +\sin8t+3$?
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1answer
55 views

non-equispaced DFT bandwidth

I need to construct Fourier transform of non-equispaced data. That is, I have signal $s(t)$, $t\in[0,T]$ sampled at non-equispaced points $t_k$, $k=0...N-1$ with sample values $s_k = s(t_k)$. For ...
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28 views

why is the DFS of a delta function equal to 1

I have a x[n] = $\delta$[n]. By formula is should be $$ X[k]= \sum_{n=0}^{N-1} \delta[n]W_N^{kn} X[k]= \sum_{n=0}^{N-1} e^{-j2*pi*kn/N} $$ The formulae isn't showing for some reason. I took a ...
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73 views

Instantaneous frequency vs fourier frequency [closed]

Lets consider a pure sine signal at $\nu$ that is chopped using square pulses (like a burst mode on signal generators). My understanding is that instantaneous frequency is $\nu$ when oscillations are ...
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30 views

Aliasing in the Short time Fourier Transform of a pulse

When attempting to take the Short Time Fourier Transform of a pulse, at the end of the pulse I'm running into problems. The signal looks like this at the end (it is a simple $sin^2$ pulse envelope, ...
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1answer
34 views

What happens to the fourier transform of sample result of $30kHz$ sinusoidal signal when sampled with sample frequency $44.1KHz$?

As the title says,w hat happens to the fourier transform of the sample output of $30KHz$ when sampled with sample frequency $44.1KHz$? I do not get how alias can appear, because fourier transform of ...
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What is the best way to construct time-domain data to minimize harmonics?

I'm attempting to use a Fourier transform in order to detect the frequency of particular types of discrete events. The events themselves are by their nature completely discrete with no duration. ...
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47 views

STFT: why overlapping the window?

For STFT, we impose window of certain size onto the original signal, then we perform fft on each window. The uncertanty about frequency and time is determined by the width of the window, however, I ...
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14 views

Short Time Fourier, What happen when window is outside the sample points

I am trying to compute STFT on the following signals..... such that they have 15 cycles of (1/50) second sine wave, with Fs=10000. The algorithm for STFT I am using is :STFT algorithm Then I set ...
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Fourier transform of triangular function

Determine $X(\omega)$. $g(t)$: I understand how to create a box from [-1,1] of amplitude 1/2. $x(t) = g(t) * g(t)$ $X(\omega) = G(\omega)G(\omega)$ the solution I am seeing says that $G(\omega) ...
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24 views

Constant-Q transform - summing complex DFT coefficients vs. summing DFT magnitudes

The constant-Q transform computes a spectrum on a logarithmic frequency axis. When analyzing music signals, this can be a more meaningful representation than the Discrete Fourier Transform (DFT), as ...
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14 views

Wiener filter of two signals of comparable magnitude

Suppose I have two signals, x(t) and y(t) (e.g. from a Lock In amplifier, such that x(t) and y(t) are 90 deg. out of phase). Assume x(t) is the clean signal, s(t), plus background noise, while y(t) is ...
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229 views

Conceptual question on FFT and chirp signal

If I take the FFT of a sinusoid I will get a plot whit all the energy of the signal concentrated at the sinusoid frequency. But what happens if I have a signal in which the frequency keeps ...
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1answer
106 views

Regarding Bode plots; $H(s)$ and $H(j\omega)$

In circuit analysis, I understand the use of Laplace Transforms to obtain the impedance of a linear RLC circuit, ie transforming from the time domain to the frequency domain. In most texts I have seen ...
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39 views

Basic Fourier Transform filtering and LTI frequency response using Matlab

Not sure if this is the right place to ask... I'm new to Matlab for LTI signal processing and wondering if anyone can help with something that I'm sure is meant to be basic. I've spent hours and hours ...
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How do I take the real part of this bandpass filter system's output?

I'm stuck on a final step in this problem. Essentially, there are the two systems above, which we'll call System 1 (Fig. 4.26, with ideal lowpass $H(jw)$) and System 2 (with $H_1(jw)$). The ...
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32 views

Motion Blur Filter

I want to implement Motion Blur Filter in C# using Emgu CV, what is the correct way to do this in fourier domain. I am currently stuck at how to perform multiply of Motion Blur filter and my Complex ...
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170 views

Why is a negative exponent present in Fourier and Laplace transform?

could anyone explain why there is a need of negative exponent in fourier and laplace transform.I looked through the web but I couldn't get anything.Does anything happen if a positive exponent is ...
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1answer
44 views

Fourier Transform Problem - absolute value, time-saving tricks, etc

I am given the following signal: $$[e^{-at}cos(w_{o}t)]u(t),\ a>0$$ Then I am told to find the Fourier Transform, which tells me I need an answer of the form: $$X(jw)=\int_{-\infty}^\infty \! ...
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DSP interview question: use of the identity in development of a significant transform

I'm preparing interview and found this question. But I don't really understand what is the question. Does it ask about Fourier transform or Z transform? How the simple identity $$xy=\frac{1}{2}x^2 ...
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1answer
44 views

Why doesn't JPEG use 1D DCT for image compression?

I know that JPEG uses 2D dct and splits the images in 8x8 blocks. Why doesn't it simply split the image in one-dimensional vectors in $\mathbb{R}^{64}$? Wouldn't it simplify the math? My guess is that ...
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How does taking the absolute value of a complex signal reflect in the frequency domain?

I have a frequency-domain representation $F[n]$ of the complex discrete one-dimensional signal $x[n]$: $F=\mathcal{F}(x)$. Is there a frequency-domain transformation of $F$ into $F'=\mathcal{F}(|x|)$? ...
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Realization of IIR resonator

The measure of a given frequency $\omega$ in a signal $x(t)$ is: $\frac{1}{N}\sum\limits^N_{t=0}x\left(t\right)e^{^{-i \omega t}}$ This is basically an average of the correlation between the signal ...
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53 views

Find the frequency response of the system

How can I find the frequency response of the following linear system
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35 views

DFT of a pressure signal from space domain to wavenumber domain

When I do the DFT of the following signal: I get the following DFT which doesn't capture any peaks at all: Why is this? I'm not really able to identify what the error is?
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1answer
52 views

Spacing between gaussian windows for STFT

I'm computing discrete short time Fourier transform. Data is split into overlapping chunks and gaussian window is used for each chunk. However, I'm not sure how much overlap there should be between ...
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168 views

[2D fourier transform]: Most people can't explain this

I am confuse of 2d magnitude plot of the spectrum frequency. So we have 2 images, the first one is shown at the top, and the expand version of the white box is shown at the second row. For the ...
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1answer
119 views

Comparing the FFT to numerical integration in Matlab

The result of calculating the fourier transform using numerical integration is: the result of using Matlab's FFT is: So where did I go wrong here? I know the FT of a Gaussian should be ...
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1answer
70 views

What is the best Algorithm to estimate the frequency for Almost-Periodic Data or complex periodic data?

I’ve got what it looks like a periodic signal but the periods seem not equally repeated, I want to estimate the PSD, particularly I need to obtain the dominant frequency of this data. I’ve estimated ...
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63 views

Purpose of Phase Information

I am learning Fourier Transform from many days but till now I am not able to understand what does phase angle image show us or tell us? They say that MAGNITUDE tells "how much" of a certain frequency ...
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34 views

Frequency of the wave in frequency domain

If we have a 1-dimensional wave in time domain, it can be represented in frequency domain with x axis indicating the frequency of the wave and y axis indicating amplitude/magnitude of the wave. But ...
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1answer
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Frequency Spectrum of an image

I have been studying about Frequency Domain from many days but still i am not able to clear one of the confusion. We say that in frequency domain an image is represented as waves. What I am able to ...
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2answers
175 views

Discrete Fourier Transform by hand

I have an assignment where I'm given the DFT of a sequence $x[n]$ as $X[k]=\{4,3,2,1,0,1,2,3\}$ and also $$y[n] = \left\{ \begin{array}[cc] xx[n/2] & \text{if n is even} \\ 0 & ...
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81 views

Audio noise detection with python

Have many audio files 1 minute long. Some of them are normal. Some of them are noise. Here is a normal file: This is a noise: And this is noise too: How do auto detect noise using python? ...