# 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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### Phase Correlation and Negative Shifts

I am implementing phase correlation algorithm to determine shift between two images. It generally works, but I am not sure how to interpret the resulting shift. Pseudocode: ...
140 views

### Feature Selection by Filtering

so there is this paper I'm reading and trying to understand fully: Towards Practical Identification of HF RFID Devices http://dl.acm.org/citation.cfm?id=2240276.2240278 I don't want to link the PDF ...
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### FFT spectre graph measurements y-axis

I am very new to this things. Sorry for probably stupid question. I don't understand what units and meaning have the values on Y-axis of Fourier Transform graph? On X-axis it is Frequency (Hz). Pretty ...
298 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 ...
171 views

### Fourier transform of a damped cosine wave with a linear frequency chirp

I want to take the Fourier transform of the following transient signal, $$f(t) = e^{-t/\tau} \cos((\omega_0 + m t)t)$$, where $m$ is some gradient parameter in units of $\rm{Hz}/s$. I thought this ...
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### Evaluate Fourier coefficients at arbitrary point using Python

Lets say I have a sinusoidal function $s$ that looks like ...
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### Convolution of signals sampled on a logarithmic grid

Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
116 views

### Use samples of Fourier transform as DFT?

Consider the LTI system given by: $H(z) = 1 - \frac{1}{2}z^{-1}+\frac{3}{4}z^{-2}$ Let $x[n] = (\frac{1}{2})^nu[n]$ be the input to the system. We want to find the output for $n = 0,1,...,N_a$, using ...
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### What's spectral “tilt”?

I am looking at article Speech-in-noise intelligibility improvement based on spectral shaping and dynamic range compression. In paragraph 2.2 the article mentions "tilt" of the spectral envelope. The ...
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### Can you use Fourier transformations (or other) to read multiple superimposed barcodes?

If you printed bar codes on tracing paper/acetate etc. and then positioned several in front of one another, could you extract the individual codes from the aggregate overlaid image? I feel intuitively ...
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### How to calculate the energy in the dirac delta function signal?

I'm having DSP for the first time, and after some classes I got confused about the following: Suppose I have a signal which its fourier transform in a frequency band $[ \omega_1,\omega_2]$ is just a ...
258 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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### To what extent can we see signals that fall between frequency bins?

I have a simple problem I would like to figure out for fourier analysis of seismic data. Let us say that we have a signal $z[n]$, of length $N$. If I take its (same size) FFT, I will get $Z[k]$, ...
742 views

### What features describe audio signals? (Besides frequency and amplitude)

I recorded sounds with a microphone and I try to distinguish them in my Java program. The frequency works quite good, but if I look at the fourier transforms it seems like there should be more ...
363 views

### Can use of Fourier transform be minimized completely with the help of Laplace and Z transform?

Fourier transform has different types like continuous Fourier transform (CFT), Discrete time Fourier transform (DTFT) and Discrete Fourier transform ( DFT). CFT can be used in case of continuous ...
2k views

### Why Fourier transform is not sufficient and we have to use Laplace transform? [duplicate]

Is there an easy way to explain the motivation behind the use of Laplace transform instead of Fourier transform? Isn't that any periodic function can be represented by sines and cosines? - Why to ...
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### When is the Fourier transform of a signal periodic?

I mean not the time-domain signal being periodic, but the Fourier transform being periodic.
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### Why does the frequency in the DFT have to be an integer?

I don't know why the result of DFT and FFT in MATLAB like below images.. fs=128; t=0:1/fs:1-1/fs; x=cos(2*pi*3.5*t); X=fft(x); N=length(x); n=0:N-1; f=fs*n/N; plot(f,abs(X)/N); If I set the ...
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### How does the RaspberryPi radio hack convert digital GPIO signals to an FM signal?

After having looked at various explanation of how the RaspberryPi FM transmitter hack works, I realize there are some fundamental pieces missing. Most explanations talk about how to construct a ...
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### Why are Fourier analysis and transform only applicable for LTI systems?

Why are Fourier analysis and transform only applicable for LTI systems? What if the system is not LTI, won't Fourier analysis or transform be possible?
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### Implementation of Fourier Domain Denoising with Hard Threshold

I just tried the Fourier denoising method with a hard threshold and my code is as follow: ...
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### FFT method input argument have to be $2^n$ ?

Does FFT method input argument have to be power of 2, i.e, $2^n$ I just realized there are many algorithm for FFT implementation,...
I cannot understand some part of the period signal's Fourier transform. Here this my note's methods, For periodic signal with period $T_0$, define as $s_{T_0}(t)$ as $$s_{T_0} (t) = \begin{... 2answers 4k views ### FFTs of a complex signal - separating the real and imaginary parts I have a complex time varying signal at a single frequency x = a + jb where a represents the contribution from the cosine basis ... 3answers 649 views ### How can I comprehend the complex coefficient of complex Fourier series? Is there a way to understand visually the complex coefficient of Fourier series (shown as C_n in many sources)? I mean something similar to this which represents e^{j\omega_0 t}: . \omega_0 \... 1answer 169 views ### Whether Fourier transform formula be considered as Convolution or Correlation? The expression for Fourier transform is given as$$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^{-j \omega t} \ dt \tag{1}$$Now, let one function be f(x) and other be e^{j\omega t} ... 2answers 755 views ### Intuitive explanation of the Fourier Transform for some of the functions Does anyone have a mechanism to understand intuitively (and automatically) why the Fourier Transform of certain functions have certain shapes (at least for some functions, not necessarily for all)? I ... 2answers 683 views ### What does boundary discontinuity in DFT imply? I have been studying about boundary discontinuity in DFT and why it is not used as transform in image compression. What i understand is that DFT is N periodic and that causes a discontinuity at the ... 3answers 1k views ### What does the negative sign mean in the image frequency domain? When I transform an image from the spatial domain to the frequency domain, some frequencies are negative. What is the meaning of the negative sign? For example: 2answers 2k views ### Find h[n] using DTFT properties Using the DTFT property, find h[n] of a system where: Is it an FIR or IIR system? 3answers 366 views ### Transfer function of a frequency shifting system There is a system which shifts frequencies of input by -Fc such that: Y(S) = X(S).H(S) But X(S) has value zero from 0 to Fc. I am confused on how the product of X(S) and H(S) becomes a positive ... 3answers 192 views ### Robust phase extraction of STFT bins I am interested in tracking how the phase of a signal at a particular frequency changes over time. The method I am using calculates a series of STFTs and takes the arctangent of the imaginary and ... 1answer 1k views ### Difference between 2\pi f and \omega in Fourier transform What is the difference when we use e^{-j2\pi f} and e^{-j\omega n} for Fourier transformation? 2answers 379 views ### Can one generate a signal with an asymmetric power spectral density? My question is as follows. I know that classically speaking, if you have some time varying signal X(t) its power spectral density S_X(f) will be symmetric around f=0 as the signal is real. This ... 1answer 2k views ### How to Flip Spectrum Around DC? Is it possible to flip a signal's spectrum around DC? I have a simple spectrum that I made up (MATLAB code): ... 1answer 183 views ### Testing discrete data for periodicity I have some data which looks roughly periodic - is there a nice way to measure this? This is an example I'm working on and I'd like a metric that I will be able to just threshold to give a decision ... 2answers 460 views ### Fourier Decomposition Hello everyone have a look at this video of Fourier Decomposition of an image(otherwise you can also refer the image which shows few plots of different extracted waves from an image) . We also know ... 3answers 567 views ### Analyse audio/music frequencies without STFT, at 1/f temporal resolution, using probe phasors at logarithmically-spaced frequencies, O(N log N)? First, some background: The STFT is the best general-purpose tool I know of for analysing a (musical or other) signal into its component frequencies. For many purposes the STFT works fine, but there ... 1answer 325 views ### Benefit to know Fourier series for image processing? [closed] I know there's a benefit of knowing the Fourier Transform for image processing, but is there a benefit to know Fourier series, or could you just skip them? Would you recommend skipping Fourier series ... 1answer 404 views ### How can I find the amplitude of the 20 Hz frequency component of a signal faster? I have a time varying discrete signal x(t) sampled at 5ms rate. I need to find the amplitude of the 20 Hz frequency component for each sample. What I do today is that for each sample I do a Short-time ... 1answer 277 views ### How can I detect clicks/ticks in a wav file? I have a long recording of a train (here is a small sample) there are a number of clicks as the wheels go over joins in the tracks. I would like to detect the location of these. Looking at the ... 2answers 246 views ### Sinc interpolation in spatial domain I have tried to perform sinc interpolation (in 1D) with the following Matlab code: ... 1answer 273 views ### Proving that the IDTFT is the inverse of the DTFT? The DTFT is given by:$$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty}x[n]e^{-j\omega n}$$The IDTFT is given by:$$x[n]=\frac{1}{2\pi}\int_{0}^{2\pi}X(e^{j\omega})e^{j\omega n}d\omega I have been ...
If i take the Fast Fourier Transform (FFT) of a cosine function, what has turned this cosine function into its complex exponential form which consists of $e^{i \omega t} + e^{-i \omega t}$ ? Because ...