Questions tagged [fourier-transform]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
441 views

Relation between the DTFT and CTFT in sampling- sample period isn't as the impulse train period

I will quote an answer of Matt L. from this post (I didn't comment there because I can't) If you have a continuous-time signal $x(t)$, then the two signals you're talking about are $$\begin{...
0
votes
1answer
279 views

Detection of Troughs and Notches in a PPG Signal

I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below... I'm having problem in finding the troughs and dicrotic notch for ...
0
votes
1answer
60 views

FFT for distance-limited sum of pairwise products

I have a sequence of fixed length $N$ input arrays ($x_0$, $x_1$, ..., $x_{n-1}$), and my goal is to compute output arrays as such: $$d_{00}[l] = \sum_{i = 0}^{N - l} x_0[i]x_0[i + l]$$ $$d_{01}[l] = ...
0
votes
2answers
64 views

What to do for the right FFT in Matlab (two peaks and incorrect amplitude)?

This is the FFT I'm using. But two peaks (did not expect the one in the beginning) are occurring and the amplitude is not as specified (expecting a value of 2). Any help is much appreciated! ...
1
vote
4answers
1k views

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 ...
0
votes
1answer
59 views

how to guess what the interference source it could be

At work, we are in an industrial area, and there is always a signal that I receive inside my office which interferences with my tests. This signal is in the 433 MHz and when I see the spectrum, ...
1
vote
0answers
32 views

Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...
0
votes
1answer
113 views

I want to get impulse response of causal system

I want to get impulse response of this causal system on first photo. So I got frequency response on second photo from this system. and now I am trying to transform this frequency response to impulse ...
0
votes
0answers
267 views

PHAT filtering for cross-correlation yields wrong results while simple cross-correlation does OK (Python)

I work with two signals, the second being perfectly delayed and attenuated, with no reverberation. I implemented cross-correlation algorithm, which yields me these results: Here is my code for these ...
1
vote
0answers
127 views

Graph signal processing

What's the intuition behind a ''Graph fourier transform'' ? I'm not so much interested in mathematical details or technical applications. I'm trying to grasp what a graph fourier transform actually ...
1
vote
4answers
1k views

DFT (FFT) of a Real Even Function Doesn't Yield Real Only DFT Signal

There are a lot of similar questions already, but I can't find one answering this problem. I used the following MATLAB code to perform the FFT on a Lorentzian input signal ...
1
vote
1answer
71 views

Accuracy of time domain signal when one frequency is absent

Suppose the known frequency spectrum of a signal is: $$ G(n\Delta f)=9,4,3,5,1,6,... $$ where $n=0,1,2...$ and $\Delta f=1$ Hz If, for some reason, we cannot sample $G$ at $n=0$ (i.e. $G(0)=9$ is not ...
-1
votes
1answer
109 views

In a periodogram, why is the modulus squared of the DFT taken rather than the DFT itself? [duplicate]

Why can't you just take the DFT itself? And how accurate is this method in spectral density estimation? Are there cases in which it is very accurate?
0
votes
1answer
45 views

How to Calculate the number of DFTs taken in a STFT

Given variables of window size (W), overlap (O), and length of the Signal (S) (in my case, length of a song) and I am trying to determine an equation that gives me the number of DFTs that would be ...
2
votes
1answer
299 views

Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
2
votes
1answer
2k views

STFT amplitude normalization, librosa library

So librosa.core.stft returns a complex single sided spectrogram. My question is: What normalization of the amplitude values should I perform afterwards? I believe I have to multiply the amplitude ...
0
votes
1answer
109 views

Question about time shifting property

I know that time shifting property of discrete-time Fourier Transform states that $x[n]\leftrightarrow X(e^{j\omega})\implies x[n-n_0]\leftrightarrow e^{-j\omega n_0}X(e^{j\omega})$ So given a signal ...
1
vote
1answer
196 views

Bandwidth of Information Signal

I have trouble finding the bandwidth of a signal. Say I have an info bearing signal m(t)=sinc(2t/pi). I found the fourier transform of the sinc function and found that the angular frequency was 1/pi. ...
1
vote
1answer
67 views

Discretization of Sinusoidal Signals

How do I should sample two continuous sinusoids of $f_1$=1/4 Hz and $f_2$=1/2 Hz at a 1 Hz rate? Can i recover both if i bandlimit after sampling at a 1/2 Hz limit?
0
votes
1answer
350 views

Should scipy.signal.coherence be 1 for single input and output signals?

I am trying to calculate the coherence between input and output signals. I thought I could work with a single input and a single output time series and calculate the coherence $\gamma^2$ between them. ...
0
votes
1answer
257 views

Signal squared in time domain

In some publication I have found a formula that for some reason squares signal in time domain. I am analyzing it now. What should be the Fourier transform of a signal that was squared in time domain? ...
1
vote
1answer
142 views

CMV: COLA constraint is not necessary

In the literature on the short-time Fourier transform (STFT) it is often stated or implied that the constant overlap-add (COLA) constraint must be satisfied in order for the STFT to be invertible. ...
2
votes
1answer
404 views

How to calculate a delay between two signals in frequency domain?

Calculation of a delay between two signals is generally done by finding the maximum in the cross-correlation of the two signals (in time domain): $$ \tau_{delay} = \arg\max_\limits{t}(f(t) \star g(t)) ...
1
vote
2answers
796 views

Hilbert transform of unit step function

How to calculate Hilbert transform, if it exists, of the signals like $u(t)$, $sgn(t)$. What properties should a function satisfy for existence of Hilbert transform. Absolute integrability of a ...
2
votes
2answers
101 views

How does sampling rate of $x[n]$ relate to sampling rate in frequency domain after DFT transformation?

I've got an analog signal $x(t)$ sampled at frequency $F_s$ to obtain samples: $$ x[n] = x(t) \bigg|_{t=n/F_s} $$ I transform this signal with DFT defined as: $$X[k] = \sum_{n=0}^{N-1}x[n]e^{-i2\pi ...
8
votes
2answers
2k views

Wikipedia equation for DFT seems to be bad?

I was writing a simple fourier transform implementation and looked at the DFT equation on wikipedia for reference, when I noticed that I was doing something differently, and after thinking about it ...
0
votes
0answers
85 views

Find cepstrum of a function with dirac function

$$x[n] = d[n] + a\cdot d[n − N_p]\ ,\ \ |a| < 1$$ I need the complex and real cepstrum of this function as well as what would happen for $N=N_p/6$ for the DFT approximation $$x_p[n] = \frac{1}{N} ...
0
votes
1answer
172 views

Uncertainty Relation between time and frequency

Typically, humans can hear sound waves in the frequency range 20 Hz to 20 kHz. If one wants to make digital record of sound such that no audible information is lost, what is the longest time interval ...
1
vote
2answers
789 views

Why is the Fourier transform valid only for absolutely integrable signals?

Why is the Fourier transform valid only for absolutely integrable signals? For example, why can't we do the Fourier transform of exponential order functions?
0
votes
2answers
482 views

Amplitude of signal and PSD peak height

So, suppose you have a superposition of cosines of the same magnitude: $\sum_{i}\cos[\omega_i t]$ When you take the Fourier transform, theoretically you'd expect to find $\delta$-like peaks of the ...
1
vote
1answer
114 views

Inverse DFT to a real signal when only odd harmonics are present

There is an old paper by L.R. Rabiner, "On the Use of Symmetry in FFT Computation" which describes (among other things) an optimized method to calculate the DFT of a real signal $x_n$, $n=0,\dots, N-1$...
1
vote
1answer
7k views

How to find the phase spectrum of a rectangular pulse? (Fourier Transform)

How to find the phase spectrum of a rectangular pulse? The Fourier transform of a rectangular pulse $$ x(t) = \begin{cases} 1, & \text{for $|t| \le \tau /2$ } \\ 0, & \text{otherwise} \end{...
1
vote
1answer
1k views

Understanding Magnitude Spectrum of Images [closed]

I am facing problem in reading Fourier domain of a given image. I don't understand what to interpret from it. For instance, consider this image. Ok, so there is a dot in the middle, with some ...
-2
votes
2answers
1k views
1
vote
3answers
145 views

Demonstrate that $x(t)$ and $\hat{x}(t)$ are orthogonal

I have to demonstrate that a function $x(t)$ and his Hilbert's transform are orthogonal, it is said: $$\int^{\infty}_{-\infty} x(t) \cdot \hat{x}(t) dt = 0$$ I have tried the exercise using Parseval'...
0
votes
2answers
2k views

Why is the size of the output of the FFT of a signal is same as the size of the input signal?

I am kind of new to the DSP domain. I was trying to get the frequencies associated with a signal by performing FFT over it. I used numpy.fft.fft for this. ...
0
votes
2answers
234 views

Understanding where the constant $2/N$ comes from in Fourier transformation

I'm implementing Fourier transformation in my analysis and I wanted dig a bit deeper on the reasons why the absolute value of Fourier transformation is usually multiplied by the constant $2/N$ to get ...
0
votes
0answers
240 views

output shape of STFT

I cant figure out why our output image is 257 * 32 , 32 I know why , but 257 I cant understand ? this is the exact word of this paper wich applied STFT on 3 channel of eeg signal : Short time Fourier ...
0
votes
2answers
252 views

Applications of Power Spectral Density [closed]

I have a class covering Power Spectral Density but I have no idea why it matters. Could someone provide some examples of its use? Thanks
0
votes
2answers
208 views

Fourier Transform Units

It is documented that 'one' of the units of the Fourier Transform [of $x(t)$ volt] is volt per Hz. That is $X(\omega)$ components will have units of volt per Hz, where $\omega$ is the angular ...
0
votes
0answers
51 views

Fast Fourier Transform MATLAB [duplicate]

I dont understand one thing when I use the function fft(x,N) in matlab, where x is the signal which I want to calculate the fourier transform and N is the number of samples. What I dont understant ...
1
vote
3answers
103 views

New to audio processing, why is my data so lopsided when I try to break into frequency ranges?

I have a wav file audio data, I broke it up into 1024-length windows (no overlap), and performed fft on each one. If I visualize this data it actually looks pretty good, but the problem is that the ...
2
votes
1answer
95 views

FFT - second and further divides and conquers - need help

​ ​Hello, I would like to ask you for help in understanding Fast Fourier Transform. Most articles about FFT describe a simple DFT example with N=8 number of samples. They divide it on half, to evens ...
0
votes
2answers
310 views

Why look at power spectral density for stochastic processes?

I have been told that for deterministic signals, it makes sense to look at their respective Fourier transforms/spectra. For stochastic processes on the other hand, I am supposed to work with power ...
1
vote
2answers
123 views

Characteristic and moment generating function of a random variable interpretation

I have been studying about moments and cumulants of a random variable. Even though the definitions of characteristic and moments generating function are very similar (only the sign in the exponential ...
1
vote
2answers
60 views

Fourier Transform Signals - Time Transformations

I was going over some review problems and came across an interesting one. Using the techniques of (linearity, time shifting, and time scaling) what are some approaches I could use to turn the ...
0
votes
3answers
740 views

Correct magnitude spectra of a cosine DFT?

I've just started my course on DSP and haven't laid my hands on MATLAB yet. I was wondering if the plot of the magnitude spectra was correct for the below shown $x(n)$:
4
votes
2answers
526 views

Why edge sharpening produces high frequency?

I have a low-resolution image in which the high frequencies are missing. When I apply an edge sharpening filter some of the missed high frequency is recovered. I am wondering why this edge sharpening ...
2
votes
1answer
189 views

Wiener Filter Additive Noise Uncorrelated

I have been trying to understand for a while now why a non-causal Wiener filter that has a frequency response of the type H(jω)=S_yx(ω)/S_xx(ω) where ...
1
vote
0answers
110 views

When Is a Power of 2 FFT Slower than Smaller Sized Non Power of 2 FFT in MATLAB

Knowing that computing an FFT is faster if the amount of samples is a power of 2 I have always tried to pad the inputs to Matlab's FFT with zeros until the next power of 2 is achieved. Matlab's ...