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How do you interpret the sign (positive, negative or zero) of the phase spectrum?

How do you interpret the sign (positive, negative or zero) of the phase spectrum of: 1)a digital filter (the phase spectrum of its frequency response aka phase response of the filter). 2)a signal in ...
Alessandro Ghilardi's user avatar
0 votes
1 answer
38 views

Morlet wavelet convolution

I use a simple formula (without normalization) from Mike Cohen's "Analzying neural time series data" book. \begin{align} \psi \left( t \right) &= e^{-\frac{t^2}{2 s^2}} \cdot e^{2 \...
Rolandos's user avatar
1 vote
1 answer
53 views

How does the shape of a frequency domain function (Fourier Transformed time domain function) change when a time shift is applied in the time domain?

When there is a time shift (or delay) in the time domain on a function, the Fourier transform gets multiplied by an exponential which corresponds to a phase shift on the original frequency domain ...
quack's user avatar
  • 11
0 votes
1 answer
41 views

Are integer multiples of a frequency in an FFT necessarily in phase?

I performed a FFT on a signal and the most prominent frequency at about 0.5 cycles/time only makes up about 6% of the total frequency distribution, which is pretty low for my purposes, so I was ...
Data2Dollars's user avatar
1 vote
2 answers
124 views

Excel FFT of Two Sine Waves Not Giving Expected Results

I did an FFT in Excel on a 440 Hz time domain sine wave, $y_1(t) = \sin(2\pi\cdot440\cdot t)$, and got the expected output in the frequency domain: a single-spike distribution with 100% of the signal ...
Data2Dollars's user avatar
1 vote
2 answers
78 views

FFT2 to RFFT2 Fourier plane and similarities

I'm trying to understand how Python's fft2 is different from irfft2. Basically, I have some continuous Fourier 2D samples that I need to put in a (n,n) grid (this can be done by a simply count-in-cell ...
Miguel Cárcamo's user avatar
0 votes
2 answers
73 views

Peak FFT Frequency Off By One Bin

I used Excel's FFT feature to compute an FFT of a 440Hz sine wave that I also generated with Excel. The peak FFT value should occur at 440 Hz. Instead, it occurred one bin later at 528 Hz, so I'm ...
Data2Dollars's user avatar
0 votes
0 answers
40 views

Comparing custom Welch periodogram with Julia's Welch periodogram

I wrote my own PSD struct in Julia for practice purposes. It involves two type of constructors: a "direct" PSD and a <...
lafinur's user avatar
  • 135
1 vote
1 answer
58 views

Ignoring Negative Frequencies from FFT on Real Time Series Seems Inconsistent With Time Series

I ran an FFT on real financial monthly time series data. If I plot the FFT frequency domain output on the interval $[0, f_s)$, the dominant frequency pair peaks occur at $f_{A1}$ $\approx$ $0.02 \ ...
Data2Dollars's user avatar
0 votes
1 answer
54 views

Binning and Frequency for FFT on Financial Time Series Data

I'm trying to analyze financial market time series data, so are there any particular concerns in using FFT for that kind of data? The data seems to be relatively covariance stationary. My sampling ...
Data2Dollars's user avatar
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0 answers
26 views

Fourier transform processing of iq data

I want to perform fourier transform on the iq data that is taken from spectrum analyzer. The purpose is to estimate phase noise from iq data.
Komal's user avatar
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0 votes
1 answer
46 views

Minimum amount of data needed for low pass filter on real time sensor data

I need to apply a low pass filter up to a period of 10 hours to my data. My sensor has a sampling rate of 1 sample every 5 minutes. I need to know how much data I at least need to have to be allowed ...
TRM's user avatar
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-1 votes
1 answer
54 views

Result of complex exponential fourier series approximation and trignometric fourier series approximation are not exactly same in MATLAB?

I have a signal and i am trying to observe its approximations using complex exponential fourier series and trignometric fourier series but i am not getting exactly same result(graph of trignometirc ...
DSP_CS's user avatar
  • 1,894
0 votes
1 answer
94 views

what will be the DC component of this function? [closed]

My answer is that the signal can be splitted into 2 regions, and cancel out the negative and positive areas under the integral, based on the definition Needed some validation on this analysis Thanks.....
Wireshark's user avatar
2 votes
2 answers
156 views

What is the difference between the DFS (Discrete Fourier Series) and DTFS (Discrete-Time Fourier Series)

I'm looking at two different books written by Oppenheim. In Discrete-Time Signal Processing (source 1) he defines the DFS to be: where, $W_N=e^{-j(2\pi/N)kn}$ , while in Signals and Systems (source 2)...
eball's user avatar
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1 vote
1 answer
123 views

beam pattern are fourier transform of the beam weight, is it true ? if it's true how?

what i understood is the equation of AF looks similar to DFT equation as we are multiplying with exponential term
Thouhidul Islam's user avatar
1 vote
2 answers
411 views

What exactly is a frequency component, and what is the phase shift from the argument of the Fourier Transform relative to?

I'm an EE undergrad that struggles heavily with the intuition behind the Fourier Transform (most likely due to a shoddy mathematical foundation). Specifically: From what I understand, the real part ...
Philip's user avatar
  • 13
0 votes
0 answers
24 views

Compare Discrete Fourier Transform for multiple signals

I have heart rate data from a wearable sensor (no ECG). I want to perform Discrete Fourier Transform to see if some patterns are present. I have over 200 signals, as each individual has heart rate ...
TRM's user avatar
  • 1
1 vote
3 answers
128 views

FOURIER TRANSFORM: How can i find the index of data points

I am a senior in high school and am currently trying to conduct an exploration of Fourier Analysis, specifically using the Discrete Fourier Transform to analyse a chord played on my piano. Basically, ...
Ralph Khouri's user avatar
0 votes
1 answer
63 views

Does upsampling require a low-pass filter?

I am currently wondering about the frequency spectrum when performing upsampling using linear interpolation. As far as I know, linear interpolation corresponds to a $\text{sinc}^2$ function. If I ...
hajo's user avatar
  • 101
13 votes
4 answers
3k views

Why is the time domain low-pass filter the "sinc" shape?

Consider: I'm looking at low-pass filters, and I see that the time domain representation of an "ideal" filter resembles the shape above whereas the frequency domain is a box. I also get the ...
thepman's user avatar
  • 133
1 vote
0 answers
45 views

CFO Estimation in LoRa Chirp Signal (Preamble part)

I am trying to estimate CFO in LoRa chirp signal (preamble part). I have seen the discussion about CFO on this forum but it is mainly related to CFO estimation in OFDM. I want to estimate the CFO in a ...
Mogambo0001's user avatar
2 votes
1 answer
102 views

What's the meaning of the amount of frequency 0 in the Fourier Transform?

In the Fourier series, I knew that the coefficient $a_0$ represents the DC value, shifting the signal up and down by the amount. Then, what's the actual meaning of the amount of frequency $0$ in the ...
Hao Wu's user avatar
  • 31
1 vote
1 answer
207 views

How can I plot a sinc function correctly?

I am generating a rectangular pulse using a piecewise function on Matlab. I have listened to some advice to use a normalization coefficient and the amplitude appears correct now. However, my issue is ...
Arcadius's user avatar
0 votes
0 answers
78 views

How to adjust the length of the window of the Fourier transform with respect to the length of the signal in Python

I ran the following code in Python, setting the window length to 5s, but he reports an error as the window length does not match the signal length. How should I adjust it please? code: ...
BaiYueChu's user avatar
0 votes
0 answers
91 views

Having problems with convolution in Fourier space

First attempt: I tried convolution in Fourier space. step: transform grayscale image ==> (real1,imag1) step: transform kernel (a simple box filter) ==> (real2, imag2) step: multiply (complex) ==...
Gianni's user avatar
  • 11
5 votes
2 answers
444 views

Integer multiples of fundamental period in sine wave

I have a simple question. Suppose I have a signal : $f(t)=\sin(2\pi \, 25t)$ We know that it's CTFT(continuous time fourier transform) will result in 2 delta's at +- $2\pi\,25$ [rad/sec]. Or ...
Sammy Apsel's user avatar
1 vote
1 answer
102 views

Finding a discrete signal using some information about its Fourier coefficients

I'm struggling to solve the following question. I've solved it partially, but I can't get complete it. We have the given information about a signal of the form ...
Danialz's user avatar
  • 113
0 votes
1 answer
205 views

What is the symbol for angular frequency?

I am reading the book Signals and Systems Laboratory with Matlab Book by Alex Palamides and Anastasia Veloni I was going through chapter 6 (Fourier transform) and I came across a confusing thing ...
DSP_CS's user avatar
  • 1,894
1 vote
1 answer
616 views

Removing zero frequency peak in fourier spectrum

I have been looking at the FFT (in python) of various simple functions. Everything was working as expected, except when I take the Fourier transform of the function: $$ f(t) = e^{-\gamma t}\cos^2\...
Angus's user avatar
  • 13
2 votes
1 answer
772 views

Real and imaginary parts of the Fourier transform of a pure cosine wave

My understanding of the Fourier transform is that the FT of a cosine wave should be non-zero in the real part and all zero in the imaginary part. This follows from the orthogonality of sine and cosine:...
Joseph's user avatar
  • 235
1 vote
1 answer
92 views

Representation of Sampling Frequency in the Fast Fourier transform

I have 21600 data in the time domain. What Sampling frequency should I use? can someone explain the effect of showing the result by selecting different sapling frequencies? Cheers
IMAN RAMZANPOOR's user avatar
3 votes
1 answer
168 views

How to get DFT spectral leakage from convolution theorem?

I have an issue, where my numerically calculated leakage from a DFT of a simple cosine does not match the theoretical prediction from the convolution theorem. I will try to present the example using ...
xaberus's user avatar
  • 33
0 votes
0 answers
28 views

pulsating current in the PWM amplifier vs. the RMS current of the fundamental sine wave after the filter

I want to know how calculate pulsating current on FET switches in a PWM class D amplifier versus RMS current of the fundamental sine wave after the filter. It depends on the positive and negative ...
German Correa's user avatar
0 votes
1 answer
98 views

Can a large drop in the PSD indicate the presence of a periodic noise?

I was wondering if a large drop in the plot of the PSD of a sensor measurement could indicate the presence of a periodic noise. Here is my PSD: Thank you.
Fred vh's user avatar
  • 25
1 vote
0 answers
127 views

Discrete Fourier transform of a 2D exponential decay

The Discrete Fourier transform of a 1D discrete decay function $d[n]=e^{-a n}$ is simply computed as the sum of a geometric series: $$\tilde{d}[k] = \sum_{n=0}^{N-1}e^{-a n}e^{2 j \pi n k/N} = \frac{1-...
that_guy's user avatar
1 vote
0 answers
75 views

Finding $A_k$ coefficients

I was able to demonstrate that for a signal $x(t)$ real, we can write the truncated Fourier series as: $x_N (t) = A_0 +\sum\limits_{k=1}^{N}A_k\cos(kω_0t + \varphi_k)$, but now I've been given the ...
Anna Smith's user avatar
3 votes
1 answer
127 views

For a real-world system of oscillating mechanical components, what kinds of frequencies should I seek in DFT?

I have a real world system I am analyzing consisting of actual mechanical components that oscillate by rotating back and forth in a fixed axle (kind of like those finger fidget spinners but my system ...
LobsterMan123's user avatar
1 vote
0 answers
63 views

Combining audio and image filters in matlab

I am trying to write audio and image filtering together code in my project. Purpose: The main aim of this project is to combine audio with image filters; like for example passing low frequencies of an ...
CompA's user avatar
  • 11
0 votes
0 answers
158 views

What happens if you use the Fourier transform of the autocorrelation of a non-WSS process to compute power spectral density?

The Wiener–Khinchin theorem states that the power spectral density of a wide-sense stationary stochastic process can be obtained through the Fourier transform of the autocorrelation of the signal i.e. ...
Tommy Wolfheart's user avatar
0 votes
2 answers
152 views

How can I use the FFT in MATLAB to get the time domain equation representation of an image? [duplicate]

My goal is to take any image and break it down to obtain its time-varying equations so it can be redrawn and store the picture as two equations. One for $x$ and one for $y$. As I understand, MATLAB's ...
ijustwannalearnrobot's user avatar
0 votes
2 answers
220 views

Proof that DFT is symmetric

I am working through the proof that the DFT is symmetric from Lyons - Understanding Digital Signal Processing I don't quite understand the use of the $N$ variable. My understanding is that in $X(N-m)$,...
Joseph's user avatar
  • 235
0 votes
0 answers
97 views

How to generate a sound closer to a saxophone using sinusoids after Fourier Transform?

Generate a sound wave of saxophone frequency and compare it to the original sound clip and play both to listen to if there is a good match. I am trying to generate a sound closer to a saxophone using ...
Adrian Surani's user avatar
0 votes
1 answer
232 views

Trying to find the Fourier Series Representation of a sum of Sinusoids

Given a signal: $$x(t) = -5\cos{(93.6\sqrt{2}\pi t - 2\pi/3)} + 3 \cos{(135.2\sqrt{2}\pi t + \pi/13)}$$ I am confused about the right process to take or if there is an easier way than following all ...
user64544's user avatar
0 votes
2 answers
128 views

Problem with transforming a tophat to obtain a sinc?

I have observed that the Fourier transform of a tophat function is a Sinc-like function with higher peak sidelobes than an actual Sinc. However, the Fourier transform of a Sinc is a tophat-like ...
visco's user avatar
  • 1
1 vote
3 answers
261 views

Sample Frequency does not matter if it is sufficiently large

I'm not able to convince a colleague on the following topic. Statement: If, and only if, the sample frequency is sufficiently large and above the Nyquist frequency it does not matter what fs is as ...
pimovietc's user avatar
0 votes
1 answer
43 views

perform fourier-type integration using DFT misunderstanding

I need to perform the following integral ($i^2 = -1$) (with a fixed value of $m$): $ \int_{\phi=0}^{\phi=2\pi} \psi(\phi) e^{-im \phi} \hspace{0.7mm} d\phi $ for all values of $m$ in $\{-N_{\theta}, -...
velenos14's user avatar
  • 135
1 vote
1 answer
159 views

sampled FT of Continuous time LTI output

I am trying to compute the sampled Fourier Transform of a Continuous Time LTI system output. $x(t)$ is the input of LTI and $h(t)$ is the impulse res. $y(t)$ is the output. we know that $$ y(t) = \...
jeff yan's user avatar
1 vote
0 answers
202 views

Fourier transform of a top-hat function in the Faraday Measurement synthesis context

I'm currently trying to calculate the Fourier transform of a top-hat function in the context of Faraday Measurement Synthesis. This is pretty straightforward, however, I cannot understand why I cannot ...
Miguel Cárcamo's user avatar
0 votes
0 answers
104 views

How to calculate DFT of signal which occurs from 3 to 8?

How can I calculate discrete fourier transform of this signal? I'm confused as in the normal cases signal always start from 0 to N-1 but in this case it starts from 3 to 8 instead. So what would be ...
hana's user avatar
  • 163

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